analysis of survey point displacements using total station...

Analysis of Survey Point Displacements Using

Total Station Measurements

A technical report by

Bevan Bird

submitted to the

Geomatics Engineering Department of

British Columbia Institute of Technology

in partial fulfillment of the requirements for the degree of

Bachelor of Technology

and the course

GEOM 8320: Geomatics Project

on

April 24, 2009

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements ii

Acknowledgements

This report exists only because of the encouragement and generous dedication of time and

effort of several people, who I would like to acknowledge. First, I would like to thank John

Ogundare for suggesting the study topic and for helping me plan the project. His technical

assistance with adjustment and deformation analysis concepts was indispensible. I also

greatly appreciate his proofreading and his advising on the finer problems in technical report

writing. I would like to thank Don Thompson for guidance in planning this project. I

appreciate the generosity of Jack Clarke in supplying the raw survey data. This allowed me

to analyze the deformation of real structures and learn about realistic survey error budgets.

Without interviews with Eddie Neumann regarding practical high precision field procedures,

the report would not have been complete. Consultations with Azadeh Koohzare were always

very informative and helped me clarify my tasks. David Martens inspired me to learn the C

programming language, and provided me a copy of the C source code for his BCITCOGO

software in 2006, to help me with my migration from BASIC. Colin Lawrence helped me

gain a thorough understanding of the necessary fundamental mathematical concepts,

including statistical hypothesis testing, matrix algebra, and the calculus. Finally, I would like

to express my thanks to my parents, Maita and Dick Bird, for their unlimited support while I

worked on this project. The valuable input of everyone who was involved is much

appreciated. To anyone whom I neglected to include here I sincerely apologize for the

unintentional exclusion.

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements iii

Abstract

A practical software suite is designed which rigorously processes survey observations (angles

and distances) to enable us to detect and visualize significant structural deformations. By

using it, three practical problems are solved. The construction of an underground light rail

rapid transit station requires excavation of a street for an entire city block. A network is

designed for monitoring the buildings at risk of being damaged by subsidence. The second

problem stems from preloading boggy ground for construction of a highway intersection. A

water main buried close by is being monitored for deformation in three dimensions. Here,

horizontal deformation is analyzed by using five epochs of total station data. We see the

importance of considering trends of more than two epochs so that surveying blunders are not

reported as deformations. Preanalysis, least squares adjustment, and congruency testing are

performed as part of a rigorous scheme for deformation monitoring. The importance of

control point stability testing is stressed; direct measurements between control points are

made so that we may confidently identify the stable and unstable points. The third worked

problem demonstrates the monitoring of leaning trees. In addition to horizontal deformation

analysis, vertical displacements are tested against their confidence intervals. In this way,

points on the trees are monitored in three dimensions.

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements iv

Table of Contents Page

Acknowledgements ii

Abstract Iii

Table of Contents iv

List of Tables vi

List of Figures viii

List of Appendices x

List of Abbreviations xi

1. Introduction 1-1

2. Goals 2-1

3. Methodology 3-1

3.1 Error Budgeting 3-5

3.2 Preanalysis 3-6

3.3 Least Squares Adjustment 3-8

3.4 Deformation Analysis 3-17

4. Software Development 4-1

4.1 Design and Use 4-1

4.2 Data Standards 4-8

4.3 Description of the Applications 4-10

4.3.1 GSI to Text 4-10

4.3.2 GSI to Coordinates 4-12

4.3.3 GSI to Tagged TRA 4-13

4.3.4 Tagged TRA to TRA 4-14

4.3.5 TRA Simulator 4-15

4.3.6 TRA Heights Updater 4-16

4.3.7 TRA Mean 4-18

4.3.8 TRA to Network 4-19

4.3.9 Network Adjustment 4-25

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements v

Table of Contents (cont.) Page

4.3.10 Deformation Analysis 4-32

4.3.11 Launcher 4-34

4.3.12 Select Project 4-34

5. Data Collection 5-1

6. Applications of Survey Suite 6-1

6.1 Monitoring High-rise Buildings Adjacent to an Excavation 6-1

6.2 Monitoring a Buried Water Main 6-8

6.3 Example: Monitoring Dangerous Trees 6-8

7. Conclusions 7-1

8. References 8-1

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements vi

List of Tables Page

3.1: Critical Values from the Kolmogorov-Smirnov Distribution 3-16

4.1: Survey Suite File Format Extensions 4-8

4.2: Supported Data Types in the Leica GSI Survey Data Format 4-12

4.3: Reduction Methods with Resulting Target Observation Types 4-20

6.1: Observation Scheme Summary for Preanalysis of High-rise Building

Deformation Monitoring Network 6-6

6.2: Accuracy Summary of Preanalysis of a High-rise Building Deformation

Monitoring Network 6-7

6.3: Statistical Summary for Minimally Constrained Adjustment of all Epochs 6-9

6.4: Statistical Summary for Minimally Constrained Adjustment of Epochs

2008-08-27 and 2008-10-21 6-16

6.5: Local Congruency Test Results for Minimally Constrained Adjustment of

Epochs 2008-08-27 and 2008-10-21 6-17

6.6: Statistical Summary for Over-Constrained Adjustment of Epochs

2008-08-27 and 2008-10-21 6-18

6.7: Local Congruency Test Results for Over-Constrained Adjustment of

Epochs 2008-08-27 and 2008-10-21 6-19


2008-08-06 and 2008-08-27 6-21

6.9: Local Congruency Test Results for Epochs 2008-08-06 to 2008-08-27 6-21


2008-08-27 and 2008-09-09 6-23



2008-09-09 and 2008-09-23 6-25


Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements vii

List of Tables (cont.) Page


2008-09-23 and 2008-10-21 6-28


6.16: Tree Deformation Monitoring Network – Statistics for Minimal Constraint

Adjustments of Epochs 0 and 1 6-34

6.17: Tree Deformation Monitoring Network – Statistics for Constrained

Adjustment of Epochs 0 and 1 Combined 6-34

6.18: Tree Deformation Monitoring Network – Final Local Congruency Test

Results 6-35

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements viii

List of Figures Page

3.1: Deformation Monitoring Survey Data Processes 3-2

3.2: Flowchart for Outlier Removal 3-12

3.3: Examples of Absolute Deformation Network Geometries 3-18

3.4: Influence of an Unstable Reference Point 3-19

3.5: Flowchart for Geometrical Deformation Analysis of an Absolute Network 3-20

4.1: Survey Suite Application Classifications 4-2

4.2: Survey Suite Preanalysis Procedure 4-4

4.3: Survey Suite Raw Data Conversion Procedure 4-5

4.4: Survey Suite Data Snooping Procedure 4-6

4.5: Survey Suite Geometrical Deformation Analysis Procedure 4-7

4.6: Leica GSI Survey Data Format in Detail 4-11

6.1: Plan for High-rise Building Monitoring 6-2

6.2: Geometry of Network Design by Preanalysis for High-rise Building

Monitoring 6-4

6.3: Detailed View of Geometry of Network Design 6-5

6.4: Geometry of a Water Main Deformation Monitoring Network at Epoch

2008-08-06 6-10


2008-08-27 6-11


2008-09-09 6-12


2008-09-23 6-13


2008-10-21 6-14

6.9: Displacement Field Between Epochs 2008-08-27 and 2008-10-21 with

Minimal Constraint Datum 6-16

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements ix

List of Figures (cont.) Page


Over-Constrained Datum 6-18









6.15: Geometry of Tree Deformation Monitoring Network for Epoch 0 6-32

6.16: Geometry of Tree Deformation Monitoring Network for Epoch 1 6-33

6.17: Tree Deformation Monitoring Network – Displacement Field from

Epoch 0 to Epoch 1 6-36

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements x

List of Appendices Page

A. Software Implementation A-1

B. Accuracy of Instruments B-1

C. Preanalysis of a Network for Monitoring High-rise Buildings C-1

D. Deformation Analysis of a Buried Water Main - Outlier Removal Example D-1

E. Deformation Analysis of a Buried Water Main - Epoch 2008-08-27 to

2008-10-21 E-1

F. Deformation Analysis for Monitoring Dangerous Trees F-1

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements xi

List of Abbreviations

BCIT British Columbia Institute of Technology

CIPA International Committee for Architectural Photogrammetry

EDM Electromagnetic Distance Measurement

GNU “GNU's Not Unix” (recursive)

LDD Land Development Desktop (©Autodesk)

MIT Massachusetts Institute of Technology

PDF Portable Document Format (©Adobe)

STL C++ Standard Template Library

SVG Scalable Vector Graphics

UNB University of New Brunswick

XML Extensible Markup Language

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements 1-1

1. Introduction

Deformation monitoring surveys are one of the most important engineering surveying

activities in that they are commonly employed for reasons of human safety or construction

insurance (Chen, 1983). Their analysis can improve our knowledge of the deformation

characteristics of structures, and can facilitate improvements to engineering designs. They

are required for the safe operation of engineered structures such as dams, bridges, viaducts,

earthworks, high-rise building, and light rail transit systems (Erol et al. 2004).

Any object, when acted upon by external forces, deforms, or exhibits changes in its size or

shape. These observable changes are manifestations of internal stresses – or pressures –

produced by the physical interaction of the external forces and the material itself. Materials

“fail” – tear – when stresses exceed certain critical values. (Chrzanowski et al., 1986). It is

this risk of failure which practically necessitates deformation monitoring surveys, which can

allow the implementation of mitigating constructive procedures or evacuations to take place

early enough to be effective in preventing loss of life and material damages (High-precision

deformation monitoring…, 2007).

Conventionally, deformation analysis is a multistep process which involves testing

coordinate differences for significance, by comparison to the accuracy of their determination,

after estimating the coordinates for each epoch by least squares adjustments of each epoch’s

respective observational network (Bin Setan, 1995).

One common problem is that if control points move due to stresses, or are merely disturbed

by localized phenomena, and they are assumed to be stable, the results of adjustments in

which the unstable point is held fixed are distorted. The result is that incorrect displacements

for all free (non-fixed) points may be reported. For this reason, testing the stability of the

control network is very important. In practice, however, control stability testing and the

extra measurements among control points required for it, are often neglected because their

effects are underestimated. (Chen et al., 1990).


The author, having worked on several deformation monitoring surveys for McElhanney

during the summers of 2006-2008, decided to pursue the subject. Common practice involves

reporting coordinate differences over time, along with the maximum coordinate error

expected for any point on the deformable object. It is simplistic to report that each point has

the same amount of expected error; network geometry plays a central role in determining the

accuracy of the coordinates of each point. John Ogundare suggested that it would be

beneficial to qualify each point individually, by adjusting all networks by least squares, so

that possibly smaller single-point displacements could be detected. The author intends to

make improvements to the error propagation computation steps prior to adjustment to support

a more rigorous adjustment.

The scope of this project can be summed up in four points:

1. There are two types of deformation monitoring survey networks: relative and

absolute. Relative networks have no known stable control points, while absolute

networks do. Due to the complexities of performing free-network adjustment with

inner constraints (a requirement when analysing relative networks) and the

subsequent S-Transformation, only absolute networks will be dealt with.

2. Only total station observations will be considered.

3. All computations will assume the measurement surface to be a plane. This

assumption is valid for small areas. Applications where no corrections to distances

and angles for deviation of earth’s curved surface from the plane need to be made

include “local property surveys or construction surveys” (State of New Jersey

Department of Transportation). The plane is not an acceptable computational surface

for large networks, such as those whose purpose is to monitor tectonic movements.

4. Deformation analysis will be limited to its geometrical aspect; deterministic modeling

will not be performed.

The author has decided to create a software application suite to support survey network least

squares adjustment and preanalysis, as well as geometrical network deformation analysis.

These processes require some supporting utilities for data conversion and screening.


The method involves first gaining a thorough working knowledge of the computational

procedures involved, second constructing the software, third using the software to solve, and

demonstrate the solution of, several practical problems. Finally general conclusions may be

inferred.

Monitoring surveys can have some of the most stringent accuracy requirements. Because

coordinate differences over time are used to determine displacement of points, and by

connection, deformation of the monitored structures themselves, a high degree of

repeatability is required. Through preanalysis, we learn that strong network geometry along

with the presence of redundant observations yield high coordinate accuracies.

Redundant observations are additional measurements which are not required for computing

the desired unknown quantities, the parameters. Network redundancy, also known as the

number of degrees of freedom, is defined as the number of observations minus the number of

unknown parameters. When there are redundant observations available, traditional

coordinate geometry formulae can yield many possible coordinate solutions, depending on

which observations are used as input. This inconsistency is remedied by least squares

adjustment.

Network geometry refers to a network plan showing stations and observations as lines

between them. Geometry is said to be “strong” when these lines form nearly equilateral

triangles. Networks with “strong” geometry and high redundancy can be said to be highly

reliable, that is, even small isolated random errors in observations are adjusted away as

residuals instead of influencing coordinates.

Observations always have some degree of error, caused by the instrument, operator, and

environment. There are three main types of errors: systematic, blunders, and random.

Systematic errors have a known magnitude and sign and must be removed. Imperfect

approximations in the corrections will produce additional “random” error. Systematic errors

are also avoided through proper instrument calibration. Blunders, mistakes or malfunctions,

must be detected and eliminated. Random errors, whose magnitudes are small and signs


unknown and generally are normally distributed, will remain in the data. Least squares, in

theory, can only deal with random errors. If systematic errors or blunders are present, results

are grossly distorted.

Least squares adjustment is a mathematical matrix method for creating a consistent set of

adjusted observations. This is accomplished by imposing the criterion of minimizing the sum

of the weighted squares of “residuals”, which are adjustments to the observations. Least

squares allows for outlier detection and qualification of observations and adjusted

coordinates.

According to Chen and Chrzanowski (1986), physical deformation interpretation involves the

iterative optimization of both deterministic and statistical models describing the movements

of object points over time. Both causative effects – loads and temperature variations – and

response effects – observed deformations – are taken into account. Geometrical analysis is

part of this process, in which statistical hypothesis testing is used to determine whether

displacements are significant, or if they are more likely due to survey errors. Expert human

interpreters are vital to successful interpretation of deformations, since local forces may

affect a point so that its movement is no longer representative of the object being monitored.

It is expected that the benefits of a more rigorous error propagation scheme will encourage

both more testing of control network stability than is currently done in practice, and

innovation in survey network designs. Also, an increased confidence to detect smaller

single-point displacements in some cases may result.

This report is organized as follows. Chapter 2 briefly outlines the goals of this project

relating to the creation and improvement of practical and economical, yet rigorous,

deformation analysis software. Chapter 3 presents the methodology for deformation

analysis, providing a theoretical background for the design and coding of the “Survey Suite”

software package. Chapter 4 summarizes the software design goals and coding

methodology, discusses the applications that are used throughout the deformation analysis

process, and gives the purpose, input/output, capabilities/limitations, and basic functioning of


each application. Chapter 5 outlines field procedures for high-precision surveying which

eliminate or minimize error sources. Also the survey equipment used for the data collection

is introduced. Chapter 6 presents worked numerical examples of error budgeting,

preanalysis, and geometrical deformation analysis. The methodology presented in chapter 3

is followed, and the software discussed in chapter 4 is used to perform the computations.

Chapter 7 concisely presents the general conclusions about what was learned through

analysis and outlines plans for further improvement to the software. Chapter 8 cites the

literature which the methodology and software designs are based upon, as well as any

necessary reference material regarding survey instrument accuracy.


2. Goals

The goals of this project are to:

• allow the author to learn about error budgeting, error propagation, preanalysis,

adjustment, and deformation analysis through a hands-on software development

approach.

• construct an easy-to-use software suite useful for rigorous pre-analysis, adjustment, or

deformation analysis of survey networks with high accuracy specifications.

• employ strict error budgeting as a part of survey network design.

• attempt to improve the accuracy and efficiency of a deformation survey network by

preanalysis.

• simplify the process of screening raw survey data.

• employ rigorous error propagation for observations before adjustment, by allowing

survey methods to be modeled more accurately.

• create deformation analysis reports and graphs to discover significant displacement

trends.

The author plans to use the software developed during the completion of this project as a

base for future research and improvement of error propagation, adjustment, and deformation

analysis techniques. The author also intends to gain a deeper understanding of the

underlying algorithms and computational problems associated with deformation surveys. It

could be useful to fine-tune the pre-adjustment error propagation process, in which assumed

standard errors of observations are computed, so that more rigorous adjustments can be

performed. It is important to take into account the variations in accuracy of observations

made with different instruments, or with different instrument or target centring techniques.


3. Methodology

This chapter gives an overview and then a detailed look at the problems associated with

deformation analysis. The theory and formulae explained here provide a foundation for the

development of adjustment and deformation analysis software. First an overview of the

methodology for completing this project is given and the phases of deformation survey

management, including network design, data reduction, adjustment, analysis, and reporting

are outlined. Section 3.1 describes, in more detail, the importance of, and the procedure for,

creating a survey error budget. Section 3.2 explains how and why preanalysis by the

computer simulation method is performed. Section 3.3 discusses the parametric least squares

adjustment algorithm. Section 3.4 covers deformation analysis, the central topic of this

report.

The steps taken to complete this report are as follows:

1. Research deformation analysis.

2. Design, build and test the “Survey Suite” software package.

3. Perform survey error budget computations for various requirement scenarios, as per

magnitudes of expected movements.

4. Perform preanalysis computations for various monitoring networks to facilitate

creation of efficient survey designs.

5. Collect or otherwise acquire raw survey data from McElhanney.

6. Convert, screen, and average total station observation data.

7. Perform geometrical deformation analysis of monitoring networks.

8. Compile conclusions based on analyses.

9. Recommend areas for further research.

The author has researched error sources, error budgeting, pre-analysis, least squares

adjustment, and geometrical deformation analysis by referring to course notes (Ogundare,

2008a, 2008b), library books and internet resources, and by conducting informal interviews

with BCIT instructors and McElhanney surveyors and managers.


The various data analysis goals drive software requirements and design, since all software

required to complete the analysis has to be acquired or constructed to allow said analysis to

be performed.

Before software development begins, a brief survey of existing software is carried out, to

attempt to reuse existing work. There are many existing least squares adjustment software

packages, but not as many deformation analysis packages. Although this project could have

used existing software for analysis, the author would not be able to achieve the project goals

of gaining a deeper understanding of deformation analysis theory and practice and attempting

to improve the practical methods. This is why the software will be designed and constructed

independently of existing adjustment and deformation analysis software. This method should

allow a fresh look at the problems, and will support further progress in the research of the

author into deformation analysis.

An overview of the process of completing a deformation monitoring survey is illustrated in

Figure 3.1.

Figure 3.1: Deformation Monitoring Survey Data Processes.

(US Army Corps of Engineers, 2002).

Depending on the structure being monitored, the maximum expected movement of points

under normal conditions can be determined by past observations of displacements of points

on or around that type of structure. The determination of the maximum expected movement


supports the creation of a survey error budget. Through iterative cycles of preanalysis

computations and survey network design modifications, the tolerance as stated in the survey

error budget is theoretically achieved. Two formal documents, the instrumentation plan and

measurement scheme are then compiled. The instrumentation plan details the procedures and

specifications for installing the survey network monuments and object points. The

measurement scheme details the type of survey instruments to use, the specific measurements

to make during each survey, and the number of each type of observation (distance, angle, or

height difference) to make. (US Army Corps of Engineers, 2002).

Critical considerations for monumentation of object points are that their movement must

properly represent the movement of the objects and the total number of these points must

“sufficiently represent the movement of the total area” (Smoltczyk, 2002).

The length of time between monitor surveys depends on the type of structure being

monitored, the magnitudes of the expected maximum displacements under normal working

conditions, the achievable survey accuracy, and the level of risk to human life. The

frequency of the surveys may be increased if velocities of displacements are excessive, or

decreased if displacements trends indicate stability (US Army Corps of Engineers, 2002). In

general, the surveys are performed at regular intervals. The frequency of resurveys can range

from “seconds to years” depending on the deformation rate, according to Chen, (1983).

During data collection, observations between points at each epoch of time, are made

carefully to limit all kinds of errors, especially those of a systematic nature. For example,

total station EDM systems are kept in good calibration regarding their system constant and

scale. Total stations’ collimation axis are also checked frequently. Field procedures such as

double centring (two-face measurement) are used to minimize both systematic and random

errors. In fact, to increase the confidence that the proper accuracy is being achieved, multiple

sets of a direction should be observed.

Data reductions must be done in a rigorous way for deformation monitoring surveys because

overly simplistic data processing methods can introduce additional errors and error tolerances


are usually small and already difficult to achieve. Furthermore, high precision field

surveying is more expensive than lower accuracy cadastral or topographic surveys, for

example, and therefore one should attempt to produce the most accurate results through more

refined computational or statistical procedures (Chen, 1983). Raw observations should be

corrected for known systematic errors, and then those representing the same quantity should

be meaned (US Army Corps of Engineers, 2002). It is at this stage that observational outliers

should be identified and eliminated from the data by a simple single variable statistical test,

usually using Student’s distribution because sample sizes are generally small in surveying.

The standard deviations of each observation have to be determined before a proper

adjustment is possible. The more rigorous the error propagation routines are, that is, the

more accurately all the sources of random error are modeled, the more correct the results of

the adjustment will be, due to realistic weighting of the observations.

Least squares adjustment is used to identify probable observational blunders in the data

collected at each epoch. Least squares adjustment is carried out for two main reasons. First,

it allows the observations to be tested for outliers in an objective way (Ogundare, 2008a).

Second, it provides quality indicators to support rigorous deformation analysis such as

congruency testing.

Deformation modeling or analysis is done to determine whether point displacements are

significant. Reference points must be suspected of moving between surveys, and are tested

for stability before the displacements of object points are examined. If there is any

significant deformation of a relative network, it can be very difficult to determine which

points have remained stable and which have moved. With absolute networks, this serious

problem is easily overcome as long as a sufficient number of stable points surround the

unstable area. However, additional measurements, especially those directly between

reference points, must be added to the network design to enable stability testing of those

supposed stable reference points. Care must be taken in the interpretation of the analysis

results, and a multidisciplinary approach has been recommended in (Chrzanowski et al.,

1986). Consultations between geomatics, geotechnical, and geophysical engineers can help in


determining whether or not point displacements are representative of deformations of the

object.

Presentation of the results may include coordinate difference spreadsheets, displacement field

plots, or summaries of significant point displacements. Quality control is vital to avoid

raising a false alarm and to ensure that when significant displacements do occur, the results

are reported accurately and promptly. Therefore as much of the overall process as possible

should be automated to minimize possibilities of human error. Automated systems can

contain bugs when first implemented, however, so they must be checked independently until

they have been proven trustworthy. The deformation survey management process will now

be examined in more detail. In particular, the theory of error budgeting, preanalysis, least

squares adjustment, and deformation analysis will be discussed. It should be noted that in the

formulae, the hat accent (as in x̂ ) signifies that the accented quantity is adjusted. Its absence

(as in x ) signifies that the quantity is unadjusted.

3.1 Error Budgeting

Creating a survey error budget is vital to the process of confidently determining the

significance of coordinate displacements. For deformation surveys, the largest semi-major

axis of any point coordinate error ellipse at 95% confidence must be less than one-fourth of

the maximum expected horizontal movement during the time interval between successive

field surveys, while assuming the structure experiences normal conditions (US Army Corps

of Engineers, 2002). The formula is given in (3.1).

EMa ��

��

�≤41

%95

max

(3.1)

where =%95

max

a Largest semi-major axis of any point coordinate error ellipse at 95%

confidence

=EM Maximum expected horizontal movement of a point.


The error ellipses are computed by preanalysis / adjustment software by propagating the

assumed standard errors of observations into the adjusted coordinates. If the tolerance is not

met, the network design should be modified and, again, pre-analysis should be used to check

if the accuracy requirement can be achieved with the new proposed survey scheme.

3.2 Preanalysis

Preanalysis by the computer simulation method involves iterative experimentation with

various configurations of the locations of points, the number and types of observations

between them, and the accuracies of the survey instruments used. The confidence level

normally used for network preanalysis is either 95% or 99%. The network design is

complete when the largest point coordinate error ellipse semi-major axis at the selected

confidence level is smaller than the maximum allowable uncertainty in point positioning

computed as part of the survey budget. During each iteration, the preanalysis algorithm

consists of the computation of a short series of matrix equations, followed by computation of

the semi-major ellipses of all the network points and the test of the largest one. The weight

matrix is computed from (3.2), assuming 2oσ is equal to unity.

1−=�

CP (3.2)

where =P Matrix of weight of observations

=�

C Matrix of variance-covariance of observations

=2oσ A priori variance factor of unit weight.

Next, the matrix of first design is computed by taking numerical partial derivatives of the

parametric function equations, as shown in (3.3).

xf

A∂∂= (3.3)

where =A Matrix of first design

=f Vector of parametric functions

=x Vector of parameters.

Next, the matrix of coefficients of the normal equations is computed by (3.4).


APAN T ⋅⋅= (3.4)

where =N Matrix of coefficients of normal equations. Next, the matrix of cofactors of the

adjusted parameters is computed by (3.5). 1

ˆ−= NQx (3.5)

where =xQˆ Matrix of cofactors of adjusted parameters. Finally, the matrix of variance-

covariance of the adjusted parameters is computed by (3.6), with the a posteriori variance

factor of unit weight ( 2ˆoσ ) set equal to unity.

xox QC ˆ2

ˆ ˆ ⋅= σ (3.6)

where =xC ˆ Matrix of variance-covariance of adjusted parameters. The semi-major axis of

the point coordinate error ellipse at 95% confidence is found by computing the square root of

the scaled larger eigenvalue of the variance-covariance matrix for a point. For each point,

the larger eigenvalue is computed in two steps, by (3.7) and (3.8).

( ) 2222 4 xyyyxx sssz ⋅+−= (3.7)

( )zss yyxx ++= 221 2

1λ (3.8)

where 22 ,, yyxyxx sss are extracted from the variance-covariance of matrix of an adjusted point

( PC ˆ ), their conventional arrangement shown in (3.9).

��

�

�= 2

2

ˆyyxy

xyxxP ss

ssC (3.9)

Since the a priori variance factor of unit weight is assumed to be known, the upper critical

value from the Chi squared distribution is used in scaling the larger eigenvalue, as in (3.10).

99.512

05.0,21%95 ⋅=⋅= λχλupper

a (3.10)

where =2

;ανχ Upper critical value from the Chi squared distribution at redundancy ν = 2

and significance level α = 0.05. The last step is to test the maximum semi-major axis of

any point coordinate error ellipse at 95% confidence against the tolerance in (3.11).


EMa ��

��

�≤41

%95

max

(3.11)

where =EM Maximum expected horizontal movement of a point. If the tolerance is not

met, modifications are made to the network design, and a new iteration is performed. Once

the tolerance is met, the design is said to satisfy the accuracy requirements, and preanalyis is

complete. Even once the tolerance is met, the network designer may wish to try to improve

the theoretical positional accuracy of some points further, or may attempt to reduce the total

number of survey measurements for economical purposes.

3.3 Least Squares Adjustment

Parametric least squares adjustment of traditional surveying observations is the most

convenient model to program using today's technology. The equations (3.12) of the

parametric model – as opposed to the conditional and general models - relate each

observation as a function of some parameters (Ogundare, 2008a).

)ˆ(ˆ xf=� (3.12)

where =�̂ Vector of adjusted observations

=)ˆ(xf Vector of functions of adjusted parameters.

The parameters (unknown quantities) include coordinates and horizontal circle orientations

(one for each set of horizontal directions). It is trivial to compute the theoretical

observations, given the approximate coordinates of involved points and the type of

observation; this requires only a set of general coordinate geometry equations and a means of

applying them to each observation. The first design matrix, the partial derivative matrix of

the observation equations with respect to the parameters, can also be computed in a

systematic, readily-programmable, way.

Parametric least squares adjustment employs, in addition to the formulae (3.2) through (3.6)

used in preanalysis, the following series of formulae, namely (3.13) through (3.22).

�−= )(xfw (3.13)


wPAu T ⋅⋅= (3.14)

uN ⋅−= −1δ (3.15)

δ+= xx̂ (3.16)

wAv +⋅= δ (3.17)

v+= ��̂ (3.18)

νσ vPvT

o

⋅⋅=2ˆ (3.19)

TANAQ ⋅⋅= −1�̂

(3.20)

�� ˆ2

ˆ ˆ QC o ⋅= σ (3.21)

�� ˆCCCv −= (3.22)

where =w Vector of observational misclosures

=)(xf Vector of theoretical (predicted) observations

=� Vector of observations

=u Vector of constants in normal equations

=δ Vector of corrections to parameters

=v Vector of residuals, corrections to observations

=2ˆoσ A posteriori variance factor of unit weight

=ν Number of degrees of freedom = the number of observations minus the number

of parameters

=�̂

Q Matrix of cofactors of adjusted observations

=�̂

C Matrix of variance-covariance of adjusted observations

=vC Matrix of variance-covariance of residuals.

Iterations of (3.3), (3.4), and (3.13) through (3.16) are performed until corrections to

parameters become insignificant (Mikhail, 1976). For coordinates, this is one-half of the

least count of the desired adjusted coordinate precision, eg. 0.00005 m for coordinates

rounded to 4 decimal places. For orientation parameters, this is one-half of the least count of


the desired adjusted azimuthal precision, eg. 0.05” for azimuths rounded to the nearest 0.1”.

Of course, this criteria is converted to radians in any implementation because no angles in

degrees can appear in the same matrix with distances in meters. The numerical partial

derivative elements of the first design matrix are only correct if all angles are in radians.

Once the solution of parameters has converged, the post-adjustment quantities can be

computed. These follow the formulae (3.17) through (3.22). It is important to note that

scaling by the a posteriori variance factor of unit weight is not always done; for example it

is not done when the a priori variance factor is considered known. In the most common

case, we do scale by the a posteriori variance factor, and it should be noted that in using

(3.22), the matrix of variance-covariance of observations must first be scaled.

The first time a single-epoch network is adjusted, it should be constrained minimally, for the

purpose of detecting and removing outliers. Minimally constrained networks are also known

as free networks with external constraints. Adjustment by minimal constraints requires that a

control point be fixed in X and Y coordinates, and the direction (azimuth) to another point be

fixed. The direction fixing can be avoided by fixing a single horizontal coordinate of another

point. It is best to fix, on the secondary point, the coordinate along the axis which has the

shorter distance along that axis between the points. This is done to prevent externally over-

constraining the network. An example of where this problem would occur is the situation

where the absolute value of the difference in the Y direction between the two datum points is

zero, according to the initial coordinates, and one has chosen to fix the secondary point’s X

coordinate (rather than the more correct choice, Y). Given this geometrical scenario, it is not

possible for the adjustment to shorten the length between these datum points; the secondary

point is free to move in the Y direction, but this can only increase the length. This is an

example of the coordinates enforcing constraints on the observations. A truly minimally

constrained network adjustment is one where the shape and size of the network is not

affected by external factors; only the position and orientation of the network are to be

enforced externally. Additionally, if elevations of points are to be determined (there are Z

coordinate parameters), the elevation of a point must be held fixed. In practice, the

horizontal network orientation by azimuth fixing is accomplished by setting a small input

standard deviation for a false azimuth observation. For small networks, with extents less


than two kilometers, a standard deviation of 0.01” can reasonably be assigned. This change

in direction corresponds to less than 0.1 mm over a distance of 2 kilometres. However, when

doing an adjustment as part of the larger deformation analysis process, one needs to be

careful not to over-constrain the direction between control points. Let us call the point which

has a direction to it fixed, the “direction point”. The iterations stop when corrections to

coordinates become small so there is a small amount of randomness in the coordinates of all

points. The direction to the direction point is always correct from the fixed point. However,

the direction from the direction point, as coordinated by the observations of one epoch, to the

same point coordinated by a different epoch will not be exactly the same because the

coordinate displacement is very small, and the randomness in the coordinates becomes

significant. The direction can differ by several degrees in practice. Deformation analysis

checks whether a coordinate difference vector extends outside of an error ellipse of

displacement. If the semi-minor axis of the error ellipse of the displacement of the direction

point is too small, the local congruency test may identify this point as unstable. The solution

is to set a standard deviation for the azimuth that gives a small semi-minor axis, of at least

0.2 mm. The shorter the length of the constrained baseline, the larger the standard deviation

must be.

Figure 3.2 shows the procedure for removing outliers. It must be followed for the data from

each epoch before one makes any comparisons between two epochs to detect deformation.

After adjustment, certain statistical hypothesis tests are done to check the quality of the

solution and to try to detect the presence of outliers. The global and local tests as well as the

goodness of fit test are commonly employed. The confidence level normally used for

network adjustments is 95%. The corresponding significance level of 5% means that there is

a 5% chance of making a type I error. A type I error is when a correct null hypothesis is

rejected. The global test of the variance factor of unit weight can be done with either a one-

or two-tailed method. The two-tailed method is more rigorous, so it will be implemented

according to Baarda (1968).


Figure 3.2: Flowchart for Outlier Removal

The null hypothesis, to be accepted if the lower and upper tests pass, is that:

• there are no systematic errors or blunders present in the observations

• the standard deviations of all observations are correct

• the mathematical adjustment model is correct and free of distortions.

An alternate hypothesis is accepted if either the lower or upper test fails. If the lower test

fails, this merely means it is likely that the standard deviations of the observations are too

pessimistic. However, if the upper test fails, and the standard deviations of the observations

are realistic (not too optimistic), there are likely blunders or systematic errors in the

observations. Also, the mathematical adjustment model may be incorrect. Since we are

using software to compute the adjustment, it is unlikely that the parametric equations will be

formed incorrectly; the most likely scenario is that a data entry error has occurred. For

example, the wrong observation type may be entered, an initial coordinate estimate may not

be accurate enough, or a point number may be incorrect. The test is done by computing a

Chi squared test statistic from the a posteriori variance factor of unit weight with (3.23), and

comparing it to the lower and upper critical values from the Chi squared distribution, at the


appropriate significance level and number of degrees of freedom, as in (3.24) and (3.25).

These two tests are to be accepted if the comparisons are true.

22 ˆoT σνχ ⋅= (3.23)

?22

2,

T

lower

χχ αν<

(3.24)

?22

2,

T

upper

χχ αν>

(3.25)

where =2Tχ

Chi squared test statistic

=ν Number of degrees of freedom

=2ˆoσ A posteriori variance factor of unit weight

=α Significance level as a probability

=2;ανχ

Critical value (upper or lower as annotated) from the Chi squared distribution

at redundancy ν and significance levelα .

If the global test fails, local tests to try to identify possible outliers, observations which are

relatively less accurate than others. The standardized residual associated with each

observation in the network is tested locally. In each case, the null hypothesis is that the

observation is accurate; the alternate hypothesis is that the observation contains either too

much random error or even a blunder. When applying the conclusion of a local test, a type I

error occurs when we remove from the network an observation which is not a blunder, based

on our incorrect conclusion that it is a blunder. The two-tailed local test (or “data

snooping”), according to Baarda (1968) is commonly used by surveyors, and it is

implemented here. The two -tailed test is done for each observation by comparing a test

statistic to the upper critical value in (3.26).

?CT < (3.26)

where =T Test statistic

=C Upper critical value.

If the comparison evaluates to true, the null hypothesis is accepted. The test statistic is

computed from the residual and the standard deviation of that residual, as in (3.27).


iv

ivT

σ= (3.27)

where =iv Residual of the ith observation

=ivσ

Standard deviation of the ith residual.

The standard deviation of the residual is computed as the square root of the ith diagonal

element of the matrix of variance-covariance of residuals, where i is the index of the

observation under scrutiny. The critical value used for data snooping in local tests either

comes from the Normal distribution if the a priori variance factor is well known or from the

Tau distribution, assuming it is not well known, as in (3.28)

)(,

)(,

2

2

2

2,

knownifZC

unknownifC

o

o

o

o

≅=

≅=

σ

στ

α

αν

(3.28)

where =αντ , Upper critical value from the Tau distribution

at redundancy ν and significance level α

=αZ Upper critical value from the Normal distribution at significance level α

=oα Significance level for local test

=2oσ A priori variance factor of unit weight


In what is called in-context testing, each observation is tested, taking into account the size of

the sample (the number of observations in the network). The smaller the sample, the stricter

the elimination criteria becomes; the larger the network, the more lenient it is. This is a

reasonable manifestation because with few observations as redundant checks, we must ensure

no observations have large errors, but when there are many redundant observations, the effect

of the presence of one outlier observation on parametric estimates is reduced. In-context

testing, implemented here according to the approximation (3.29), uses a significance level

which is lower for local tests than for the global test, whereas out-of-context testing uses the

same significance level for both tests.


noαα ≈ (3.29)

where =oα Significance level for local test

=α Significance level for global test

=n Number of observations.

The Tau distribution (Pope, 1976) is defined in terms of Student’s distribution according to

(3.30).

αν

αναν

νν

τ,1

2

,1,

)1( −

−

+−

⋅=

t

t (3.30)

where =αντ , Critical value from the Tau distribution

at redundancy ν and significance level α


=α Significance level

=αν ,t Critical value from Student’s distribution

at redundancy ν and significance levelα .

The goodness of fit test for normality of standardized residuals using the Kolmogorov-

Smirnov method, works even for small populations, and so it is implemented in this project.

The method, according to �epek (2008) and Lawrence (2005), which is presented here,

assumes the mean and standard deviation of “the data” is not well known. “The data” refers

to the standardized residuals for all observations in the complete network. It could also refer

to the standardized residuals for a class of observations, such as horizontal angles, but the

isolation of the necessary values post-adjustment is not yet implemented. The test for

normality is performed by comparing a test statistic to the upper critical value, with (3.31).

?CDM < (3.31)

where =MD Test statistic, modified maximum discrepancy

=C Critical value from Kolmogorov-Smirnov distribution.

If the test evaluates to true, the standardized residuals are said to be “normally distributed”.

The test statistic can be computed by (3.32).


��

��

� +−⋅=

��

�

��

��

� −−−=→=

nnDD

zZn

izZ

ni

D

M

nifor

ii

85.001.0

)(1

,)(maxmax)1(

(3.32)

where =D Maximum discrepancy between Normal distribution and measured distribution

=i Index number of each standardized residual

=n Total number of standardized residuals

=()Z Cumulative frequency from Normal distribution

=iz The ith standardized residual.

The upper critical value, for the desired significance level (usually 0.05), is extracted from

Table 3.1.

Table 3.1: Critical Values from the Kolmogorov-Smirnov Distribution. (Lawrence, 2005).

Significance Level Critical Value

0.15 0.775

0.10 0.819

0.05 0.895

0.025 0.955

0.01 1.035

If the standardized residuals are normally distributed, there is an indication that the

observational data is free of systematic errors. An example of the alternate situation is that

when a two dimensional network is adjusted with the horizontal coordinates of two points

fixed, and those coordinates are not accurate and do not agree with the measurements

between them, the observations must be distorted to fit the poorer quality control values.

This distortion will tend to be in one direction, for example the distances may all be scaled

down, left skewing the histogram of standardized residuals by an over abundance of negative

residuals.


3.4 Deformation Analysis

There are four types of deformation models: congruence, kinematic, static, and dynamic.

Congruence and kinematic models are restricted to the pure geometrical description of the

deformation process, whereas static and dynamic models are cause-response models which

“quantify the reaction of the construction to external [influences]” like temperature, wind or

traffic loads. (Eichhorn, 2007).

Here, deformation modeling is restricted to geometrical congruence analysis. According to

Chrzanowski et al. (1986), the geometrical aspect of the analysis of deformation surveys

involves only “the geometrical status of the deformable body, the change of its shape and

dimensions”. Detection of point displacement trends is the goal of the analysis.

It is “rather simple” to determine the geometrical state of the deformable body when it is

surveyed from an absolute network (Chen, 1983, Chrzanowski et al., 1986). An absolute

network contains enough stable reference points arranged in such a pattern as to consistently

define the datum for adjustments of every epoch. Figure 3.3 illustrates two examples of

absolute networks. In part b. of the figure, which depicts the monitoring of a linear feature

such as a buried water main, the unstable traverse points are required for two reasons. First,

to allow for relative stability checks of the two stable areas. Second, coordinate accuracy

requirements can not be achieved, given the distances from stable reference points to object

points, as determined by preanalysis. A numerical example of a scenario such as this is given

in chapter 6.

The most critical problem in geometrical deformation analysis is determination of a stable

reference datum. If points which have moved during the time period between the two

observation epochs are held fixed in the adjustments, points which have not moved will

exhibit coordinate displacements. The problem is that, left unchecked, unstable reference

points can distort the results of any analysis and cause deformations to be interpreted

incorrectly. This phenomena is illustrated in Figure 3.4. In this example of a simple absolute

deformation monitoring network, reference point B has moved from location B to B’


between two observation epochs, but is assumed to have remained stable (in its original

location). Minimal constraint adjustments of the two epochs of observations are carried out

with point A fixed and the direction to point B fixed. The resulting (exaggerated) coordinate

difference vectors are shown. Stable reference points C and D and object points (101-103)

all, incorrectly, appear to have moved.

Figure 3.3: Examples of Absolute Deformation Network Geometries. a. Single stable area,

all reference points stable. b. Separate stable areas surrounding a large unstable area,

necessitating some unstable traverse stations.

To perform geometrical deformation analysis of a network between two observation epochs,

a common stable datum is identified and applied in its adjustment, then statistical tests of the

significance of displacement of object points are performed, and finally the significant

displacements are reported. This method, as applied to an absolute network, is shown by the

flowchart in Figure 3.5.


Figure 3.4: Influence of an Unstable Reference Point. (Chen et al., 1990).

One commonly used technique for determining the stability of control points and significance

of object point displacements is the congruency testing method as proposed in (Chen, 1983).

According to Chen (1983), the global congruency test was first derived by Pelzer, H., in his

1971 publication on the analysis of geodetic deformation networks. The global congruency

test is usually done using the entire cofactor matrix of adjusted parameters (after the

elimination of nuisance parameters). Here, a simplified method is used; the co-variance

between coordinates of different points is ignored.


��

��

��

��

��

��

!"��#��

��

!��

��

$��

!"��#��

��

%�

Figure 3.5: Flowchart for Geometrical Deformation Analysis of an Absolute Network


After the outliers in the observations of each epoch are removed, deformation analysis can be

performed as follows:

1. Define the minimal constraint datum by fixing coordinates of one point and an

azimuth pseudo observation. Assume all points (except the fixed one) are unstable.

2. Adjust the network with both epochs of observations and with the initial input

coordinates.

3. Test the stability of each control point by congruency testing.

4. If most control points appear to be biased by a constant amount, the fixed point may

be unstable, so fix a different point and return to 1.

5. The points which pass the test are assumed stable.

6. Perform a minimal constraint adjustment with the initial input coordinates.

7. Check adjustment statistics for signs that an unstable point was considered stable. If

one doubts the stability of any points, do not consider them stable, and return to 6.

8. Fix the stable points as part of the datum. Remove the azimuth pseudo observation.

9. Adjust the network. The input coordinates are from the result of the last adjustment.

10. If more stable control points can be identified, return to 5.

11. Test the significance of displacement of each control and object point by congruency

testing.

12. Report the size and direction of the significant displacements and deliver a plotted

displacement field to aid interpretation.

Once two epochs are chosen for deformation analysis, the observations from both epochs are

combined into a single network and adjusted together. By this method, points which are fixed

or presumed stable are represented as single points. The remaining (suspected unstable)

points are each treated as two points in the adjustment – one for each epoch. (Ogundare,

2008a). Adjustment allows computation of the displacements and their cofactors, which

enable statistical congruency testing.

Congruency tests reveal whether point displacement should be considered significant, or if

the apparent displacement is small enough to be “more likely due to survey error” (US Army

Corps of Engineers, 2002). If the global congruency test fails, a network is suspected of


geometrical deformation. This means one or more points are not stable. Following a failed

global congruency test, the local congruency test is performed for each non-fixed point. If

the local congruency test passes, a point is probably stable, but if it fails, that point is

probably unstable. One should suspect the stability of control points which pass the local

congruency test by only a small margin.

Once the stable reference points have been identified, they are considered single, and no

longer double, points in a new minimally constrained adjustment, with the initial coordinates

used as input. Results are distorted if unstable points are mistakenly considered stable. If the

variance factor increases substantially when a point is first considered stable, the residuals of

observations involving that point grow, or an initially passed goodness of fit test fails, the

point may actually be unstable. It should be assumed unstable, and later tested by a more

informed local congruency test, based on an over-constrained datum with the more likely

stable points held fixed. If an unstable point is held fixed as part of the datum, the same three

signs may indicate that a mistake was made.

The method of congruency testing is implemented here with horizontal and vertical

differences tested separately. More advanced techniques which integrate all three

dimensions in a single test are presented in (Bin Setan, 1995) and (Sütti and Török, 1996).

The following detailed discussion of congruency testing is closely based on (Ogundare,

2008b).

The quantities extracted from least squares adjustment, shown in (3.33), for each epoch,

include network redundancy, the a posteriori variance factor of unit weight. An adjusted

coordinates vector and a cofactor matrix. The nuisance parameters have been removed from

the vector and associated matrix. These are the input quantities for geometrical deformation

analysis.


��

�

�

��

�

�

x

o

Q

x

ˆ

2

ˆσν

(3.33)

where =ν Number of degrees of freedom

=2oσ A priori variance factor of unit weight

=x̂ Vector of adjusted coordinates

=xQˆ Matrix of cofactors of adjusted coordinates.

The adjustment yields either 1D, 2D, or 3D coordinates for each point. The cofactor matrix

for each point matches in dimension, as shown in (3.34).

[ ] [ ]

��

�

�

�

=��

�

�

�

=

��

�

�=�

�

�

�=

==

2

2

2

33

2

2

22

21 1

zzyzxz

yzyyxy

xzxyxx

DD

yyxy

xyxxDD

zzD

qqq

qqq

qqq

q

Z

Y

X

x

qq

qqq

Y

Xx

qqZxD

(3.34)

Clearly, the 1D and 2D versions of x and q can be extracted from the 3D versions.

Displacement vectors for 1D and 2D analysis are defined by (3.35). It should be noted that

the two epochs discussed here are referred to as epoch 0 and epoch 1.

[ ] [ ]

DDD

DDD

qqqY

X

Y

Xd

qqqZZd

dD

dD

222

111

10

01

2

10011

+=��

�

�−�

�

�

�=

+=−=

(3.35)

where =md Vector of displacement of dimension m

[ ] =e Vector of coordinates from epoch e

=mdq Submatrix of cofactors of displacement of dimension m.


Before analysis can begin, the variance ratio test must be done, to see it the variance factors

are similar enough to be pooled together. First, the test significance level is selected (usually

0.05). Then the ratio (test statistic) is computed and tested in a two tailed F-test, as in (3.36).

?2

,,1

20

2

2,, 1010

upper

o

olower FF αννανν σσ

<< (3.36)

where =ανν ,, 10F

Critical value (upper or lower as annotated) from Fisher’s F distribution,

at redundancy 1: 0ν , redundancy 2: 1ν , and significance level:α

=α Significance level for the test

=eν Number of degrees of freedom for epoch e

=eo2σ A priori variance factor of unit weight for epoch e.

If the test fails, this indicates an observation weighting incompatibility between the two

adjustments, or an improper weighting scheme (Chen et al., 1990). As a remedy, the

standard deviations of observations input into the adjustments are made more realistic, so that

the variance factors become closer to unity. Only if the test passes may we continue with the

analysis. The next step is to compute the pooled variance factor – by (3.37) – and pooled

redundancy, by (3.38).

10

12

102

02

ννσνσνσ

+⋅+⋅

= ooo (3.37)

where =2oσ Pooled variance factor of unit weight.

The pooled variance factor is simply the mean of the variance factors from each epoch,

weighted by their respective redundancies, and the pooled redundancy is simply the sum of

the redundancy of each epoch.

10 ννν += (3.38)

where =ν Pooled redundancy.

The next step is to determine which points have common horizontal and vertical coordinates

in both epochs. The points with a common vertical component can be tested by (3.39). The

null hypothesis, to be accepted if the statement evaluates to true, is that the point’s elevation


is stable. The alternate hypothesis is that the point’s displacement in the Z dimension is

significant.

?1 zD Id < (3.39)

where =zI Vertical confidence interval.

The critical value for vertical displacement significance tests either comes from the Normal

distribution if the pooled redundancy is greater than 30 or else from Student’s distribution.

The vertical confidence interval is computed with (3.40). Recall that Ddq

1is defined in

(3.35).

Ddoz qCI1

2 ⋅⋅= σ (3.40)

where =C Critical value

=2oσ Pooled variance factor of unit weight.

The critical value must be determined first, by (3.41), and the chosen distribution depends on

the size of the pooled redundancy.

�

�

�

>��

≤��

=

)30(

)30(

2

2,

ν

ν

α

αν

ifZ

ift

C (3.41)

where =αν ,t Critical value from Student’s distribution at redundancy ν and significance

level α

=αZ Critical value from the Normal distribution at significance level α

=α Significance level for vertical displacement significance test

=ν Pooled redundancy.

For 2D congruency testing, we count the number of points being considered as the number of

points with common 2D coordinates, minus those which are fixed in both X and Y in the

adjustments. The rank of the common cofactor matrix is given by the number of points being

considered minus the number of datum defects removed for the successful adjustment of the

horizontal parameters of the network, as in (3.42).


Dnd −= 2ν (3.42)

where =dν Rank of the common cofactor matrix

=n Number of points being considered

=D Datum defects that were taken care of.

The number of datum defects that were taken care of is usually 3. Two of which are for the

coordinates of a fixed point, and the third is for the fixed orientation (or a fixed coordinate).

If no distances are measured in the network, an additional defect would need to be removed.

This would be very rare in practice. Today, distances can be measured to the same or greater

level of relative accuracy, with less effort, than angles, for the usual line lengths of several

hundred metres. In deformation monitoring surveys, which have stringent error budgets, it is

more economical to measure distances. In this project, it is assumed that distances are

measured. For each point under consideration, the quadratic form of its corresponding

displacement vector can be found by (3.43).

DdT

D dqdRD 22 2

⋅⋅= (3.43)

where =R Quadratic form of displacement vector

Dd2 and Ddq

2 are defined in (3.35).

Since the co-variance between coordinates of different points is ignored in this project, the

quadratic form of the displacement of all common points is not computed from the complete

displacement vector ( d ) and complete matrix of cofactors of coordinate differences ( dQ ), as

is the correct procedure, as in (3.44)

1̂0ˆ

01 ˆˆ

xxd

dT

TOT

QQQ

xxd

dQdR

+=−=

⋅⋅=

(3.44)

Here, the quadratic form of the displacement of all common points is simply computed as the

sum of the quadratic forms for each point, by (3.45).

�=

=n

ppTOT RR

1 (3.45)

where =TOTR Quadratic form of displacement of all points


=pR Quadratic form of displacement vector for point p

=n Number of points being considered.

This simplification is made for convenience. The choice was made because it is common for

a deformation network not to have all the same points observed in every epoch, and therefore

the matrices directly derived from the adjustment would be incompatible. The global

congruency test can now be performed. The null hypothesis, that the points under

consideration have remained stable, is accepted if (3.46) evaluates to true.

}} �

��

≅

≅<

⋅ ∞ )(

)(2

,,

2,,

2 knownifF

unknownifFR

apriorid

apriorid

oupper

oupper

do

TOT

σ

σ

νσ αν

ανν

(3.46)

where =dν Rank of the common cofactor matrix

=2oσ Pooled variance factor of unit weight

=ν Pooled redundancy

=α Significance level for global congruency test

=upperrrF α,2,1 Upper critical value from Fisher’s F distribution, at redundancy 1: r1,

redundancy 2: r2, and significance level: α

=2apriorioσ A priori variance factor of unit weight.

If the global congruency test fails, at least one point exhibits significant displacement, and it

must be identified. The simplest method to determine the individual unstable point, is to find

the one which contributes the most to TOTR . R has already been computed for all points by

(3.4k). To perform the local congruency tests, an upper critical value must be computed [see

(3.4o)] to allow comparisons. Note that, being a local test, it is recommended that the

significance level be made in context, by the approximation (3.47).

no

αα ≈ (3.47)

where =oα Significance level for local congruency test

=α Significance level for global congruency test

=n Number of points being considered, same as in (3.42).


The local congruency test of each point follows (3.48).

}} �

�

�

≅

≅⋅<

)(

)(2

2upper,2

2

2upper,,2

2knownif

unknownifFR

apriorio

apriorio

o

o

o

p

σχ

σ

σ α

αν

(3.48)

where =ν Pooled redundancy

=2apriorioσ A priori variance factor of unit weight

=2oσ Pooled variance factor of unit weight

=upper,,2 o

F αν Upper critical value from Fisher’s F distribution, with a redundancy 1 of 2,

a redundancy 2 of ν , and a significance level ofα

=upper

,22

oαχ Upper critical value from Chi squared distribution, with 2 degrees of

freedom and a significance level ofα

=2apriorioσ A priori variance factor of unit weight.

The null hypothesis is that the point is stable. Points which fail the test cannot be part of the

stable reference network. Once all stable points have been verified, a final adjustment of the

observations from both epochs is performed with those points fixed, yielding final adjusted

coordinate differences. The global and local congruency tests are repeated and the

displacements of unstable points are reported, since they have been shown to be statistically

significant. If an overall picture of the geometrical status is required, a more refined analysis

(not implemented here) can be performed where the displacement trends for the entire

deformable body are approximated by a least squares fitting of a deformation model to the

displacements at observed object points, similar to the concept of a trend surface.


4. Software Development

This chapter contains a short description of the design of the Survey Suite software package,

including its applications and data formats. Section 4.1 presents the overall design of the

software and gives examples of its use. Section 4.2 introduces the file formats used by the

applications of Survey Suite. Section 4.3 describes each application’s uses, limitations, and

input data requirements.

4.1 Design and Use

The software suite necessary for the completion of the analysis tasks proposed in this project

will be known as the Survey Suite. The suite of applications was generally designed from

the top down, and built from the bottom up. Many small general purpose classes were

combined into utility-type applications which each do one task. Most of the applications can

be classified as non-interactive utilities. However, two applications provide interactive

interfaces, namely Launcher and Select Project. The design of the practical solution to the

problem of geometrical deformation analysis of absolute networks consisting of raw total

station data includes the software applications depicted in Figure 4.1. The classification of

each application is shown. The Data Conversion applications are required in the case of

preanalysis or in converting raw total station data. The Data Pre-processing/Screening

applications are required in preparation of the data for adjustment. The Data Analysis

applications are used to perform preanalsyis, adjustment, and deformation analysis. Finally,

the Interface applications are used to execute the previously mentioned applications or

change the current analysis project. The purpose of each application is as follows:

• Launcher is a user interface to Survey Suite, a menu which allows quick execution of

all the utilities.

• Select Project allows one to change the current project.

• GSI to Text converts GSI data into a format that is easy for one to read, for manually

investigating problems in the data.


• GSI to Coordinates extracts the coordinates from a GSI file to provide initial

estimates for network adjustment.

• GSI to Tagged TRA and Tagged TRA to TRA are used together to convert GSI data

into TRA data.

• TRA Simulator is used for preanalysis; it creates the theoretical total station

observations according to a network design.

• TRA Heights Updater systematically substitutes heights of targets and instruments

based on point number.

• TRA Mean averages TRA data and converts it to face left form.

• TRA to Network performs reduction and error propagation computations upon TRA

data.

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• Network Adjustment performs parametric least squares network adjustment or

preanalysis.

• Deformation Analysis performs geometrical deformation analysis of a pair of

adjusted survey networks.

Each utility application performs a type of data conversion or processing according to the

instructions it finds in its assigned specifications file within the instructions folder in the

current project folder. The instructions, in the form of a hierarchical tree of text strings,

generally include the names of input file(s) and the values for any relevant option settings.

All settings always have a default value, for simplicity of use, so no specification is

necessary in the most common cases. While parsing the instructions, each application

recognizes certain key terms, and if one appears at the appropriate level of the instruction

“tree”, it extracts the information immediately beneath that key node. According to these

imported settings, each application reads its input data, performs computations, and produces

output data.

A particular procedure, such as outlier removal, can be described by a flowchart. Each step

involves either the execution of one of the utilities, with certain settings, or manual data-

editing. The flowchart for preanalysis is shown in Figure 4.2. Network design, the first step,

involves providing initial coordinate estimates for all the network points, proposing the

measurement scheme, and specifying the particular reduction methods and accuracies of the

survey observations. The three applications are executed, and the semi-major axes of the

error ellipses are manually checked against a tolerance determined in the error budget. The

flowchart for raw data conversion is shown in Figure 4.3. This procedure is to be followed

only if one has GSI data; if one has TRA data, the procedure is skipped. The specific

manually editing tasks to be performed will be explained later. The flowchart for data

snooping is shown in Figure 4.4. This procedure must be followed for every observational

epoch of a network so that outlier observations can be detected and removed before

deformation analysis is performed.


Figure 4.2: Survey Suite Preanalysis Procedure


Figure 4.3: Survey Suite Raw Data Conversion Procedure

Finally, the flowchart for geometrical deformation analysis is shown in Figure 4.5. This

procedure is followed for each pair of observational epochs of a network. The set of stable

points is identified and the best coordinates for these points are derived from a minimally

constrained adjustment of the observations of both epochs with the initial input coordinates.

A second adjustment in which the stable points are held fixed to these new coordinates yields

coordinate differences and their accuracies based on a common stable datum. Local

congruency tests are used to determine the significance of the displacement of each point.

Generally, not all the applications will needed in every analysis task. In practice, the most

common procedures are raw data conversion, data snooping, and geometrical deformation

analysis. Preanalysis is more performed less often.


Figure 4.4: Survey Suite Data Snooping Procedure


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For information about the implementation of the software, see Appendix A.


4.2 Data Standards

In this section, all the file formats used by the Survey Suite are listed, along with some

general data type rules. The Specification format is described.

All the file formats used by the suite, along with their file extensions, are listed in Table 4.1.

Table 4.1: Survey Suite File Format Extensions

File Format Extension

Specifications spec

Leica GSI survey data gsi

Tagged TRA survey data ttra

Leica TRA survey data tra

Coordinates xyz

Observation Scheme os

Network Observations obs

Adjusted Survey Network asn

Datum Definition fix

Some of these file formats are used by several of the applications, which are each described

in detail in section 4.3. The Leica TRA survey data format is central to the software suite. A

couple of notes which apply to all or most file formats follow.

1. A limitation that applies to all formats is that point numbers can be only a positive

non-zero integer less than about 4 billion – no alphabetical characters are allowed.

2. To put comments or metadata information into a .ttra, .tra, .xyz, .os, .obs, .asn, or .fix

file, put an asterisk ( * ) at the beginning of each line. Lines beginning with an

asterisk will be ignored.

The run settings or instructions for each application are composed in the Specifications

format. The basic format of the Specification files is a new invention and resembles an

extremely simplified XML. It is hierarchical and each node contains string data. There are


no differentiations between the nodes; they are all the same type of entity. It is a rudimentary

format well-suited to outlining instructions (or settings) for tasks, which can vary from

simple to extremely complex, depending on the task.

The text strings in this format cannot contain the angle bracket ( <, > ) characters, since these

are the delimiters and the parsing method is simplistic (character-at-a-time with out look-

ahead). Also, whitespace at the beginning or end of a string is ignored. This means

filenames with spaces at the beginning can not be referenced; so they must first be renamed.

Whitespace within the string is preserved, so filenames containing spaces may be used.

All the applications parse the system specifications file. It contains information which is

important to all the applications, such as file system paths. An example of the file follows.

In this example, the suite’s root directory is “W:\Programming\DevCpp-Projects\Survey

Suite” on the home machine of the author. The folder containing the projects the suite can

work with is the “projects” folder located in the root just defined. The current project is

“GEOM 8353 L4 p2 q2” in this case. The suite uses InkScape (open source vector graphics

editing software) to display the SVG network plots and to convert them into PDF files.

Therefore, the applications must know the InkScape’s install path as well. This is

“C:\Program Files\Inkscape” for this installation.

Configuration <

Install Path < W:\Programming\DevCpp-Projects\Survey Suite >

Projects Path < projects >

Current Project < GEOM 8353 L4 p2 q2 >

External Applications <

InkScape < C:\Program Files\Inkscape >

>

>

In the instructions for all applications, filenames are to be written without extensions. The

correct extension is appended according to the context. The remaining file formats will be

introduced as necessary in the discussions of the input data required by each application.


4.3 Description of the Applications

Each application will be discussed with regard to its purpose, input, output, capabilities, and

limitations. The internal operation of the applications which are most important in the

context of deformation analysis will also be described.

4.3.1 GSI to Text

GSI to Text converts GSI data into a format that is easy for one to read. The purpose is to

facilitate understanding the data in a GSI file so one may manually investigate potential

problems. The input includes:

• a Leica GSI survey data file, the format of which is described below

• optional coordinate system shifts (X, Y, Z).

Note that coordinate system shifts may be positive or negative integers only.

The Leica GSI survey data format is a raw format which is downloaded from Leica survey

instruments. There are 8-byte and 16-byte variants. This is the size of the data block in each

field. A surveyor using grid coordinates in the field (such as Universal Transverse Mercator)

must choose 16-byte GSI because 8-byte GSI cannot both store large coordinate values and

retain precision to the thousandth or ten-thousandth of a metre. Because of this limitation of

the 8-byte GSI format, it is less commonly used. This software suite currently supports only

16-byte GSI. A file is made up of many numbered rows, each of which follow the format

illustrated by Figure 4.6. There are two types of rows, “code” and “observation.” An

example of each type will be examined. An example code row follows.

*410125+0000000000000010 42....+0000000000001600

The first two bytes after the asterisk, ‘41’, signify “code”. Looking at next four bytes, we see

that this row is the 125th in its file. Taking the sign byte and the next 16 bytes together as the

value of this first field, we know the code is +10. The next field – starting with a space –

stores an attribute (signified by the ‘42’ data type identifier) of +1600. This row means

“Instrument setup location to be specified on the next row, and the height of the instrument is

1.600 metres.”


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An example observation row (originally all on the same line) follows.

*110128+0000000000009002 21.324+0000000008945401

22.324+0000000008937150 31..06+0000000001857629

The first two bytes after the asterisk, ‘11’, signify “observation”. This row is the 128th in its

file. Taking the sign byte and the next 16 bytes together as the value of this first field, we

know the point number is 9002. The ‘21’ in the second field means the data type is

“Horizontal Circle Reading.” The value is 89°45’40.1”. In the third field, ‘22’ signifies

“Vertical Circle Reading,” and the value is 89°37’15.0”. The fourth field represents a “Slope

Distance” (‘31’), the units are ten thousandths of a metre (the ‘6’ before the sign byte), and

the value is 185.7629 metres. If the byte before the sign byte was ‘0’, the units would be

thousandths of a metre.

The first two digits of the 6-byte data type identifier are all that are needed (currently) to

ascertain the field’s data type. All of the supported data types are listed in Table 4.2. Other

data types, including “Record ID” and “Time” will most likely be supported in the near

future; they will be added as work requires them.


Table 4.2: Supported Data Types in the Leica GSI Survey Data Format

Data type Description Identifier

PointID point number 11

HCR horizontal circle reading 21

dHCR change in horizontal orientation 25

VCR veritcal circle reading 22

SD slope distance 31

X coordinate of sideshot 81

Y coordinate of sideshot 82

Z coordinate of sideshot 83

STNX coordinate of station 84

STNY coordinate of station 85

STNZ coordinate of station 86

HT height of target 87

HI height of instrument 88

BS backsight point number 79

CODE thematic code 41

ATTRIBUTE information in addition to code 42

The output of the GSI to Text application is a human-readable view of the raw survey data.

The output of this utility for the example rows previously used to explain the Leica GSI

survey data format is shown below. The code row sample output follows.

{CODE 10} {ATTR0 1600}

The observation row sample output follows.

{PointID 9002} {HCR 89.45401}

{VCR 89.37150} {SD 185.7629}

4.3.2 GSI to Coordinates

GSI to Coordinates extracts only the coordinates from a GSI file and exports them in the

format suitable for network adjustment. The purpose is to provide approximate point


locations for least squares adjustment. The input is the same as for GSI to Text. The output

is a Coordinates file, in which the coordinates have been shifted by the (optionally) specified

amounts. The utility currently does not export coordinates in a customizable format for

compatibility with other software, as Network Adjustment does.

4.3.3 GSI to Tagged TRA

GSI to Tagged TRA converts the raw survey data from GSI format to Tagged TRA survey

data format. This utility is always used in conjunction with Tagged TRA to TRA. The input

is a Leica GSI survey data file. The settings are explained presently. “Duplicate Back Sight”

is an option which, when active, causes all back sight rows to be duplicated as intermediate

sights immediately afterward. This is an option to support Microsurvey CAD least squares

adjustment. Survey Suite’s TRA to Network utility considers the back sight as a de facto set

of survey observables, so this option should not be activated when one is using only the

Survey Suite software package for adjustment or analysis. “Has 10-20 Codes” is an option

which, when active, causes the utility to interpret 10-20 coding for the instrument setup and

back sight information, including heights. When it is inactive, codes are ignored and native

Leica GSI instrument setup and back sight information is used to produce the output. This

option must be inactive when one needs to extract free station data. The output is a Tagged

TRA survey data file.

The utility can interpret free station data, including the starts and ends of setups,

automatically, provided that coordinates are provided at the top of the GSI file, or in another

GSI file referenced prior to the raw survey data file in the settings. It can also interpret

regular setup and back sighting, as done using the built-in functions on the Leica TCA2003

total station. Finally, it can interpret 10-20 coding, a code and attribute method of setting up

and back sighting, developed at McElhanney for control, legal, and topographic work.

One thing to watch for is the different ways that instrument setup and backsight information

is stored in GSI files. The Leica GSI survey data format can vary based on instrument make

and can be customized further using Leica’s software. There are also differences in the way


instrument setup locations and back sight information are stored, based on surveyors’ field

procedures or habits. Because of this, the conversion algorithm cannot perfectly interpret the

data from all makes of Leica instruments.

4.3.4 Tagged TRA to TRA

Tagged TRA to TRA converts Tagged TRA survey data format to Leica TRA survey data

format. This utility is always used in conjunction with GSI to Tagged TRA. The output

from this utility is ready to be averaged by TRA Mean, have height errors corrected by TRA

Heights Updater, or prepared for adjustment by TRA to Network. The input is a Tagged

TRA survey data file, the format of which is described presently. The output is a Leica TRA

survey data file.

The purpose of the Tagged TRA survey data format is as an intermediate format between

GSI and TRA proper. Tagged TRA is simply the TRA format, with some “tags” added. The

reason for its existence is that when interpreting Freestation data from a GSI file, ambiguity

arises as to which line in the file signifies the beginning of each setup. One resolves this

ambiguity manually in a file-editing step. One first moves the free station start tag (*FS+)

and indicates the intended “backsight” point by positioning the backsight tag (*BS). Next,

station end tag (*FS-) is positioned correctly. Finally, one checks that all tags indicating

changes in horizontal orientation (*dHCR) are legitimate, by referring to the field notes and

the Freestation log file. It is fine to leave multiple station occupation (OCC) lines; the height

from the last one will be used. This is implemented in this way to be convenient for the

analyst. A sample of the Tagged TRA survey data format follows. In the sample, the file has

already been manually edited, and is ready to be converted to TRA format.

*FS+

! POINT H. I. HRZ ANGLE VER ANGLE SLP DIST HRZ OFF DESCRIPTION

IS 2 0.520 291.41495 82.51263 21.3717 .000 TH

IS 7 0.520 257.45557 100.18108 3.9956 .000 TH

*BS:

IS 5 1.300 5.28033 87.13488 28.8051 .000 TH

IS 6 1.300 7.41287 87.56433 20.7472 .000 TH

*dHCR 338.21071


OCC 103 1.750 CTRL

IS 6 1.300 346.02444 87.56466 20.7453 .000 TH

IS 2 0.520 270.02523 82.51308 21.3715 .000 TH

OCC 103 1.752 CTRL

IS 25 0.000 54.22213 108.26400 10.4235 .000 TH

*FS-

The utility can rotate horizontal directions (arising from freestation data) according to the

input tags. It can reorder the observations, placing the requested back sight point first. It can

also remove repeated occupation lines in a single setup, adopting the final height of

instrument as true.

Be warned that the utility will rotate the horizontal directions, literally, according to the

“*dHCR” tags. If incorrect tags are left in the data, the resulting horizontal circle readings

will be incorrect. This can arise when the field surveyor presses the button [STORE] twice

after a free station, or when free station results are stored, and then more points are measured

and added to the solution. One is advised to refer to the field notes and log files downloaded

from the instrument, while reviewing the Tagged data.

4.3.5 TRA Simulator

TRA Simulator creates theoretically error-free total station observations, according to an

Observation Scheme file, and given a set of coordinates. The purpose is to allow preanalysis

of a proposed network. It is the first utility that is run in that scenario. The output from this

utility is ready to be prepared for preanalysis by TRA to Network. The input includes:

• an Observation Scheme file, the format of which is described below

• a Coordinates file.

The first step in preanalysis is for one to manually type an Observation Scheme file, which

outlines the proposed total station observations. The Observation Scheme format is very

simple: there is only one keyword, “AT”, point numbers are the default data field, and

heights can be (optionally) defined. Whenever height is not defined, the default height will


be assumed by TRA Simulator, according to its settings. There are two types of row: the

instrument setup, and the target to be sighted. Referring to the following sample, the first

bolded row means “the instrument will be setup at point 4000 at a height of 1.7 metres.” The

second bolded row means “a reading of the horizontal circle, vertical circle and slope

distance to a target at the default height above point 302 will be made.” All targets to be

sighted from the current instrument location (point 4000) are listed before “moving the

instrument” to point 4001. A sample from an Observation Scheme file follows.

AT 4000 1.7

302

230 0.2

214 0.2

AT 4001 1.7

...

The output is a Leica TRA survey data file. This utility can create TRA measurements by

inversing between pairs of points, taking the heights of the instrument and target into

account. No interactive graphical interface showing proposed network geometry has been

designed yet. It would be helpful to be able to click to add or remove setups or observations

between points, and almost instantly be presented with the pertinent results of preanalysis.

This improvement is planned for the near future.

4.3.6 TRA Heights Updater

TRA Heights Updater updates heights of targets and instruments based on point number. It

makes these heights substitutions in a TRA file, producing a modified copy. The output from

this utility is ready to be averaged by TRA Mean or prepared for adjustment by TRA to

Network. The utility is used to systematically fix erroneous heights of instruments or targets,

based on what those heights should be for particular points. It is mainly useful for

preparation for error propagation in a plan to rigorously adjust a 2D network, where accurate

centring errors need to be computed based on heights which were not previously entered in


the data because of the non-necessity of their observation relating to the proposed 2D

application of the field work. The input includes:

• Leica TRA survey data

• Heights Rules file.

The heights rules file simply contains a row for each point number that should have its

heights changed. Each row has two fields, point number and new height (in metres),

separated by spaces or tabs. In the following practical example, points 1 and 6 are forced

centring pillars, and the approximate height of an instrument setup on a pillar is 0.235 metres.

Points 1000 through 1071 will have their heights set to zero so that elevations of the targets

(not the points) can be computed. Subsequently, the elevations of the points will be

subtracted to indirectly determine the heights of targets above the points. The problem here

is that the heights can not be easily measured with a tape measure, because the points are

several metres underground.

1 0.235

6 0.235

1000 0

1001 0

... (68 rows omitted) ...

1070 0

1071 0

Once the heights are computed, they can substituted into the TRA survey data by using this

utility with a new heights rules file. The ultimate goal of this process is to determine the

horizontal centring errors of targets over these points, to support a rigorous adjustment that

will report realistic error ellipses for all network points.

The output is a Leica TRA survey data file. A limitation of the application is that ranges of

point numbers cannot yet be specified in the heights rules file. The utility works by checking

the point numbers for matches to those in the heights rules file, and when a match is made,

the height is updated before the modified data row is written to the output file.


4.3.7 TRA Mean

TRA Mean averages Leica TRA survey data, converts it to face left form, and reports some

statistics for quality checking purposes. The purposes are to screen raw total station survey

data as part of a quality control process and prepare data for error propagation by TRA to

Network. The input is a Leica TRA survey data file – with observations on both faces. This

format is described after the settings are outlined. By default, the option “Only export single

face without double” is on and so single face observations will only be exported without the

presence of double faced observations to any particular point during a setup. Usually,

especially for precise work, this option should be active. The tolerance settings are the

maximum values allowed for splits in the three observable quantities for which no warnings

will be reported. The units are seconds for HCR and VCR and millimeters for SD.

Leica TRA survey data format is a format much easier on the eyes, much easier to edit, and

more compatible with third party software than the GSI data format is. It is a common

survey data format similar in format to the Softdesk FieldBook (FBK) format. It closely

resembles traditional field note entries. If desired, it can be imported into Microsurvey CAD,

to be used in survey traverse computations or a least squares network adjustment. There are

two types of rows: the occupation row, and the observation row. A station occupation row

starts with “OCC”, and specifies the station point number and height of instrument above the

point. Each observation row is a survey observation, a record which corresponds to a

pointing of the theodolite, the reading of both horizontal and vertical circles, and a distance

measurement. These rows start with either “BS” for backsight, or “IS” for intermediate

sight. When performing simple traverse computations, the backsight is used to orient each

setup’s horizontal circle, so that azimuths and then coordinates can be computed. In the

context of least squares adjustments, however, no distinction is made between a backsight

and any other sight. All sights made from a station are taken into account in the

determination of the unknown orientation parameter, which is the angular difference between

the horizontal circle readings and the corresponding inversed azimuths between network

points. Every observation row then specifies the station point number and height of target

above the sighted point. The horizontal and vertical circle readings, in sexigesimal-decimal


degrees follow. The slope distance and horizontal offset in metres and point description

conclude the observation row. Like the GSI format, it also uses the sexigesimal-decimal

degrees numeric format for angles but the difference is that TRA uses a decimal point. A

sample of the Leica TRA survey data format follows.


OCC 103 1.752 CTRL

BS 5 1.300 343.49104 87.13488 28.8051 .000 TH

IS 2 0.520 270.02566 82.51263 21.3717 .000 TH

IS 7 0.520 236.07028 100.18108 3.9956 .000 TH

IS 6 1.300 346.02358 87.56433 20.7472 .000 TH

IS 6 1.300 346.02444 87.56466 20.7453 .000 TH

IS 2 0.520 270.02523 82.51308 21.3715 .000 TH

IS 25 0.000 54.22213 108.26400 10.4235 .000 TH

The output is a Leica TRA survey data file with observations on face left only. The utility

means the observations and reports standard deviations, the variation range, and the number

of observations on each face, for each point observed from each setup. One should be

warned that a known defect occurs when observations to a target are made on both faces but

the backsight point is observed only on one face. The backsight will not be reported in the

new setup in the ouput, since it is not possible to compute a correct meaned backsight

observation from observations made only on one face.

4.3.8 TRA to Network

TRA to Network converts Leica TRA survey data to the Network Observations format, by

performing reduction and error propagation computations. The purpose is to prepare survey

data for Network Adjustment. The conversion process consists of selection or reduction of

the total station observations, with error propagation. There are five reduction (or planned

coordinate computation) methods. TRA data provides HT, HCR, VCR, and SD for each

target sighting. The various reduction methods and the observation types that will be

exported according to each are given in Table 4.3.


Table 4.3: Reduction Methods with Target Observation Types

Reduction Method Observation Types Exported

1D VD

2D HCR, HD

3D HCR, VCR, SD

HZ_DN HCR

3D_DN HCR, VCR

The purpose of the various reduction methods is to give the survey data analyst a finer degree

of control over the coordinate computation process which will occur during adjustment.

Suppose, for example, that a fixed-height pogo, plumbed over a benchmark (with only its

elevation known), is sighted with the total station. Only one equation will be necessary in the

subsequent least squares adjustment of this observation: the observed trigonometric height

difference. Therefore, in this case, one would choose to reduce this observation by the 1D

method. As a second example, suppose a high-precision industrial metrology survey job

must be processed. The relative standard EDM error over distances as short as 2 metres

(1:2000 or 500 ppm for a ± 1mm EDM) is unacceptable. So the intersections of horizontal

and vertical angles from multiple instrument locations, combined with the free station (zero

instrument centring error) method are to be used. In this case, one would choose the 3D_DN

reduction method. Finally, suppose observations are made to high-precision horizontal

control points. It would be best to choose the 2D method because the vertical coordinates for

these points are not well known.

The input is a Leica TRA survey data file with observations in face left form only. In the

settings for TRA to Network, it should be noted that all errors are to be quoted at standard

confidence. The first purpose of the settings is to specify which reduction method to apply to

each set of observations (HCR, VCR, and SD) in the source TRA file. The second purpose is

to specify the characteristics of the measurement system, that is the instrument and target

configuration used for each set of observations. The accuracies of the survey instrument are

to be given. The accuracy of the EDM is quoted in two parts, the constant, in millimetres,

and the scalar, in parts per million. The combined pointing and reading error in horizontal


and vertical angles for one set (two faces) is quoted in seconds of arc. The total station

leveling (or compensator) error is quoted for one set in seconds of arc. The number of sets of

angles which are observed may be specified (the default is one). A set of angular

observations is a pair – one reading of each angle on each face. One can also specify

whether or not the instrument or target is re-leveled, or re-centred between each set.

However, re-leveling of the target is not taken into account in error propagation, because the

effect is negligible. The centring method for both the instrument and target are to be

specified in two parts. There is the constant centring error in millimetres and the height

dependent centring error in millimetres per metre of height. The accuracy, in millimetres,

with which the heights of instruments or targets are measured is also specified. In addition,

there is a free station mode – a method where the instrument or target is not set up above a

physical point on the ground, but is located arbitrarily. With this method, there is no centring

error nor height measurement error, as long as the instrument or target remains level, and the

ground is perfectly stable. The criteria for deciding what exactly to do with each set of

observations, depends on the “at” and “to” points. A planned improvement will also

incorporate ranges of heights of instruments and targets as criteria. The output is a Network

Observations file.

This utility applies rigorous predicted error source accumulation to total station survey data,

so that measurements made with different instrument or target configurations can be adjusted

together, with the observations weighted appropriately. One should be aware that, in the

error propagation routine implemented, random error caused by horizontal refraction is

ignored. This can only be done if we make the assumption that there are no temperature

gradients across the line of sight. This occurs if the temperature of the air and that of any

objects near the line of sight has stabilized. Random error in vertical circle readings caused

by atmospheric refraction is also ignored. The actual amount of this random error will vary

greatly with temperature, pressure, wind currents, location, and time of day. The

deformation monitoring surveys the author has worked on generally have short sight

distances to minimize all types of random errors, and also the surveys are performed before

sunrise to minimize random refraction effects.


The internal operation of the utility will now be explained. First, the raw survey data is

imported and converted to mark-to-mark form. This is a form that assumes instrument and

target heights are zero for all observations, so that observations equations in least squares

adjustment can relate the coordinates of the points directly, without heights of instruments

and targets appearing in those formulas. Second, error propagation is performed. Third,

selections of desired observation types are carried out. The mark-to-mark reductions do not

take into account the height differences with respect to the geoid between the instrument and

target points. The effects of earth curvature are also ignored. Deformation monitoring

surveys of engineering structures are usually confined to a small geographic area, so this

should be an acceptable approximation. The mark-to-mark vertical height difference is

computed first, by (4.1).

HTHIVCRSDVD −+⋅= )cos(' (4.1)

where ='VD Vertical height difference (mark-to-mark)

SD = Slope distance

VCR = Vertical circle reading

HI = Instrument height in metres

HT = Target height in metres.

The mark-to-mark horizontal distance is computed as (4.2).

)sin(' VCRSDHD ⋅= (4.2)

where ='HD Horizontal distance (mark-to-mark). The mark-to-mark slope distance is

computed from the first two quantities, by (4.3).

22 ''' VDHDSD += (4.3)

where ='SD Slope distance (mark-to-mark). The horizontal circle reading remains

unchanged, as in (4.4).

HCRHCR =' (4.4)

where ='HCR Horizontal circle reading (mark-to-mark)

HCR = Horizontal circle reading.


The mark-to-mark vertical circle reading is computed by a two step formula, as in (4.5).

)0'(,180''''

tan' 1

<°+=

��

��

�= −

VDifVCRVCRVDHD

VCR (4.5)

where ='VCR Vertical circle reading (mark-to-mark).

After the mark-to-mark reductions of the observed quantities have been performed, error

propagation for those quantities is carried out. This discussion of error propagation is based

on (Ogundare, 2008b). All formulas will be presented in the order that the computations are

carried out. That is, later formulas will reuse the terms and values defined by earlier ones.

Several basic error quantities must be defined first. The instrument and target total centring

errors in metres are given by (4.6).

HT

HI

trgtdh

trgtcon

trgt

instdh

instcon

inst

ccc

ccc

⋅+=

⋅+=

...

...

σσσσσσ

(4.6)

where =instcσ

Instrument total centring error in metres

=inst

conc .σ Instrument constant centring error in metres

=inst

dhc ..σ Instrument height dependent centring error in metres.

The formula for target total centring error is the same as for the instrument, except each term

refers to a target quantity rather than an instrument one. After computation by (4.6), both the

total centring error of the instrument and of the target, respectively, are to be divided by the

square root of the number of sets of angles, if the instrument or target, respectively, is re-

centred between each set. The computation of leveling error ( Lσ ) in radians follows (4.7)

CL σσ = (4.7)

where =Cσ Theodolite compensator error in radians. However, if the instrument is re-

leveled between each set, leveling error is given by (4.8).

nC

Lσσ = (4.8)

where =n number of sets of angles. The error in the mark-to-mark horizontal circle

reading is given by (4.9).


2222

' '')tan( ��

��

�+��

�

��

�+��

�

��

�+��

��

�=HDHDVCRn

trgtinst ccLAHCR

σσσσσ (4.9)

where ='HCRσ Error in horizontal circle reading (mark-to-mark) in radians

=Aσ Theodolite directional error in radians

The error in the observed slope distance is given by (4.10).

( ) ( )22 SDsc EDMEDMSD ⋅+= σσσ (4.10)

where =SDσ Error in slope distance in metres

=cEDMσ EDM constant error in metres

=sEDMσ EDM scalar error in ppm.

The error in the observed vertical circle reading is given by (4.11).

( )22

LA

VCR nσσσ +�

�

��

�= (4.11)

where =VCRσ Error in vertical circle reading in radians. The error in the mark-to-mark

horizontal distance is given by (4.12).

( ) ( ) ( ) ( )2222' )cos()sin(

trgtinst ccVCRSDHD VCRSDVCR σσσσσ ++⋅⋅+⋅= (4.12)

where ='HDσ Error in horizontal distance (mark-to-mark) in metres. The error in the

mark-to-mark vertical height difference is given by (4.13).

( ) ( ) ( ) ( )2222' )sin()cos(

trgtinst heightheightVCRSDVD VCRSDVCR σσσσσ ++⋅⋅+⋅= (4.13)

where ='VDσ Error in vertical height difference (mark-to-mark) in metres

=instheightσ Instrument height accuracy in metres

=trgtheightσ Target height accuracy in metres.

The error in the mark-to-mark slope distance is given by (4.14).

2

'

2

'' ''

''

��

��

� ⋅+��

��

� ⋅=SDVD

SDHD

VDHDSD σσσ (4.14)


where ='SDσ Error in slope distance (mark-to-mark) in metres.

The error in the mark-to-mark vertical circle reading is given by (4.15).

2

2'

2

2'' ''

''

��

��

� ⋅+��

��

� ⋅=SDHD

SDVD

VDHDVCR σσσ (4.15)

where ='VCRσ Error in vertical circle reading (mark-to-mark) in radians.

Following these computations, the requested quantities are exported.

4.3.9 Network Adjustment

Network Adjustment performs parametric least squares network adjustment and produces

reports and Adjusted Survey Network files for Deformation Analysis to test for congruency.

It is also used to perform preanalysis to aid in survey network design. The input includes:

• a Network Observations file, the format of which is described below

• optionally, a file listing known outliers, which is in the Network Observations format

• a Coordinates file, also described in this section

• optionally, a Datum Definition file, also described in this section

• optionally, a Stable Points listing file, also described in this section

The default mode of operation is to adjust a single network. To support rigorous geometrical

deformation analysis, it is also possible to adjust two epochs of observations together in a

single network, with the stable points represented as single points in the network, and

unstable points represented as pairs of points, one for each epoch. When two epochs are

involved, two Network Observations file, with their optional known outliers lists, are

supplied as input.

Network Observations is a format for communicating all kinds of measurements, along with

their accuracies at standard confidence. It is suitable for total station observations or derived

quantities and for leveled height difference observations, but not for GPS baselines, because

no cofactor matrix is supported. The utility TRA to Network generates files of this format.


The supported observation classes (first level) and types (second level) with abbreviated

identifiers are as follows:

• Coordinate

o X

o Y

o Z

• Coordinate Difference

o 0X (dX)

o 0Y (dY)

o 0Z (dZ)

o Vertical Distance (VD)

• Horizontal Direction

o Azimuth (AZ)

o Horizontal Circle Reading (HCR)

• Vertical Direction

o Vertical Circle Reading (VCR)

• Distance

o Horizontal Distance (HD)

o Slope Distance (SD).

Note that Vertical Distance is the same as 0Z. It exists out of user-friendliness. Vertical

Distance would be used for leveled height differences or reduced trigonometric height

differences, while 0X, 0Y, and 0Z would be used for simplistically-qualified GPS baselines,

for example. The observation type “horizontal angle” is not supported since it can be

represented as a pair of horizontal directions with the same associated horizontal orientation

parameter. This is not an inconvenience for data which has been collected electronically,

since it is already in that form. The observation must specify the following:

• associated network point numbers for the stations to be labeled “at” and “to”

• type

• value

• standard deviation.


There are two unit categories of observation types: linear and angular. All the observation

types are linear, except for AZ, HCR, and VCR, which are angular. For linear observations,

the units for both “value” and “standard deviation” are metres. For angular observations, the

units for “value” are sexigesimal-decimal degrees (e.g. 120°14’57.3” is entered as

120.14573), while for “standard deviation”, decimal seconds of arc are used (e.g. 1’05.3” is

entered as 65.3; 2.0” is entered as 2). In the following sample from a Network Observations

file, the results of three reduction methods (1D, 2D, and 3D) are evident. The original TRA

observations from 4000-307 (and also 4001-302) were reduced by the 2D method; the sight

to 9001, 1D; and the sight to 5003, 3D. Also, notice the keyword orient. It signifies a

new instrument location, and it can also be used whenever the horizontal orientation has been

changed. The reason that it is necessary is that a requirement of least squares adjustment is

that correlated horizontal directions must be organized into sets which share an unknown

orientation parameter.

4000-307 HCR 10.34426 1.163

4000-307 HD 104.75502 0.001138

4000-9001 VD 0.080005111 0.0005105

4000-5003 HCR 100.13518 0.5005

4000-5003 VCR 81.254101 1.841

4000-5003 SD 21.066578 0.0009865

orient

4001-302 HCR 169.21458 1.142

4001-302 HD 107.1342 0.001139

The Coordinates format is contextual; depending on the number of fields, the meaning of

each field changes. The fields are delimited by any number of consecutive spaces. The first

field is always the point number. Referring to the following sample Coordinates file, point 2

is 2 dimensional, that is the X and Y coordinates are defined. Point 3 is 3 dimensional, with

X, Y, and Z coordinates defined. Point 1 is 1 dimensional, with only its Z coordinate

defined. There are also optional two functional operators() and !, which can be used to

modify the characteristics of each coordinate for a point, independently. A coordinate is, by


default, free. The parentheses wrap the standard deviation of the coordinate. The

exclamation point represents that the coordinate is fixed. All the coordinates of the points in

the sample are free.

2 1531.9850 1178.1440

3 1534.3455 1135.5646 6.3563

1 5.9573

In the Datum Definition format, only the exclamation point and question mark are supported

as functional operators. The exclamation point is used to fix a coordinate, while the question

mark is used to free it. In this format, the status of all three coordinates must be given, in the

order X, Y, and Z. An example in which point 2 is fixed in X and Y, point 3 is fixed in X

only , and point 1 is fixed in Z only. This is an example of a minimum constraints datum for

the adjustment of a horizontal network with some points for which computed elevations are

desired.

2 ! ! ?

3 ! ? ?

1 ? ? !

The Stable Points format is a way to list point numbers of point which are to be assumed

stable between epochs. It is used only when one intends to adjust two epochs of observations

together. Any combination of spaces, tabs, commas, or new lines may be used as delimiters.

In the following example, point 1, 2, 4, 100, and 101 are deemed stable.

1,2 4

100 101

When adjusting two epochs of observations together, points not fixed in the Datum

Definition or declared stable are assumed to be unstable. The adjustment will yield two sets

of coordinates for these points, allowing their stability to be tested by a local congruency test.


The Network Adjustment utility produces the following output:

• For each epoch of observations,

o An Adjusted Survey Network file

o Report

o A Coordinates file (the adjusted coordinates)

o Exported coordinates file (in a customizable format for compatibility with

other software)

• Plot showing network geometry lines and confidence ellipses.

This utility supports the following features:

• Parametric adjustment of 1D, 2D, or combined 2D and 1D networks

• Global test of variance factor of unit weight

• Goodness of fit test for normality of standardized residuals using the Kolmogorov-

Smirnov method

• Local tests of standardized residuals, for outlier detection

• Option to scale stochastic quantities by the computed a posteriori variance factor

• Exported Coordinates

o Conventional delimited files

o Delimiter options: space, tab, comma

o Fields (in any desired order): point number, northing, easting, elevation.

A limitation is that the goodness of fit test is done on the network of observations as a whole,

not on each type of observational class. The variance factor is also computed for the whole

network.

Various least squares adjustment software handle “side-shots points” differently. Side-shots

points are those that have observations relating them to the network, but an instrument is

never setup over them, only a target. Some software, like the adjustment program in LDD

Survey Module, does not (by default) adjust side-shots points along with the station points as

parameters during the adjustment iterations. The software can be forced to adjust side shot

points as it does station points by telling it in the input survey data that a setup was done on


those points. No real observations need to be introduced; a pair of station setup and back

sight entries are sufficient for each side shot points. There can be a good reason for the LDD

approach: if measurements to the side shot points are of a lower accuracy – due to the use of

a prism pole with an out-of-adjustment level bubble – than the main traverse – which may

employ precise target carriers over all station points – then, if the individual observation are

not weighted according to the actual measurement methods, the side shot points, if treated as

stations in the adjustment, will cause distortion of the main traverse. The adjustment utility

in the Survey Suite takes the opposite approach; all unknown coordinates become parameters

in the adjustment, regardless of whether a point was used as an instrument station. The

difference is that when using the Survey Suite, the individual observation can be weighted

according to the actual measurement methods. The instructions to the TRA to Network

utility can be used to describe the accuracy of every measurement. Thus, a skilled analyst

can prevent distortion of the main traverse, for example, by being a little pessimistic in

estimating the target centring accuracy over the side shot points. The advantage to the

Survey Suite approach is that all network points coordinates will be more accurate, and the

estimates of their accuracies will also be more realistic. Note that the preceding discussion of

side shot points only applies where there are redundant measurements. A side shot point

with observations from only a single station will be treated the same by both approaches. If

one wishes to force a side shot point not to be adjusted as a station, one may change the point

number of each redundant set of measurements in the TRA file, by adding an additional 1000

for each subsequent measurement, for example. This way, each set of measurements will

yield a different point solution. One may then compare these adjustment results, before

deciding how to deal with the redundancy. In some cases, the redundancy is present only as

a check, and so the redundant solutions can be verified for degree of scattering, and then

discarded. However, for deformation monitoring surveys, all measurements are made

carefully and accurately, and redundancy is used to increase network reliability, and that is

part of the reason the approach was implemented as described.

Since only the plane is supported as a computational surface, the utility can only be used for

small areas where distortions due to earth curvature are negligible. The adjustment method

“free network with internal constraints” is not supported. An additional type of parameter


could be added: the unknown scale factor for a set of distances measured with a particular

EDM. The goodness of fit test should also be done on each class of observation, such as

distances, horizontal angles, or vertical angles. The variance factor could also be computed

for each class of observation to enable checks against inappropriate weighting of entire

observation classes. It would also be useful to plot a histogram of the standardized residuals

to visualize the test. A further improvement to the adjustment process is proposed, in which

heights of instruments and targets are considered as observations in the adjustment. This

would prevent the need to reduce observations to mark-to-mark form before the adjustment,

and would allow blunder detection of heights of instruments and targets. However, this has

not yet been designed since there are unresolved issues regarding the handling of correlated

heights of instruments or targets.

Following the methodology in sections 3.2 – 3.3, preanalysis or least squares adjustment is

performed, and the post-adjustment tests are carried out (but not in the case of preanalysis).

Finally, the textual report is generated, the adjusted coordinates are exported (if requested),

and the network plot is created. The plot is generated in the SVG format, and a Windows

batch file is created to tell InkScape, via a command line, to display it (if desired), and

convert it into PDF format. Regarding the implementation, first, the utility records the

observations and initial coordinates – along with whether those coordinates are free, fixed, or

weight-constrained – which comprise the network, and then proceeds to

• build the observations vector ( � ),

• determine the set of coordinate parameters,

• build the parameters vector ( x ), including the necessary orientation parameters,

• perform iterations until the solution converges, and

• extract, test, and report the adjusted quantities.

Theoretically, the parametric model equations must be created in the form of equations

(3.12). The equations are never actually created, but they could be, since the meta data

required for their creation is maintained. General formulas which relate the observations to

the parameters, (4.16) through (4.24), for the various observation types are called the

“parametric observation equations”. These equations are used to compute the misclosure

vector during each iteration. In all cases, the observations are between two points, in the


direction from point “at” to point “to”. The instrument is over the “at” point and the target is

over the “to” point.

12 XXdX −= (4.16)

12 YYdY −= (4.17)

12 ZZdZ −= (4.18)

dZVD = (4.19)

��

��

�

−−= −

12

121tanYYXX

AZ

(4.20)

β∆−= AZHCR (4.21)

��

��

�= −

dZHD

VCR 1tan

(4.22)

212

212 )()( YYXXHD −+−= (4.23)

212

212

212 )()()( ZZYYXXSD −+−+−= (4.24)

where =∆β Orientation parameter

=),,( 111 ZYX Coordinates of point “at”

=),,( 222 ZYX Coordinates of point “to”

Observation type abbreviations are defined near the start of this section.

The partial derivatives of these equations with respect to the parameters, including the

coordinates and orientation parameters, are used to compute the elements of the first design

matrix.

4.3.10 Deformation Analysis

Deformation Analysis performs deformation analysis of two supplied adjusted survey

networks, and reports the results in textual and graphical formats. The purpose is to perform

reference network stability tests, and once deformations are localized, statistically test

whether object point displacements are significant. The input is a pair of Adjusted Survey

Network files, the format of which is described presently.


The Adjusted Survey Network format summarizes the resulting parameters of a least squares

network adjustment. In addition to the network redundancy and a posteriori variance factor

of unit weight, it includes the adjusted coordinates and the upper triangular portion of the

3X3 cofactor matrix for each point. The coordinates section is in the Coordinates format; see

the description in section 4.2.9, Network Adjustment. The cofactors section follows a strict

format. The variances and co-variances are extracted, un-scaled, from the cofactors matrix of

parameters. The seven fields are separated by single spaces. Each row is defined in general

mathematical form as follows.

(Point Number)

2xxσ

xyσ

xzσ

2yyσ

yzσ

2zzσ

A sample Adjusted Survey Network file follows.

redundancy is 1

variance factor is 0.037341181

coordinates

1 1000.0000! 1000.0000!

2 1531.9850(0.0026) 1178.1440(0.0068)

3 1898.2162(0.0026) 955.9573(0.0094)

cofactors

2 6.5142217e-006 -1.1477883e-005 0 4.5978982e-005 0 0

3 6.5773465e-006 2.1921975e-006 0 8.7888527e-005 0 0

The output includes:

• Deformation analysis report containing congruency tests results

• Plot showing horizontal and vertical displacement vectors and confidence regions.

The utility can perform global and local congruency tests in the horizontal and vertical

planes, separately. Coordinate displacement trends for two epochs are reported by means of

a textual report and a vector graphics plot depicting the network’s displacement field. The

limitations are that coordinate trend graphs, 3D congruency testing, and deterministic

modeling are not yet supported.


Following the methodology in section 3.4, congruency tests are performed, and the textual

report is generated. The same graphical plotting functions as in Network Adjustment are

used here.

4.3.11 Launcher

Launcher is an interactive console application that lets one execute any utility in the suite at

the press of key. It continues running after utility execution. The purpose is to provide a

menu for executing utilities and to save the time of the analyst.

4.3.12 Select Project

Select Project is an interactive console application that lets one change the current project.

The purpose is to allow one to quickly switch the focus to different datasets. The application

can select project folders contained in the designated projects folder, as defined by the

“Projects Path” field in the system instructions file. It can start a Windows Explorer pointed

to current project folder. However, the application cannot yet browse the project path

recursively. Therefore, only one level of projects in visible at a time. The author, having

accumulated numerous projects during testing and performing the computations for this

report, simply moves the folders around manually in Windows Explorer, and organizes them

in a multiple level hierarchy organized first by survey job, then by date. Practically, this

avoids having to look at an excessively long list whenever one wants to change projects. The

application works by generating a list of the folders in the designated projects folder, and

displays a menu which allows one to pick a folder by pressing the appropriate numeric key.

It then updates the “Current Project” field in the system instructions file.


5. Data Collection

Field procedures for high-precision surveying which eliminate or minimize error sources are

given. Then the instrumentation used for data collection for the surveys discussed in chapter

6 will be listed.

The type of targets used to survey the monitored points depend on the type of structure. In

some cases, prism targets are permanently mounted on structures. In others, reflective tape

targets are mounted, as when monitoring smooth building faces or reinforced concrete

excavation walls. In still others, the monitored points are marked by nails, which are

surveyed conventionally by centring a prism target above the points.

When setting up a survey network, and before any data collection is done, it is suggested that

the points should be numbered in a systematic way to simplify data processing. Organized

point numbering schemes allow for systematic error propagation for survey observations.

Assign each class of point a point number range. Point should be classified by type of

monumentation and accessibility. Forced centring pillars, brass cap monuments, traverse

hubs, monitored points are example classes. Monitored points may be further broken down

into points underground, at ground level, and mounted on above-ground structures. As an

example, forced centring pillars might be numbered in the range 1-99.

In practice, the best way to reduce the random error caused by horizontal refraction is to keep

the line of sight in the middle of the open space between any obstacles. The effects of

atmospheric refraction on vertical angles must also be minimized, by keeping the line of

sight away from the tops or bottoms of objects which may be of a different temperature than

the surrounding air. Further, the surveys should be performed when the temperature of the

air and that of any objects near the line of sight has stabilized. This is why many precise

surveys are carried out in the early morning before the sun rises, or late at night, after sunset.

The surveys are generally carried out with some degree of redundancy to provide checks on

the repeatability of the observations. In some instances, the free station procedure is

employed so that instrument centring error is eliminated. In those cases, the initially entered


height of instrument often needs to be corrected, by staking out a benchmark point with a

fixed height prism pole, and computing the correction so that the total station reports correct

elevations. An independent check to another benchmark is then carried out. When it is

necessary to traverse in 3 dimensions, a correction is applied to heights of instruments and

targets measured along a slope, which takes into account the slope height measured, the

horizontal radial dimension of the instrument or target, and the curvature of the measuring

tape’s path. At every instrument station, a distant, stable, clearly visible prism should be

designated as the “back sight” target – a horizontal reference point. This point is used to re-

orient the instrument if the tripod head twists or if the instrument goes off-level and must be

re-leveled and re-centred. The data should be collected digitally rather than hand-booked.

This allows for faster performance of the survey, which reduces the errors associated with

possible settling of the instrument or targets, and prevents the occurrence of numerical

transposition blunders. Observations to all points from every station should be made at least

once on both faces of the instrument. If a difference in horizontal angle, vertical angle, or

slope distance is larger than expected, the set of observations should be repeated. The

differences that may be expected depends on the accuracy of the instrument, the skill levels

of the surveyors, the current atmospheric conditions, and the distance from the station to the

target. Clearly, a more practiced surveyor can make more refined judgments of when to

throw away and repeat observations.

For height difference determinations, digital levels (Leica DNA03) with invar rods (for

example, the Leica GPCL2) are used. For horizontal or 3-dimensional coordination, high

precision total stations (Leica TCA2003) with regular round prism targets (Leica GPR121)

are used. Above points at or below ground level, the prism targets are centred using precise

target carriers (Leica GZR3) or mini reflector poles (Leica GLS14). For the accuracies of the

instruments, see Appendix B.


6. Applications of Survey Suite

This chapter demonstrates the application of the theory explained in chapter 3 to practical

problems involving computations of error budgets, preanalysis, and deformation analysis.

The software described in chapter 4 is used to solve the problems. In section 6.1, survey

error budgeting and preanalysis are used in the creation of a design for an urban high-rise

building monitoring network needed due to the construction of an underground light rail

rapid transit station. Section 6.2 presents the horizontal deformation analysis results for a

five-epoch buried water main monitoring campaign. First a comparison of two epochs with

similar network configurations is performed, then a chronological comparison of the four

consecutive pairs of epochs are presented. In this way, a surveying blunder is discovered.

Section 6.3 presents a three-dimensional deformation analysis of points attached to leaning

trees.

6.1 Monitoring High-rise Buildings Adjacent to an Excavation

For the installation of an underground station of a light rail rapid transit system, an

excavation is first constructed which extends beneath the foundations of the adjacent

buildings. This practice is potentially dangerous in that the high-rise buildings are

susceptible to damage due to the possibility of subsidence. Let us assume that the maximum

expected horizontal movement of points on the exterior walls of buildings is specified by

geotechnical engineers as 8 mm. The size of the semi-major axis of the point coordinate

error ellipses at 95% confidence – yielded from preanalysis – must be, at a maximum, one

fourth of that, or 2 mm.

High precision surveying in a highly populated area presents some interesting network design

problems. Station locations are constrained by road and pedestrian traffic, and sight lines are

often obstructed by changing construction activities. Preanalysis will be used to help design

a measurement scheme. The design success criteria is that the semi-major axes of all the

point coordinate error ellipses at 95% confidence must be, at most, 2 mm. Figure 6.1 shows

the scenario for which a survey network and measurement scheme must be designed. Three


streets, along with the relative locations of building outlines, reference points (300 series),

temporary benchmarks (9000 series), and monitored points (5000 series) are shown. In

reality, for the targets along the building faces adjacent to Third Avenue, there are two levels

of monitored points, to allow tilting to be observed. For our purposes, a simplification is

sufficient. The accuracy of the points (not included) several metres higher up the building

fronts will be very similar to that of the lower points. The problem is simplified further by

ignoring obstructions of sight lines by construction equipment and fencing. In reality, one

needs to visit the site to find possible instrument setup locations and practical locations for

secondary control points, and to make sure sight lines are not obstructed. The reference

points are coordinated in 3 dimensions by initial control surveys using the Leica TCA2003

total station and Leica DNA03 digital level. Elevations of the temporary benchmarks are

periodically determined by running double run leveling loops from the reference points.

Points on the faces of buildings ‘A’ through ‘D’ must be monitored for possible

displacements in three dimensions.

Figure 6.1: Plan for High-rise Building Monitoring


The problem of locating the necessary total station setups and the secondary control points

and deciding which observations to make from each setup to achieve the required accuracy of

positioning the monitored points in an efficient way will be solved by the trial and error and

preanalysis computer simulation approach. One possible solution – a satisfactory design – is

given here. Interested readers may refer to Appendix C for a log of the run settings, input

data, and output associated with the final results presented here. In the proposed

measurement scheme, there are a total of 107 sets of raw horizontal angle, vertical angle, and

slope distance observations, made from seven instrument locations, all of which are free

stations to eliminate instrument centring error. The Leica GPR121 prism targets are centred

using precise target carriers (Leica GZR3) or mini reflector poles (Leica GLS14). The

reference points employ precise target carriers, while the secondary control points employ

mini reflector poles. Free stations 4000, 4001, 4002, and 4003 tie the reference points to the

new secondary control points (points 201-208), and also make observations to some

monitored points. All the monitored points are reflective tape targets fixed to the building

faces. Free stations 4004 and 4005 are required to observe the positions of monitor points

5004, 5005, 5014, and 5015. A scheme without free station 4004 yields semi-major axes of

2.7 mm for points 5004, 5005, 5014, and 5015, so free station 4004 is needed. Every

monitored point must be observed from two locations, as demonstrated by the test of

temporarily removing free station 4004. Free station 4007 is required because it is not

possible to observe monitored point 5019 from free station 4004 because a corner of building

‘D’ obstructs the potential sight line, as is apparent in Figure 6.1. Therefore, if free station

4007 were to be removed, monitored point 5019 would only be observable from free station

4000. One might ask if point 5019 could be observed from both free stations 4000 and 4001.

It could be if monitored point 5019 were a prism mounted on the building, in which case it

could be pointed toward free station 4001. However, in this scenario all monitored points are

tape targets. It is not accurate to observe a tape target from a glancing or oblique angle; the

observed distance would vary greatly with even minute pointing differences in horizontal

direction, due to the geometry of the intersection of the beam with the target’s flat face. The

ideal viewing geometry for observing a tape target is from directly in front of it, ie.

perpendicular to the building face. Plots showing the network geometry, station connections

(grey lines), horizontal error ellipses, and vertical confidence intervals (offset to the right of


the points) follow. Figure 6.2 shows the geometry of the entire network to provide context.

The point numbers and error ellipses for the monitored points are too crowded in this view to

be useful, however. Figure 6.3 gives a more restricted view, and is more useful for

comparing the sizes and shapes of the error ellipses of the various monitored points.

Figure 6.2: Geometry of Network Design by Preanalysis for High-rise Building Monitoring

The scale bar for error ellipses indicates that the largest semi-major axis of any point is 2.0

mm in length. The vertical error bar is displayed at the same confidence level (95%) and at

the same scale as the error ellipses. The error ellipses are given with respect to the eight

fixed reference points 300, 301, 302, 303, 305, 307, 308, and 309.


Figure 6.3: Detailed View of Geometry of Network Design


The statistics of the measurement scheme are summarized in Table 6.1.

Table 6.1: Observation Scheme Summary for Preanalysis

of High-rise Building Deformation Monitoring Network

Number of instrument stations 7

Number of observations 251

Number of parameters 110

Number of degrees of freedom 141

Coordinate Differences 7

Horizontal Directions 100

Vertical Directions 44

Distances 100

4000 32

4001 32

4002 29

4003 32

4004 44

4005 47

4007 35

Obsevation Scheme Summary

Number of each type of observations

Number of observations from each station

This analysis considers total station observations only; the elevations of leveled benchmarks

are assumed errorless. In reality, their accuracy would be better than ± 1 mm at 95 %

confidence. For realistic vertical confidence intervals, this ± 1 mm error should be

combined with the results which follow. The maximum semi-major axis of any monitored

point coordinate error ellipse at 95% confidence is 2.0 mm in length; this occurs for point

5014.


Table 6.2: Accuracy Summary of Preanalysis

of a High-rise Building Deformation Monitoring Network

Point Semi-Major Semi-Minor Azimuth Vertical

Number Axis (m) Axis (m) (D.MMSS) Interval (m)

5000 0.0019 0.0009 62.0956 0.0005

5001 0.0015 0.0009 69.4158 0.0004

5002 0.0013 0.0010 74.4458 0.0004

5003 0.0013 0.0009 81.5208 0.0005

5004 0.0019 0.0012 96.4432 0.0005

5005 0.0019 0.0012 84.0913 0.0005

5006 0.0013 0.0009 98.4250 0.0005

5007 0.0013 0.0010 103.0901 0.0005

5008 0.0015 0.0009 111.4406 0.0005

5009 0.0019 0.0010 121.2626 0.0005

5010 0.0019 0.0010 117.1533 0.0005

5011 0.0015 0.0009 108.5528 0.0004

5012 0.0013 0.0010 102.4407 0.0004

5013 0.0015 0.0010 67.0533 0.0004

5014 0.0020 0.0013 83.5843 0.0005

5015 0.0019 0.0012 95.4259 0.0005

5016 0.0013 0.0010 81.2028 0.0005

5017 0.0014 0.0010 85.2838 0.0005

5018 0.0014 0.0009 68.4629 0.0005

5019 0.0015 0.0009 67.5814 0.0005

5020 0.0016 0.0009 68.4335 0.0005

5021 0.0019 0.0010 60.0414 0.0005

Confidence level: 95%

A point’s geometrical view of the network greatly affects its coordinate accuracy. In general,

stations from which observations to monitored points are made should be situated so that

they are surrounded – as much as possible – by other network points. This was done by

positioning the secondary control points so that they are viewed with the widest range of

directions possible at free stations 4004, 4005 and 4007.


6.2 Monitoring a Buried Water Main

An existing water main is buried close to gravel preload piles for highway construction.

There is a concern for the stability of the buried concrete pipe. To prepare for monitoring,

the pipe is excavated and points are attached to the top of the pipe. Vertical, capped, PVC

access pipes allow surveyors to set targets over these monitoring points. The water main is

monitored weekly to monthly, depending on current trends resulting from analysis of

previous epochs. A Leica TCA2003 total station is used to make measurements to determine

the horizontal positions at each epoch. A Leica DNA03 digital level is used to determine

elevations of the monitored points. Only horizontal deformation will be analyzed here.

To determine realistic target centring errors, the approximate elevations of both the

underground monitoring points and the prisms set above them are determined from level

runs, and trigonometric total station observations, respectively. Using the trigonometric data

from the dates 2007-11-27, 2008-08-19, 2008-08-25, and 2008-11-18, the average elevations

of the targets are computed. The largest range of elevations was 0.54 m for point 1018.

However, all the rest agreed within 0.30 m. The typical heights of targets over all the

monitored points are computed by subtracting the baseline leveled elevations of the

underground points from the average trigonometric target elevation. These heights are then

entered into a Heights Rules file as input for the utility “TRA Heights Updater.” The heights

of targets are substituted after running the utility “TRA Mean.” All the instrument and target

heights are manually checked to confirm that they are realistic.

Before deformation analysis can be performed, the network of total station observations at

each epoch is adjusted with minimal constraints to check the internal consistency of the

observations. If any observations fail the local tests, the worst offender – the “outlier” – is

removed from the network, and the remaining observations are re-adjusted. This continues

iteratively – under the control of the analyst, and not automatically, because human

interpretation is usually necessary – until all local tests pass. This has been done for five

observation epochs. The collection dates of the data are 2008-08-06, 2008-08-27, 2008-09-

09, 2008-09-23, and 2008-10-21. The overall measurement scheme is not the same for all


these epochs, so different minimally constrained datums may be applied. For epochs 2008-

08-27 and 2008-10-21, the coordinates of point 517 are held fixed and the azimuth from

point 517 to point 518 is constrained to 122°46’00” ± 0.5”. For the remaining epochs, point

517 is held fixed, but the azimuth from point 516 to point 517 is constrained to 263°37’05” ±

0.1”.

Figures 6.4, 6.5, 6.6, 6.7, and 6.8 give plan views of the network geometry for epochs 08-06,

08-27, 09-09, 09-23, and 10-21, respectively. Table 6.3 summarizes the results of the

minimally constrained adjustments of each epoch after outlier are removed. Note the

similarity in the variance factor for all five epochs.

Table 6.3: Statistical Summary for Minimally Constrained Adjustment of all Epochs

Epoch (2008-MM-DD) 08-06 08-27 09-09 09-23 10-21

Number of observations 171 120 160 158 93

Number of parameters 69 37 80 80 36

Number of degrees of freedom 102 83 80 78 57

Variance factor of unit weight 0.263 0.268 0.297 0.239 0.247

A description of the site and the monumentation is in order. The area surrounding the

construction site was originally boggy, before preloading began. Points 514, 515, 516, 517,

518, 1435, and 1436 are brass cap monuments installed in concrete blocks set at ground

level. Points 1001 through 1027 are object points fixed to the buried water main. The

remaining points are less likely to be stable because they are located in the area possibly

affected by preloading. Points 650, 651, 652, 9000, and 9002 are nails in asphalt on the

highway shoulders and median. Point 9001 is a wooden traverse hub set in rocks which may

be disturbed by trucks hauling gravel. For our purposes, the hub needs only to remain stable

during the duration of each survey, which is one evening. Points 1 and 6 are forced centring

pillars. The nature of the ground contributes to the instability of the pillars; changes in the

level of the water table may affect these points.


Figure 6.4: Geometry of a Water Main Deformation Monitoring Network

at Epoch 2008-08-06



at Epoch 2008-08-27

The size and orientation of the error ellipses depends on the choice of datum. Error ellipses

“grow” away from the fixed points according to the laws of random error propagation. For

instance, compare the size of the ellipses for points 1435 and 9002 in Figure 6.5. Point 9002

is further away and its positioning is also more susceptible to error.



at Epoch 2008-09-09



at Epoch 2008-09-23



at Epoch 2008-10-21


An example of the outlier removal process, as performed on epoch 2008-08-27 data, is

presented in Appendix D. The first time the adjustment is performed, the variance factor is

0.42505. After two outliers are removed, one at a time, the variance factor becomes 0.26832.

The low variance factor indicates that the initial estimation of the accuracies of the

observations are pessimistic, and also that the measurements are most likely of high quality.

The results of the outlier removal process applied to each epoch are two Network

Observations files, one containing the observations and the other, a list of outlier

observations to exclude.

First, as a relatively simple example, let us examine network deformation between the epochs

2008-08-27 and 2008-10-21. The settings and some intermediate results and their discussion

are presented in Appendix E. Refer to Figures 6.5 and 6.8 for views of the network geometry

for each epoch. It is helpful to view the minimally constrained network geometry plots,

because these give an overall picture of the relative sizes and shapes of the error ellipses

generated for each network based on the datum choice. A poor choice of datum may result in

distorted analysis results. Ideally, the error ellipses for both networks should be almost

circular. Circular error ellipses will enable the possibility of detecting equally small

displacements of their respective points in any direction. When additional stable points are

identified and held fixed, the error ellipses shrink.

This analysis should be placed in its context. Comparison of two epochs of an observational

network is not always conclusive. The most important analysis activity takes into account

trends over a series of epochs.

Initially, a minimally constrained datum is defined, which holds fixed the X and Y

coordinates of point 517, and the azimuth from point 517 to point 518 is assigned a value of

122°46’00” and a standard deviation of 0.5”. Table 6.4 summarizes the results of the

adjustment of the two epochs together.


Table 6.4: Statistical Summary for Minimally Constrained Adjustment of

Epochs 2008-08-27 and 2008-10-21

Both Epochs Test Result

Number of iterations 2




Variance factor of unit weight 0.2596

Global test of variance factor 109.1369 < 36.3391 < 174.6478 Fails on low end

Goodness of fit test 1.1506 < 0.8950 Fails

Local tests 3.5044 < 3.6807 All pass The global congruency test (49.27 < 1.57) fails at the 95% confidence level, so the network is

suspected of geometrical deformation. The displacement field is depicted in Figure 6.9.

Points 6, 1008, 9001 and 9002 are not stable. The displacements and local congruency test

statistics for all points are shown in Table 6.5.

Figure 6.9: Displacement Field Between Epochs 2008-08-27 and 2008-10-21

with Minimal Constraint Datum

Table 6.5: Local Congruency Test Results for Minimally Constrained Adjustment of

Epochs 2008-08-27 and 2008-10-21


9.71

Point Amount Azimuth Test Displacement

Number (m) (D.MMSS) Statistic Significant?

1 0.004 0.0000 9.55

6 0.003 15.1518 32.58 Yes

518 0.001 303.4124 7.13

650 0.001 171.5212 1.16

651 0.001 201.4805 5.20

652 0.001 246.0215 3.33

1001 0.004 203.3746 4.36

1002 0.002 240.1518 1.03

1003 0.001 218.3935 0.15

1004 0.002 236.5834 2.18

1008 0.008 346.3823 26.23 Yes

9001 0.071 28.0039 1024.87 Yes

9002 0.008 22.5001 15.44 Yes

Displacement

Upper Critical Value :


Based on these results, points 1, 517, 518, 650, 651, 652, and 1001 through 1004 can now be

considered stable. However, when the adjustment is performed, an outlier observation is

reported, which indicates that an unstable point (point 1) has been incorrectly considered

stable. The mistake is corrected, all the truly stable points are held fixed in both X and Y,

and the azimuth pseudo observation is removed. Table 6.6 summarizes the results of the

adjustment.


Table 6.6: Statistical Summary for Over-Constrained Adjustment of

Epochs 2008-08-27 and 2008-10-21

Both Epochs Test Result






Global test of variance factor 135.7900 < 44.4814 < 207.9954 Fails on low end

Goodness of fit test 1.0219 < 0.8950 Fails

Local tests 3.3385 < 3.6784 All pass

The global congruency test (812.68 < 2.04) fails at the 95% confidence level, so the network

is suspected of geometrical deformation. The final displacement field is depicted in Figure

6.10. Only points 1, 6, 1008, 9001 and 9002 are not stable. All other points are fixed.


with Over-Constrained Datum


Point 9001 is not shown because the large displacement of this point is expected and is not

representative of ground displacement. During the time interval between these two surveys,

the hub was damaged so a replacement hub was reinstalled by the author in the close vicinity.

The displacements and local congruency test statistics for all the unstable points are shown in

Table 6.7.

Table 6.7: Local Congruency Test Results for Over-Constrained Adjustment of

Epochs 2008-08-27 and 2008-10-21

9.71



1 0.004 4.0508 50.80 Yes

6 0.004 18.5310 225.07 Yes

1008 0.009 348.5637 42.06 Yes

9001 0.072 27.5950 5264.25 Yes

9002 0.009 23.2209 106.57 Yes

Displacement

Upper Critical Value :


The results of the analysis show that object point 1008 has been displaced significantly

during the interval between the surveys. The coordinate differences for this point of 9 mm in

a northerly direction (azimuth 349°) should be checked independently by analysis of

additional epochs, before those concerned about possible deformation of the pipe become

worried about its integrity. Further analysis of this specific problem may be performed by

considering the data collected on dates close to 2008-08-27 and 2008-10-21. The pillar

points 1 and 6 also show significant displacement between the epochs. Perhaps the area in

which they are installed – originally a marshy meadow – has something to do with the

inconsistencies of these points with respect to those installed in asphalt or concrete on or near

the existing highway (the 500 and 600 series points). Traverse point 9002 may also have

moved. We can be more sure of these results after analysis of additional pairs of epochs are

performed. The surveys which extend past points 9001 and 9002 and connect to another

group of stable control points will provide more answers. These two points are only


intermediate traverse points in the overall monitoring scheme, and are located in the

suspected unstable region. Since only two epochs have been analyzed, the overall

displacement trends have not been discovered. Also, the repeatability of the surveys has not

been confirmed; computation of probable survey errors would require knowledge of the

displacement trends. If the surveys can be confirmed to be more accurate than originally

expected, the initial accuracies of the observations should be made more optimistic, by

reducing the standard deviations of the various centring errors.

Analyzing additional epochs of observation networks will provide checks on repeatability of

positioning and allow elimination of outlier survey data, with respect to displacement trends.

Outliers, in this context, are blunders or systematic errors. Comparisons of four consecutive

pairs of epochs will be presented in chronological order, then the significant results will be

discussed.

When analyzing epochs where the network configuration differs, a minimal constraint datum

is chosen which would constrain each epoch even if each were adjusted separately. In all

cases, point 517 is held fixed. For the analysis of deformation of the network between

epochs 2008-09-09 and 2008-09-23, the azimuth from point 516 to point 517 is constrained

to 263°37’05” ± 0.1”. For the other three analyses, the azimuth from point 517 to point 518

is constrained to 122°46’00” ± 0.5”. The confidence level is 95% in all cases.


Between epochs 2008-08-06 and 2008-08-27, points 517 and 518 are held fixed. Table 6.8

summarizes the results of the adjustment.


Epochs 2008-08-06 and 2008-08-27

Both Epochs





Table 6.9 gives the results of the global and local congruency tests of the free common

points, along with displacements and their significance.

Table 6.9: Local Congruency Test Results for

Epochs 2008-08-06 to 2008-08-27

10.96 < 2.63

8.28



1 0.004 31.5158 10.70 Yes

6 0.002 105.5643 14.89 Yes

1008 0.005 194.5553 7.29

Displacement

Upper Critical Value for Local Test :


Global Congruency Test:


The displacement field is depicted in Figure 6.11.




Between epochs 2008-08-27 and 2008-09-09, points 517, 1, 650 and 651 are held fixed.

Table 6.10 summarizes the results of the adjustment.


Epochs 2008-08-27 and 2008-09-09

Both Epochs








Epochs 2008-08-27 to 2008-09-09

8.65 < 1.70

10.54



6 0.001 21.0215 29.44 Yes

518 0.002 302.5419 12.09 Yes

1001 0.001 68.1155 0.44

1002 0.001 70.0101 0.54

1003 0.002 98.3151 1.46

1004 0.003 218.3935 2.58

1008 0.007 14.1414 25.14 Yes

9001 0.003 33.4124 20.61 Yes

9002 0.004 27.4927 37.48 Yes

Displacement





Between epochs 2008-09-09 and 2008-09-23, points 517, 514, 515, 516, 518, 605, 9000,

9002, 650, and 1 are held fixed. Table 6.12 summarizes the results of the adjustment.


Epochs 2008-09-09 and 2008-09-23

Both Epochs









Epochs 2008-09-09 to 2008-09-23

1.90 < 1.41

12.46



6 0.002 280.3711 17.34 Yes

1001 0.004 205.5632 4.22

1002 0.002 227.0716 0.93

1003 0.001 327.5941 0.22

1004 0.003 345.3147 2.51

1006 0.001 260.3216 0.61

1008 0.003 265.5452 3.03

1009 0.004 272.4335 7.67

1011 0.003 68.3308 2.76

1012 0.000 315.0000 0.02

1013 0.002 191.1836 0.68

1014 0.001 219.4820 0.19

1015 0.002 172.3407 1.51

1016 0.002 39.4820 0.69

1017 0.002 190.4704 1.18

1018 0.003 64.1350 3.46

1019 0.005 256.4534 7.64

1020 0.001 270.0000 0.28

1021 0.007 195.5643 13.06 Yes

1022 0.004 19.5859 4.08

1024 0.001 106.4157 0.29

1026 0.005 208.4839 5.98

1027 0.004 316.0451 3.55

Displacement





Between epochs 2008-09-23 and 2008-10-21, points 517, 518, 650 and 9002 are held fixed.

Table 6.14 summarizes the results of the adjustment.


Epochs 2008-09-23 and 2008-10-21

Both Epochs








Epochs 2008-09-23 to 2008-10-21

6.18 < 1.70

10.57



1 0.002 0.0000 26.38 Yes

6 0.003 48.0046 58.60 Yes

1001 0.001 281.1836 0.08

1002 0.001 270.0000 0.36

1003 0.002 238.3414 1.15

1004 0.003 168.4124 1.89

1006 0.003 29.1456 3.02

1008 0.002 317.2922 1.16

1009 0.000 326.1836 0.06

Displacement





From the analysis so far, the position of point 1008 on 2008-08-27 is anomalous. Between

epochs 2008-08-06 and 2008-08-27, the displacement of the point was 5 mm at an azimuth of

195° and insignificant according to the local congruency test (7.29 < 8.28). Between epochs

2008-08-27 and 2008-09-09, the displacement of the point was 7 mm at an azimuth of 14°

and significant (25.14 < 10.54). These “displacements” are nearly equal and opposite. These

results imply that there was significant survey error in positioning the point on 2008-08-27.

Now, if we skip over this epoch, and analyze the deformation between epochs 2008-08-06

and 2008-09-09, we reveal the following results. The variance factor for the adjustment is

0.29028. Point 1008 is displaced 2 mm at an azimuth of 233°, insignificant according to the

local congruency test (1.48 < 12.16). For this interval, no object points exhibit significant

displacement, but the control points 518, 605, and 9000 do. We are concerned only with

displacement of the object points; control point stability is tested for every analyzed interval

as has been demonstrated. There is now another instance of significant object point

displacement which could be investigated by analyzing survey data observed after 2008-10-

21. Between epochs 2008-09-09 and 2008-09-23, the displacement of point 1021 (7 mm,

196°) is reported as barely significant (13.06 < 12.46). I would suspect that since all the

other points on the water main – both east and west of this point – were not displaced during

that interval, this point most likely has not been displaced either. In conclusion, the water

main was most likely not deforming during the interval between 2008-08-06 and 2008-10-21.


6.3 Monitoring Dangerous Trees

In a forest, some trees are suspected of leaning and becoming dangerous to hikers, so a

monitoring survey is required. Points near the tree tops and bases are marked by nails set in

the trunk. Control monuments are 3’ X ½” rebar at ground level, with the point marked by a

punch mark. Measurements are made with a Leica TCA 2003 total station. The trees sway

in the wind up to 2 cm laterally, so additional errors in observations to these points are

expected. Therefore coordinates resulting from each survey will have additional uncertainty,

as will coordinate differences. As a result, the smallest amount of displacement detectable

will be larger than if the monitored points were on the ground. This error is propagated

randomly in preparation for least squares adjustment by assigning ± 1 cm of target centring

standard error for observations to monitored points. The standard error of target centring is

derived from the maximum amount the trees may move divided by 2, which is approximately

1.96, or the critical value from the normal distribution at 95 % confidence. A smaller error is

expected in the coordinates of points near the tree bases. Target centring standard error of ±

3 mm is assigned. When the trees sway, their vertical movement is negligible. The vertical

centring of all targets is set to ± 3 mm at standard confidence. For the standard errors in

instrument centring and for target centring on points on the ground, ± 0.5 mm per metre of

height above the point is assumed. There are two epochs of survey observations, dated 2006-

01-19 (epoch 0) and 2007-10-16 (epoch 1). The data sets presented have been reduced to a

subset of their original size, to allow a more focused analysis of a smaller area. Refer to

Appendix F for the settings, input data, and some intermediate results. Points 37, 721, and

723 are monitored points near the bottoms of trees. Point 731 is a monitored point near a

tree’s top. Points 1, 2, 3, 64, and 99 are control points. Note that points 101 and 102

(surveyed at epoch 1) are free station points and so are not physical points on the ground.


Figure 6.15 gives a plan view of the network geometry for epoch 0.

Figure 6.15: Geometry of Tree Deformation Monitoring Network for Epoch 0


Figure 6.16 gives a plan view of the network geometry for epoch 1.

Figure 6.16: Geometry of Tree Deformation Monitoring Network for Epoch 1

Minimal constraints adjustments are performed with the X, Y, and Z coordinates of point 1

fixed and the azimuth from point 1 to point 2 is constrained to 16°00’02” ± 1”. The results of

these two adjustments are shown in Table 6.16.


Table 6.16: Tree Deformation Monitoring Network –

Statistics for Minimal Constraint Adjustments of Epochs 0 and 1

Epoch 0 Epoch 1

Number of iterations 2 2

Number of observations 58 40

Number of parameters 30 33

Number of degrees of freedom 28 7

Variance factor of unit weight 0.4674 0.5227

The confidence level for all the tests is 95%. The global test – the Chi squared test of the

variance factor – fails on the low end for epoch 0 (15.3079 < 13.0884 < 44.4608) but passes

for epoch 1 (1.6899 < 3.6590 < 16.0128). No blunders are present in the observations. For

both epochs, the local tests of standardized residuals pass every observation for both epochs.

The goodness of fit test for normality of standardized residuals fails for epoch 0 but passes

for epoch 1. The variance factors are compatible because the two-tailed variance ratio test

(0.3595 < 0.8943 < 4.3775) passes. A minimally constrained adjustment and local

congruency testing identifies the points 1, 37, 64, and 99 as being stable in three dimensions.

These four points are fixed in the X, Y, Z axes. The statistical summary of the final

adjustment of the observations from both epochs combined together is shown in Table 6.17.


Statistics for Constrained Adjustment of Epochs 0 and 1 Combined

Epochs 0 and 1






At a confidence level of 95%, the global test fails on the lower end (33.1618 < 23.8073 <

72.6160), all the local tests pass, and the goodness of fit test fails (1.0046 < 0.8950). The


horizontal global congruency test fails (24.06 < 2.10). Horizontally, points 3 and 731 fail the

local congruency test. Points 2, 3, 723 and 731 fail the vertical displacement significance

test. The final results are shown in Table 6.18.


Final Local Congruency Test Results

Point Amount Azimuth Test Displacement Interval

Number (m) (D.MMSS) Statistic (m) (m)

2 0.004 352.3015 8.47 -0.004 ±0.004

3 0.007 261.2304 34.36 -0.003 ±0.003

721 0.009 164.4114 7.22 0.000 ±0.005

723 0.008 136.0123 5.61 0.007 ±0.005

731 0.105 156.0534 112.8 -0.014 ±0.012


Upper Critical Value = 9.64

Displacement

VerticalHorizontal

Final results indicate that control point 3 may have been displaced 7 mm horizontally. Point

731, near a tree top, exhibits displacement of 10.5 cm in a direction within 9 degrees of the

direction of the coordinate difference of the tree base, point 721. This direction is, logically,

downhill. These results indicate that the tree with points 721 and 731 fixed to it was leaning

downhill more in October 2007 than it was in January 2006.


Figure 6.17 shows the network’s displacement field from epoch 0 to epoch 1.

Figure 6.17: Tree Deformation Monitoring Network –

Displacement Field from Epoch 0 to Epoch 1

Note that points 1 and 2 are not included in the view so that greater deformation detail can be

seen.


7. Conclusions

Preanalysis, least squares adjustment, and congruency testing should be performed as part of

a rigorous scheme for deformation monitoring. Preanalysis ensures that the methods are

capable of detecting small enough changes in the deformable body. Congruency testing

allows for control stability testing and helps us to report only significant displacements.

Computing a survey error budget is the vital first step in deformation monitoring. An

example has been presented in section 6.1, which was used as the tolerance for the

preanalysis of a high-rise building monitoring network. Preanalysis can be a valuable tool

which tells us if we can achieve accuracy tolerances. It can also be used to improve the

design of an existing survey network, so that either higher accuracies are achieved or less

field work is required for their execution. In practice, survey networks range in size from

just a few metres across to global proportions. Survey methods which are ideal in the sense

that accuracy, time, and cost are optimized differ, depending mainly on the size of the

network. Preanalysis allows a surveyor to experiment with different measurement schemes

without leaving the office: approximate station locations and proposed measurements are the

only requirements

It is important to incorporate tests for reference point stability into every monitoring

measurement scheme. Without direct measurements between reference points, it is generally

not possible to confidently identify stable points. Great care should be taken in making

judgments about which points are stable and which are not. One should not assume points

are completely stable based merely on the rigorous monumentation method employed.

Deforming structures do so due to incredible forces in the earth underfoot, and these forces

may cause large areas of land to shift in interesting and, usually, unpredictable ways. In

addition to the congruency testing method, the post adjustment tests (global, local, and

goodness of fit), can also be useful in testing whether individual points are stable between

epochs. It is also important to consider trends of more than (the minimal) two epochs so that

serious surveying blunders can be detected are not reported as deformations. The goals of


this project have been met; the method employed is rigorous and practical. However, further

software development is planned.

An interactive graphical user interface (front end) should be constructed for Survey Suite.

This will increase the speed with which an analyst can perform computations, and will also

reduce the initial learning curve. The utilities will each be made into functions of this single

application. By using iteration, software-analyst interaction, and possibly automation,

deformation analysis will be made easier and faster.

Raw data conversion and rigorous error propagation should be implemented for digital level

observations, since many deformation monitoring campaigns are concerned mainly with

subsidence.

In error propagation, observations are assumed to be the averaged result of observations on

both faces. If an observation is made on one face only, this should be taken into account.

Also, the system for specifying the random observation errors should be simplified.

Preanalysis should work interactively, so that one may manipulate the network design via a

graphical interface (with orthogonal and perspective views) and almost instantly be presented

with the results important to the particular situation.

Least squares reporting should include, broken down into each class of observation,

normality tests and histograms of standardized residuals, a posteriori variance factors, and

maximum corrections to observations.


8. References

Aguilera, D. G, Lahoz, J. G., Serrano, J. A. S. (2007). First Experiences With the

Deformation Analysis of a Large Dam Combining Laserscanning and High-Accuracy

Surveying. XXI International CIPA Symposium, 1-6 October 2007, Athens, Greece.

Baarda, W. (1968). A testing procedure for use in geodetic networks. Netherlands Geodetic

Commission, Publications on Geodesy, New Series 2(5).

Bin Setan, H. (1995). Design and Implementation of Computer Programs for Analysis and

Detection of Spatial Deformation. Buletin Ukur, 6(2), 84-98.

�epek, A. (n.d.). GNU Gama. Retrieved December 16, 2008 from

http://www.gnu.org/software/gama/

Chen, Y. Q., (1983). Analysis of Deformation Surveys - A Generalized Method. Department

of Geodesy and Geomatics Engineering, Technical Report No. 94. Fredericton, N.B.:

UNB.

Chen, Y. Q., Chrzanowski, A. (1986). An Overview of the Physical Interpretation of

Deformation Measurements. Deformation Measurements Workshop. Cambridge,

Massachusetts: MIT.

Chen, Y. Q., Chrzanowski, A., Secord, J. M. (1990). A strategy for the analysis of the

stability of reference points in deformation surveys. Canadian Institute of Surveying

and Mapping Journal, 44(2), 141-149.

Chrzanowski, A., Chen, Y. Q., Secord, J. M. (1986). Geometrical Analysis of Deformation

Surveys. Deformation Measurements Workshop. Cambridge, Massachusetts: MIT.

Eichhorn, A. (2007). Tasks and Newest Trends in Geodetic Deformation Analysis: A

Tutorial. Institute for Geodesy and Geophysics, Department of Engineering Geodesy.

Vienna, Austria: Vienna University of Technology.

Erol, S., Erol, B., Ayan, T., 2004. A General Review of the Deformation Monitoring

Techniques and a Case Study: Analysing Deformations Using GPS/Levelling. Civil

Engineering Faculty, Geodesy Division. International Society for Photogrammetry

and Remote Sensing. Commission VII, WG VII/5. Istanbul, Turkey: Istanbul Technical

University.


High-precision deformation monitoring plays a critical role in New York subway

construction project. (2007, March 1). Point of Beginning Magazine.

Lawrence, C. (2005). MATH 4511: Statistics for Geomatics. Lecture Notes. Burnaby, B.C.:

BCIT.

Leica Geosystems AG. (2004). Leica TCA1800 • TCA2003 • TC2003: High-performance

total station robust, precise and universally useful. Heerbrugg, Switzerland: Author.

Retrieved March 13, 2009, from http://www.leica-geosystems.com/

common/shared/downloads/inc/downloader.asp?id=3030

Leica Geosystems AG. (2006). Leica DNA Digital Levels: Advantages that move you ahead.

Heerbrugg, Switzerland: Author. Retrieved March 13, 2009, from http://www.leica-

geosystems.com/common/shared/downloads/inc/downloader.asp?

id=1308

Leica Geosystems AG. (2008). Leica Geosystems Original Accessories Program 2008/2009.

Heerbrugg, Switzerland: Author. Retrieved March 13, 2009, from http://www.leica-

geosystems.com/common/shared/downloads/inc/downloader.asp?

id=6335

Mikhail, E. M.. (1976). Observations and Least Squares. Washington, D.C.: University Press

of America, Inc.

Ogundare, J. (2008a). GEOM 8353: Special Topics in Adjustments. Lecture Notes. Burnaby,

B.C.: BCIT.

Ogundare, J. (2008b). GEOM 8353: Advanced Topics in Precision Survey. Lecture Notes.

Burnaby, B.C.: BCIT.

Pope, A. J. (1976). The Statistics of Residuals and the Detection of Outliers. NOAA

Technical Report, NOS 65 NGS 1. Washington, D.C.: U.S. Department of Commerce.

Smoltczyk, U. (2002). Geotechnical Engineering Handbook. Darmstadt, Germany: Betz-

Druck GmbH.

State of New Jersey Department of Transportation. (2007). Control Surveys and State Plane

Coordinate Systems. In Survey Manual. Retrieved March 1, 2009 from

http://www.state.nj.us/transportation/eng/documents/survey/Chapter2.shtm

Sütti, J., Török, C. (1996). Testing 3D displacement vectors by confidence ellipsoids. Acta

Montanistica Slovaca Ro�ník 1(4), 301-310.


US Army Corps of Engineers. (2002). Structural Deformation Surveying. Engineering and

Design Manual EM 1110-2-1009. Washington, D.C.: Author.

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements A-1

Appendix A. Software Implementation

The suite of applications are written purely in C++, a powerful, object-oriented, compiled

programming language. The Bloodshed Dev-C++ Integrated Development Environment is

used for compilation and linking of the 750 kilobytes of source code. The applications are

currently all 32-bit Windows console applications, that is, no graphical interfaces have yet

been designed.

In software engineering, the goal is to create a well-organized, readable, maintainable,

reusable, purely orthogonal implementation with minimal redundancy. (Orthogonality is the

condition that a statement does only what is expected and causes no side effects.) When

managing a software development project of this size, it is beneficial to employ both a set of

coding conventions and various common programming paradigms. For example, proper use

of abstraction through object oriented design allows for compression (more meaning

conveyed with less code) which can reduce maintenance work load by shrinking the code

base. Moreover, generic programming, for example the use of data structures and algorithms

from the STL, allows one to ignore some low-level details, and concentrate rather on the

high-level tasks at hand, resulting in a stable, reliable, and consistent code.

Code reuse is a serious consideration in controlling the amount of new source code which

must be constructed. Some components of third party open source software were reused in

implementing this project, including the Matrix TCL Lite C++ template class v1.13,

statistical distributions from the Boost C++ library v1.36.0, the KStest function from GNU

Gama v1.9.05 (�epek, A., 2008), and libplotter v.2.4.1 (part of the GNU Plotting Utilities

library for vector graphics and data plotting). Internal reuse (within this project) is also

employed, by creation of shared general purpose utility classes. This produces the added

benefits of consistently functioning applications, and modular, easy to upgrade code.

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements B-1

Appendix B. Accuracy of Instruments

The accuracies of the instrumentation used for data collection, as quoted by the

manufacturer, follow. These accuracies are used as input for error propagation in the

computations in chapter 6. It should be noted that all the images referenced by URLs in the

foot notes were retrieved on February 24, 2009.

With the Leica DNA03 digital level (see Figure A.1), high precision height differences can

be observed, and first order leveling can be achieved. The standard deviation of height

difference measurement per km double-run, in accordance with ISO 17123-2, is ± 0.3 mm

when using invar staffs and electronic measurements. The time required for a single

measurement is typically 3 seconds, but a close measurement (with a range less than 5 m)

may take longer. With standard staffs, the accuracy falls to ± 1.0 mm. Using the level

optically, the accuracy is degraded still further, to ± 2.0 mm. The telescope magnification is

24X, and the shortest possible focussing length is 0.6 m (for optical measurement) or 1.8 m

(for electronic measurement). (Leica Geosystems AG, 2006).

The accuracy (standard deviation) of the horizontal and vertical circles of the TCA2003, in

accordance with ISO 17123-3, is ± 0.5”. Compensator setting accuracy is ± 0.3”, achieved

with an electronic dual axis compensator. Accuracy (standard deviation) of distance

measurement by invisible infrared coaxial laser, in standard mode, in accordance with ISO

17123-4 is ± 1 mm ± 1 ppm. A phase measurement time of 3.0 s is required. The telescope

magnification is 30X, and the shortest possible focussing length is 1.7 m. The centring

accuracy, by laser plummet, is ± 1.0 mm at height of 1.5 m. See Figure A.2 for photos of this

total station. (Leica Geosystems AG, 2004).

The centre of the Leica GPR121 prism (see Figure A.3) has no offset from the rotation axis

of the holder. This means no error is introduced by misalignment of the prism with respect to

the total station. This “precision circular prism” has an anti-reflection coating to cut down on

glare. It is pre-mounted in a metal holder and has a removable target plate. The centring


accuracy is ± 1.0 mm. The maximum possible range is 3500 m (in infra red mode). (Leica

Geosystems AG, 2008).

The Leica GZR3 precise target carrier (see Figure A.4) allows targets to be centred almost

perfectly over well-defined survey marks. The standard deviation of constant centring error

is ± 0.3 mm. The height dependent centring error caused by the optical plummet is 0.5 mm

for every 1.5 m of height above the point. The plate bubble is accurate to 2” per 2 mm

graduation. (Leica Geosystems AG, 2008).

The Leica GLS14 mini reflector pole (see Figure A.5) allows almost exact positioning of the

reflector over a punched survey mark. It provides a prism height of 0.2 m, when used with

the GPR121 prism holder combination. (Leica Geosystems AG, 2008). No accuracy is

quoted, but the author has empirically determined the centring repeatability of this system to

be within ± 0.5 mm. The method was to replace the point of the pole in a punch mark 20 m

distant from the total station, rotate the prism around the pole 90° for each of four

measurements, manually sight the prism, and measure the distance, while staking out the

point by coordinates, to allow immediate comparison of coordinate differences. Because of

this result, the centring accuracy of the Leica GPR121 prism will be assumed to be ± 0.5 mm

for error propagation.


a.

b.

Figure A.1: Leica DNA03 Digital Level and Leica GPCL2 Invar Bar Code Level Staff.

a. Keypad and interface display.1 b. Front view.2 c. Invar rod (2m length).3

1 http://leica.loyola.com/products/levels/images/dna_lg.jpg 2 http://img.directindustry.com/images_di/photo-g/digital-level-50793.jpg 3 http://www.northernsurveysupply.com/AccessoriesCatalogue/LevellingStaffs/StaffImages/Page1/

GPCL2InvarStaffPage1.jpg

c.


a. b.

Figure A.2: Leica TCA2003 Robust Precision Total Station.

a. Front view.4 b. Mounted on forced centring pillar for dam deformation monitoring.5

Figure A.3: Leica GPR121 All-in-one Prism with Holder, Prism, and Target Plate.6

4 http://engineeringsurveyor.com/images/tca2003.jpg 5 Aguilera et al., 2007 6 http://leica.loyola.com/products/accessories/images/gpr121_lg.jpg


Figure A.4: Leica GZR3 Precise Target Carrier with Optical Plummet.

a. Side view. 7 b. Level bubble and scope.8

Figure A.5: Leica GLS14 Mini Reflector Pole.9

7 http://www.surveyequipment.com/shop/images/gzr3_precCarrier_01.jpg 8 http://www.iltopografo.com/grafic/gzr3.jpg 9 http://www.sisirl.com/images/GLS14.jpg

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements C-1

Appendix C. Preanalysis of a Network for Monitoring

High-rise Buildings

This is additional information to accompany the example of the preanalysis of a survey

network for monitoring deformation of high-rise buildings in section 6.1. Preanalysis

requires the applications TRA Simulator, TRA to Network, and Network Adjustment. Since

the three steps are performed consecutively each time the measurement scheme or network

geometry is changed, it is helpful to use a WindowsTM batch file; an example follows.

Preanalysis.bat

"TRA Simulator.exe"

"TRA to Network.exe"

"Network Adjustment.exe"

First the contents of the required specifications files are presented.

TRA Simulator.spec

Simulate <

Observation Scheme < scheme >

Default Height < 1.6 >

Coordinates < Initial Coordinates >

Export < network >

>

TRA to Network.spec

Centring Method <

ID < Mini Pogo >

Error < 2.5 >

Error Constant < 0.5 >

>

Centring Method <

ID < Fixed >

Error < 0 >

Error Constant < 0 >

>

Centring Method <

ID < Optical Plummet >

Error < 0.3333 >



>

Survey Instrument <

ID < TCA 2003 >

EDM < 1+1 >

Directional < 0.5 >

Compensator < 0.3 >

>

Measurement Scheme <

ID < Free to Mini >

Survey Instrument < TCA 2003 >

Sets < 1 >

Instrument <

Free Station < Yes >

Re-Level < No >

Re-Centre < No >

>

Target <

Centring < Mini Pogo >

Height Accuracy < 0.5 >

>

>


ID < Free to Monitor >

Like < Free to Mini >

Target <

Centring < Fixed >

Height Accuracy < 0 >

>

>


ID < Free to Tripod >

Like < Free to Mini >

Target <

Centring < Optical Plummet >


>

>

Observation Reduction RuleSet <

ID < Buildings >

Default <

Reduction < 2D >

Measurement Scheme < Free to Mini >

>

But <

to < 9000-9100 >


Reduction < 1D >

Measurement Scheme < Free to Mini >

>

But <

to < 300-399 >

Reduction < 2D >

Measurement Scheme < Free to Tripod >

>

But <

to < 5000-5999 >

Reduction < 3D >

Measurement Scheme < Free to Monitor >

>

>

Convert TRA to Network <

Input File < network >

Output File < network >

Reduction RuleSet < Buildings >

>

Network Adjustment.spec

Network Pre-Analysis <

Observations < network >


Datum < Datum >

Report Name < Simulation >

Plot Name < Simulation >

Show Plot < y >

>

The complete set of input data – coordinates, datum definition, and observation scheme – are

presented next.

Initial Coordinates.xyz

201 3325.2005 6516.9092 19.3

202 3332.4545 6510.3399 20.2

203 3340.0935 6510.3399 20.2

204 3346.8739 6514.9821 19.3

205 3325.5546 6582.7652 20.94

206 3329.845 6588.0588 21.92

207 3339.2948 6588.0025 21.87


208 3346.2986 6583.2448 20.7

300 3242.1837 6486.9926 18.934

301 3244.9161 6506.0399 19.174

302 3242.6991 6591.5626 22.542

303 3241.6657 6609.0557 22.975

305 3428.6163 6611.9477 20.681

307 3428.6651 6590.7745 20.424

308 3427.686 6507.9493 19.588

309 3428.3596 6487.9594 19.564

4000 3325.4062 6487.8772 19.2

4001 3348.6888 6487.4615 19.2

4002 3325.4057 6608.743 21

4003 3347.2606 6608.552 21

4004 3324.8187 6550.0608 20.3

4005 3346.6359 6549.8299 20.2

4006 3346.25 6570.74 20.3

4007 3324.86 6525.39 20.1

5000 3305.6158 6589.5473 24.3

5001 3322.9014 6586.2743 23

5002 3323.5808 6573.1414 23

5003 3323.5521 6558.3273 23

5004 3306.6488 6553.2412 23.1

5005 3308.1768 6547.0367 23.8

5006 3323.4482 6543.488 24

5007 3323.4416 6527.8269 24

5008 3323.439 6513.4874 24

5009 3306.1669 6510.4143 21.5

5010 3368.7503 6589.5321 24.3

5011 3348.1534 6586.9803 23

5012 3347.9912 6573.1685 23

5013 3348.1178 6557.6378 23

5014 3372.1232 6553.0237 23.2

5015 3366.2334 6546.7037 23.2

5016 3347.962 6544.0189 24

5017 3347.9235 6534.1308 24

5018 3347.9683 6523.3978 24

5019 3352.0657 6519.8101 24

5020 3352.2165 6512.8259 24

5021 3371.697 6510.4362 22

9000 3345.5911 6592.2384 20.9

9001 3324.0314 6592.3512 21.08

9002 3347 6510 19.3

9025 3347.7349 6538.5198 19.96

Datum.fix

300 ! ! ?

301 ! ! ?


302 ! ! ?

303 ! ! ?

305 ! ! ?

307 ! ! ?

308 ! ! ?

309 ! ! ?

9000 ? ? !

9001 ? ? !

9002 ? ? !

9025 ? ? !

scheme.os

AT 4000 1.6

9002 0.2

300 1.6

301 1.6

308 1.6

309 1.6

201 0.2

202 0.2

203 0.2

204 0.2

5009 0

5021 0

5018 0

5019 0

5020 0

AT 4001 1.6

9002 0.2

300 1.6

301 1.6

308 1.6

309 1.6

201 0.2

202 0.2

203 0.2

204 0.2

5009 0

5021 0

5007 0

5008 0

5006 0

AT 4002 1.6

9001 0.2

302 1.6


303 1.6

305 1.6

307 1.6

205 0.2

206 0.2

207 0.2

208 0.2

5000 0

5010 0

5011 0

5012 0

AT 4003 1.6

9000 0.2

302 1.6

303 1.6

305 1.6

307 1.6

205 0.2

206 0.2

207 0.2

208 0.2

5000 0

5010 0

5001 0

5002 0

5003 0

AT 4004 1.6

9025 0.2

201 0.2

202 0.2

203 0.2

204 0.2

205 0.2

206 0.2

207 0.2

208 0.2

5014 0

5015 0

5004 0

5005 0

5011 0

5012 0

5013 0

5016 0

5017 0


AT 4005 1.6

9025 0.2

201 0.2

202 0.2

203 0.2

204 0.2

205 0.2

206 0.2

207 0.2

208 0.2

5014 0

5015 0

5004 0

5005 0

5006 0

5007 0

5008 0

5003 0

5001 0

5002 0

AT 4007 1.6

9002 0.2

201 0.2

202 0.2

203 0.2

204 0.2

205 0.2

206 0.2

207 0.2

208 0.2

5013 0

5016 0

5017 0

5018 0

5019 0

5020 0


For demonstrative purposes, part of the intermediate data – the first setup of both the TRA

and network observations – are presented.

network.tra


OCC 4000 1.600 CTRL

BS 9002 0.200 44.18242 92.24286 30.9419 .000 TH

IS 300 1.600 269.23276 90.10592 83.2276 .000 TH

IS 301 1.600 282.42572 90.01050 82.5139 .000 TH

IS 308 1.600 78.53491 89.47122 104.2315 .000 TH

IS 309 1.600 89.57153 89.47507 102.9541 .000 TH

IS 201 0.200 359.35386 92.33498 29.0618 .000 TH

IS 202 0.200 17.25145 90.58242 23.5459 .000 TH

IS 203 0.200 33.10436 90.51140 26.8412 .000 TH

IS 204 0.200 38.22481 92.09114 34.6010 .000 TH

IS 5009 0.000 319.30487 88.38483 29.6405 .000 TH

IS 5021 0.000 64.01067 88.39542 51.5091 .000 TH

IS 5018 0.000 32.25229 85.39047 42.2019 .000 TH

IS 5019 0.000 39.51258 85.36041 41.7214 .000 TH

IS 5020 0.000 47.03355 85.00228 36.7623 .000 TH

...


network.obs

* Meta data <

* Process <

* Name < TRA to Network >

* Version < 1.2 > >

* Input < network.tra >

* Output < network.obs >

* Date/Time < 2009 April 04 - 03:22:47 PM > >

4000-9002 VD 0.10000118 0.0005093

4000-300 HCR 269.23276 2.609

4000-300 HD 83.227175 0.00144

4000-301 HCR 282.42572 2.631

4000-301 HD 82.513896 0.00144

4000-308 HCR 78.53491 2.105

4000-308 HD 104.23078 0.001442

4000-309 HCR 89.57153 2.13

4000-309 HD 102.95346 0.001442

4000-201 HCR 359.35386 7.122

4000-201 HD 29.032709 0.001414

4000-202 HCR 17.25145 8.776

4000-202 HD 23.542502 0.001414

4000-203 HCR 33.10436 7.702

4000-203 HD 26.838219 0.001414

4000-204 HCR 38.22481 5.986

4000-204 HD 34.57657 0.001414

4000-5009 HCR 319.30487 0.5001

4000-5009 VCR 85.33421 0.807

4000-5009 SD 29.72136 0.0009972

4000-5021 HCR 64.01067 0.5

4000-5021 VCR 86.53155 0.6276

4000-5021 SD 51.571188 0.0009996

4000-5018 HCR 32.25229 0.5005

4000-5018 VCR 83.29331 0.8773

4000-5018 SD 42.353281 0.0009917

4000-5019 HCR 39.51258 0.5005

4000-5019 VCR 83.25042 0.8887

4000-5019 SD 41.874517 0.0009915

4000-5020 HCR 47.03355 0.5007

4000-5020 VCR 82.31589 1.041

4000-5020 SD 36.935981 0.0009886

...


Finally, the preanalysis report is presented.

=========================================================================================

Parametric Least Squares Network Pre-Analysis Report

=========================================================================================

=========================================================================================

Statistical Summary

=========================================================================================

Number of observations : 251

Number of parameters : 110

Number of degrees of freedom : 141

Number of each type of observations:

Coordinate Differences : 7

Horizontal Directions : 100

Vertical Directions : 44

Distances : 100

Number of instrument stations : 7

Number of observations from each station:

4000 : 32

4001 : 32

4002 : 29

4003 : 32

4004 : 44

4005 : 47

4007 : 35


=========================================================================================

Error Ellipses

Confidence level: 95.0%

=========================================================================================

Point Semi-Major Semi-Minor Azimuth Vertical

Number Axis Axis (D.MMSS) Interval

-----------------------------------------------------------------------------------------

201 0.0017 0.0016 133.06419

202 0.0017 0.0016 116.20015

203 0.0017 0.0016 95.39353

204 0.0017 0.0016 78.36527

205 0.0017 0.0016 50.36023

206 0.0017 0.0016 61.17547

207 0.0017 0.0016 84.42245

208 0.0017 0.0016 110.20220

4000 0.0013 0.0009 92.18510 0.0004

4001 0.0013 0.0008 85.35017 0.0004

4002 0.0013 0.0008 85.51402 0.0004

4003 0.0013 0.0008 91.47263 0.0004

4004 0.0011 0.0010 88.38005 0.0004

4005 0.0011 0.0010 87.48062 0.0004

4007 0.0014 0.0011 114.55458 0.0004

5000 0.0019 0.0009 62.09556 0.0005

5001 0.0015 0.0009 69.41576 0.0004

5002 0.0013 0.0010 74.44582 0.0004

5003 0.0013 0.0009 81.52077 0.0005

5004 0.0019 0.0012 96.44321 0.0005

5005 0.0019 0.0012 84.09131 0.0005

5006 0.0013 0.0009 98.42498 0.0005

5007 0.0013 0.0010 103.09009 0.0005

5008 0.0015 0.0009 111.44060 0.0005

5009 0.0019 0.0010 121.26259 0.0005

5010 0.0019 0.0010 117.15332 0.0005

5011 0.0015 0.0009 108.55280 0.0004

5012 0.0013 0.0010 102.44071 0.0004

5013 0.0015 0.0010 67.05325 0.0004

5014 0.0020 0.0013 83.58430 0.0005

5015 0.0019 0.0012 95.42590 0.0005

5016 0.0013 0.0010 81.20279 0.0005

5017 0.0014 0.0010 85.28379 0.0005

5018 0.0014 0.0009 68.46289 0.0005

5019 0.0015 0.0009 67.58135 0.0005

5020 0.0016 0.0009 68.43352 0.0005

5021 0.0019 0.0010 60.04138 0.0005

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements D-1

Appendix D. Deformation Analysis of a Buried Water Main -

Outlier Removal Example

This is additional information to accompany the example of the deformation analysis of a

buried water main in section 6.2. As an example, in which all the steps are described, outlier

removal is performed on the data from epoch 2008-08-27. The confidence level is 95%.

First the contents of the specifications files are shown.

GSI to Tagged TRA.spec

GSI to Tagged TRA <

Input File < data >

Duplicate Back Sight < n >

Has 10-20 Codes < y >

>

Tagged TRA to TRA.spec

Tagged TRA to TRA <

Input File < data >

>

TRA Mean.spec

Mean TRA <

Input File < data >

Tolerances <

HCR < 12 >

VCR < 12 >

SD < 1 >

>

>

TRA Heights Updater.spec

Update Heights <

Input File < data-meaned >

Use Rules < heights rules >

>

TRA to Network.spec

Centring Method <

ID < Laser Plummet >

Error < 0.6666 >


>

Centring Method <



Error < 0.3333 >


>

Centring Method <

ID < Forced Centred Instrument >

Error < 0.0 >


>

Centring Method <

ID < Forced Centred Target >

Error < 0.0 >


>

Survey Instrument <

ID < TCA 2003 >

EDM < 1+1 >

Directional < 0.5 >

Compensator < 0.3 >

>


ID < Tripod to Tripod >


Sets < 1 >

Instrument <

Free Station < No >

Re-Level < No >

Re-Centre < No >

Centring < Laser Plummet >


>

Target <



>

>


ID < Pillar to Tripod >

Like < Tripod to Tripod >


Sets < 1 >

Instrument <

Centring < Forced Centred Instrument >


>

>



ID < Pillar to Pillar >

Like < Pillar to Tripod >


Sets < 1 >

Target <

Centring < Forced Centred Target >


>

>


ID < Tripod to Pillar >

Like < Tripod to Tripod >


Sets < 1 >

Target <

Centring < Forced Centred Target >


>

>


ID < Water main >

Default <

Reduction < 2D >

Measurement Scheme < Tripod to Tripod >

>

But <

at < 1-31 >

Reduction < 2D >

Measurement Scheme < Pillar to Tripod >

>

But <

to < 1-31 >

Reduction < 2D >

Measurement Scheme < Tripod to Pillar >

>

But <

at < 1-31 >

to < 1-31 >

Reduction < 2D >

Measurement Scheme < Pillar to Pillar >

>

>


Input File < data-meaned-heights updated >

Output File < data-meaned-heights updated-net >

Reduction RuleSet < Water main >


>


Adjust Network <

Observations < data-meaned-heights updated-net >

Observations to Exclude < outliers >


Datum < Datum >

Allow Sloppy Approximation < y >

Report Name < - >

Confidence Level < 95 >

Plot Name < - >

>

The observations to be excluded (suspected outliers) can be identified by placing a copy of

them in a Network Observations file, designated to contain the outlier entries. This file, since

it is referenced in the instructions for Network Adjustment, is started now, but will remain

empty until the adjustment is run.

outliers.obs

*** [ empty file ]

The file containing the tabulated approximate heights of targets or instruments over all the

network points follows. Pillar points have not been included because the error propagation

rule for instruments or targets on forced centring pillars includes no height-dependent error,

as one can see in the instructions for TRA to Network.

HEIGHTS RULES.txt

514 1.6

515 1.6

516 1.6

517 1.6

518 1.6

605 1.6

602 1.6

650 1.6

651 1.6

652 1.6

1435 1.6

1436 1.6

1791 1.6


6000 1.6

6001 1.6

6002 1.6

9000 1.6

9001 1.6

9002 1.6

1001 2.93

1002 2.65

1003 2.73

1004 2.63

1006 2.69

1008 2.84

1009 2.81

1011 2.61

1012 2.67

1013 2.58

1014 2.84

1015 3.54

1016 2.95

1017 3.91

1018 2.88

1019 3.89

1020 2.26

1021 4.73

1022 2.83

1024 2.67

1026 2.68

1027 3.69

1030 2.6

1031 3.3

The initial coordinates follow.


1 9480.678 7617.011 3.4677

2 9752.485 7462.385 10.6307

4 10270.6476 6995.2516 3.0547

5 10240.99 7140.027 6.6465

6 9329.696 7663.307 3.2958

7 9477.1981 7479.3146 2.5631

9 10380.495 7014.879 4.3994

31 10288.839 7071.833 4.7154

52 9306.4028 7672.2585 3.1478

54 9560.547 7565.602 6.235

159 9561.48 7600.503 1.979

511 10227.06 7260.0117 5.0071


512 10307.3616 7309.3887 5.0306

513 10392.8086 7343.1365 5.0186

514 9795.0745 7522.1112 5.6361

515 9804.9296 7540.1024 5.5824

516 9991.9756 7767.4081 5.601

517 9281.9392 7687.9914 3.1837

518 9204.094 7738.096 3.2335

519 9561.486 7600.527 4.462

601 9491.3932 7580.4053 3.0828

602 9559.7956 7556.3986 4.821

603 9648.7085 7514.873 7.5297

604 9681.4974 7494.861 8.4737

605 9763.086 7473.359 7.8537

606 9377.2542 7611.596 0

607 10079.1797 7241.5967 10.4461

620 9491.389 7589.218 4.09

650 9380.874 7612.759 3.5183

651 9264.984 7656.852 3.1697

652 9184.321 7712.089 0

1435 9136.509 7781.546 3.2398

1436 9103.664 7760.333 3.0709

2095 10372.5546 7022.2449 3.1193

2202 10289.6308 7102.4289 4.2816

2203 10169.4473 7190.2271 7.5194

2485 10311.446 7080.9612 3.7409

3001 10283.1936 7000.7257 2.9948

6000 9366.88 7621.777 0

6001 9560.548 7565.605 4.81

6002 9600.198 7584.565 0

9000 9752.696 7461.436 9.5

9001 9596.48 7577.623 2.35

9002 9560.547 7565.606 4.826

1001 9290.653 7638.67 1.4173

1002 9273.846 7649.428 1.7503

1003 9250.64 7664.482 1.8283

1004 9227.919 7678.951 1.9313

1006 9384.308 7631.198 0.8691

1008 9414.02 7621.085 0.9261

1009 9512.527 7594.966 0.6567

1011 9532.345 7590.166 0.7074

1012 9536.273 7594.68 0.4469

1013 9552.4176 7584.415 0.7125

1014 9549.8879 7590.8566 0.4105

1015 9589.738 7570.481 0.0857

1016 9584.077 7577.589 -0.0372

1017 9599.465 7565.893 0.2354

1018 9598.229 7570.944 0.8669


1019 9631.796 7547.133 0.1211

1020 9620.605 7558.977 0.9039

1021 9651.6743 7534.2725 -0.1423

1022 9655.685 7537.501 0.7926

1024 9687.538 7517.772 1.004

1026 9719.487 7499.784 1.1401

1027 9742.2321 7493.394 -0.11

1029 10235.2734 7158.1113 1.0812

1030 10241.0907 7106.7431 1.0329

1031 10244.3111 7080.0594 0.9952

The minimum constraints datum definition follows.

Datum.fix

517 ! ! ?

518 ? ! ?

The TRA survey data follows.

data.tra


OCC 650 1.600 CTRL

BS 9002 1.600 104.42129 89.36033 185.7617 .000 TH

IS 9001 1.600 99.15134 90.21551 218.4588 .000 TH

IS 9001 1.600 279.15195 269.38113 218.4589 .000 TH

IS 1 1.600 87.33277 90.46409 99.9060 .000 TH

IS 1 1.600 267.33367 269.13243 99.9061 .000 TH

IS 6 1.600 314.38358 91.12559 71.9465 .000 TH

IS 6 1.600 134.38404 268.47130 71.9465 .000 TH

IS 517 1.600 307.14529 90.09268 124.2919 .000 TH

IS 517 1.600 127.14586 269.50398 124.2919 .000 TH

IS 518 1.600 305.19595 90.04319 216.7045 .000 TH

IS 518 1.600 125.20097 269.55363 216.7045 .000 TH

IS 651 1.600 290.49373 90.08084 123.9951 .000 TH

IS 651 1.600 110.49479 269.52011 123.9951 .000 TH

IS 652 1.600 296.48276 90.00109 220.2247 .000 TH

IS 652 1.600 116.48318 269.59528 220.2249 .000 TH

IS 9002 1.600 284.42160 270.24006 185.7617 .000 TH

IS 1008 1.600 75.54320 91.46137 34.1891 .000 TH

IS 1008 1.600 255.54369 268.13489 34.1906 .000 TH


OCC 6 1.600 CTRL

BS 9002 1.600 112.56180 89.21233 250.6894 .000 TH


IS 1 1.600 107.02467 89.56187 157.9213 .000 TH

IS 1 1.600 287.02486 270.03463 157.9215 .000 TH

IS 1 1.600 107.02404 89.56215 157.9213 .000 TH

IS 9001 1.600 107.48130 89.58278 280.2088 .000 TH

IS 9001 1.600 287.48187 270.01415 280.2088 .000 TH

IS 650 1.600 134.38387 88.47085 71.9458 .000 TH

IS 650 1.600 314.38460 271.12584 71.9461 .000 TH

IS 651 1.600 264.18080 88.54381 65.0454 .000 TH

IS 651 1.600 84.18131 271.05285 65.0454 .000 TH

IS 652 1.600 288.32518 89.26008 153.3476 .000 TH

IS 652 1.600 108.32570 270.34088 153.3480 .000 TH

IS 517 1.600 297.19537 88.44105 53.7740 .000 TH

IS 517 1.600 117.19559 271.15577 53.7740 .000 TH

IS 518 1.600 300.46114 89.30414 146.1880 .000 TH

IS 518 1.600 120.46170 270.29218 146.1881 .000 TH

IS 9002 1.600 292.56227 270.38471 250.6894 .000 TH


OCC 6 1.600 CTRL

BS 652 1.600 288.33013 89.26006 153.3481 .000 TH

IS 651 1.600 264.18213 88.54382 65.0458 .000 TH

IS 518 1.600 300.46187 89.30425 146.1880 .000 TH

IS 518 1.600 120.46304 270.29258 146.1881 .000 TH

IS 517 1.600 297.20039 88.44130 53.7739 .000 TH

IS 517 1.600 117.20089 271.16019 53.7740 .000 TH

IS 650 1.600 134.38580 88.47104 71.9459 .000 TH

IS 650 1.600 314.39022 271.13008 71.9461 .000 TH

IS 1 1.600 107.02508 89.56210 157.9213 .000 TH

IS 1 1.600 287.03041 270.03460 157.9215 .000 TH

IS 9001 1.600 107.48268 89.58271 280.2088 .000 TH

IS 9001 1.600 287.48356 270.01420 280.2089 .000 TH

IS 9002 1.600 112.56300 89.21224 250.6893 .000 TH

IS 9002 1.600 292.56393 270.38434 250.6893 .000 TH

IS 651 1.600 84.18250 271.05305 65.0455 .000 TH

IS 652 1.600 108.33140 270.34106 153.3480 .000 TH


OCC 517 1.600 CTRL

BS 652 1.600 283.51568 89.48387 100.5464 .000 TH

IS 518 1.600 302.45587 89.57433 92.5751 .000 TH

IS 518 1.600 122.46110 270.02254 92.5752 .000 TH

IS 651 1.600 208.34062 89.55004 35.4546 .000 TH

IS 651 1.600 28.34085 270.05104 35.4545 .000 TH

IS 650 1.600 127.15007 89.50403 124.2891 .000 TH

IS 650 1.600 307.15110 270.09301 124.2892 .000 TH

IS 6 1.600 117.19529 91.15484 53.7734 .000 TH

IS 6 1.600 297.19586 268.44208 53.7732 .000 TH

IS 1002 1.600 191.51116 90.09051 39.4038 .000 TH


IS 1002 1.600 11.51125 269.51022 39.4039 .000 TH

IS 1001 1.600 169.58391 90.08356 50.0864 .000 TH

IS 1001 1.600 349.58447 269.51330 50.0865 .000 TH

IS 1 1.600 109.39127 90.16384 211.0391 .000 TH

IS 1 1.600 289.39214 269.43317 211.0392 .000 TH

IS 1003 1.600 233.05198 90.01083 39.1444 .000 TH

IS 1003 1.600 53.05324 269.59015 39.1445 .000 TH

IS 1436 1.600 112.05228 270.00189 192.3932 .000 TH

IS 1436 1.600 292.05116 89.59528 192.3933 .000 TH

IS 1436 1.600 112.05244 270.00184 192.3934 .000 TH

IS 1436 1.600 292.05115 89.59519 192.3932 .000 TH

IS 652 1.600 103.52102 270.11332 100.5462 .000 TH


OCC 518 1.600 CTRL

BS 6 1.600 120.46154 90.29261 146.1880 .000 TH

IS 517 1.600 122.45474 90.02285 92.5757 .000 TH

IS 517 1.600 302.45586 269.57387 92.5757 .000 TH

IS 650 1.600 125.20039 89.55447 216.7022 .000 TH

IS 650 1.600 305.20116 270.04234 216.7023 .000 TH

IS 651 1.600 143.08485 90.00306 101.5280 .000 TH

IS 651 1.600 323.08545 269.59390 101.5282 .000 TH

IS 652 1.600 217.14325 89.31318 32.6704 .000 TH

IS 652 1.600 37.14333 270.28413 32.6705 .000 TH

IS 1004 1.600 158.03196 90.01254 63.7635 .000 TH

IS 1004 1.600 338.03295 269.58433 63.7636 .000 TH

IS 1436 1.600 102.29081 269.58230 102.8621 .000 TH

IS 1436 1.600 282.29015 90.01461 102.8620 .000 TH

IS 1435 1.600 302.44050 89.58296 80.3462 .000 TH

IS 1435 1.600 122.44148 270.01373 80.3462 .000 TH

IS 6 1.600 300.46204 269.30403 146.1879 .000 TH


OCC 1435 1.600 CTRL

BS 650 1.600 359.59595 89.57260 296.9885 .000 TH

IS 651 1.600 9.30384 90.01084 179.0363 .000 TH

IS 651 1.600 189.30481 269.59087 179.0364 .000 TH

IS 652 1.600 200.49370 270.09411 84.3232 .000 TH

IS 652 1.600 20.49308 89.50328 84.3231 .000 TH

IS 1436 1.600 112.30452 90.07457 39.0998 .000 TH

IS 1436 1.600 292.30476 269.52275 39.0998 .000 TH

IS 518 1.600 178.06241 269.58308 80.3458 .000 TH

IS 518 1.600 358.06201 90.01421 80.3458 .000 TH

IS 6 1.600 356.50087 90.19404 226.5034 .000 TH

IS 6 1.600 176.50180 269.40348 226.5027 .000 TH

IS 650 1.600 180.00158 270.02508 296.9886 .000 TH



OCC 651 1.600 CTRL

BS 518 1.600 323.08478 89.59450 101.5285 .000 TH

IS 517 1.600 28.33490 90.05018 35.4534 .000 TH

IS 517 1.600 208.33530 269.55102 35.4534 .000 TH

IS 6 1.600 84.18072 91.05290 65.0449 .000 TH

IS 6 1.600 264.18062 268.54433 65.0449 .000 TH

IS 650 1.600 110.49447 89.52084 123.9924 .000 TH

IS 650 1.600 290.49493 270.08025 123.9924 .000 TH

IS 652 1.600 304.23557 89.50114 97.7614 .000 TH

IS 652 1.600 124.24043 270.10060 97.7614 .000 TH

IS 1435 1.600 134.08391 270.01007 179.0371 .000 TH

IS 1435 1.600 314.08292 89.59130 179.0372 .000 TH

IS 518 1.600 143.08545 270.00292 101.5285 .000 TH

IS 518 1.600 323.08466 89.59468 101.5284 .000 TH


OCC 652 1.600 CTRL

BS 650 1.600 116.48367 90.00039 220.2232 .000 TH

IS 6 1.600 108.32566 90.34114 153.3485 .000 TH

IS 6 1.600 288.33038 269.26000 153.3486 .000 TH

IS 517 1.600 103.52008 90.11333 100.5466 .000 TH

IS 517 1.600 283.52068 269.48391 100.5465 .000 TH

IS 518 1.600 37.14316 90.28437 32.6708 .000 TH

IS 518 1.600 217.14421 269.31311 32.6708 .000 TH

IS 1435 1.600 145.27401 269.50319 84.3236 .000 TH

IS 1435 1.600 325.27345 90.09405 84.3236 .000 TH

IS 651 1.600 124.24053 90.10087 97.7617 .000 TH

IS 651 1.600 304.24146 269.50082 97.7618 .000 TH

IS 650 1.600 296.48463 270.00083 220.2231 .000 TH


The meaning report follows.

data-meaning_report.txt

================================================================================

Mean Observations Report

Standard deviations and [largest splits] of observations

Angles in seconds. Distances in metres.

================================================================================

--------------------------------------------------------------------------------

Station 650 Backsight 9002

--------------------------------------------------------------------------------

Point # Observations

Number FL FR HCR VCR SD

1 1 1 6.4 [ 9.0] 3.7 [ 5.2] 0.0001 [0.0001]

6 1 1 3.3 [ 4.6] 6.3 [ 8.9] 0.0000 [0.0000]

517 1 1 4.0 [ 5.7] 4.7 [ 6.6] 0.0000 [0.0000]

518 1 1 7.2 [10.2] 5.8 [ 8.2] 0.0000 [0.0000]

651 1 1 7.5 [10.6] 6.7 [ 9.5] 0.0000 [0.0000]

652 1 1 3.0 [ 4.2] 2.6 [ 3.7] 0.0001 [0.0002]

1008 1 1 3.5 [ 4.9] 1.8 [ 2.6] 0.0011 [0.0015]

9001 1 1 4.3 [ 6.1] 4.5 [ 6.4] 0.0001 [0.0001]

9002 1 1 2.2 [ 3.1] 2.8 [ 3.9] 0.0000 [0.0000]

Warnings:

1008 has large split in slope distances.

IS 1008 1.600 75.54320 91.46137 34.1891 .000 TH

IS 1008 1.600 255.54369 268.13489 34.1906 .000 TH

--------------------------------------------------------------------------------


--------------------------------------------------------------------------------



1 2 1 4.3 [ 8.2] 4.0 [ 7.8] 0.0001 [0.0002]

517 1 1 1.6 [ 2.2] 5.8 [ 8.2] 0.0000 [0.0000]

518 1 1 4.0 [ 5.6] 2.3 [ 3.2] 0.0001 [0.0001]

650 1 1 5.2 [ 7.3] 4.9 [ 6.9] 0.0002 [0.0003]

651 1 1 3.6 [ 5.1] 4.7 [ 6.6] 0.0000 [0.0000]

652 1 1 3.7 [ 5.2] 6.8 [ 9.6] 0.0003 [0.0004]

9001 1 1 4.0 [ 5.7] 6.6 [ 9.3] 0.0000 [0.0000]

9002 1 1 3.3 [ 4.7] 7.4 [10.4] 0.0000 [0.0000]

Warnings:

None


--------------------------------------------------------------------------------


--------------------------------------------------------------------------------



1 1 1 9.4 [13.3] 4.9 [ 7.0] 0.0001 [0.0002]

517 1 1 3.5 [ 5.0] 10.5 [14.9] 0.0001 [0.0001]

518 1 1 8.3 [11.7] 5.9 [ 8.3] 0.0001 [0.0001]

650 1 1 3.0 [ 4.2] 7.9 [11.2] 0.0001 [0.0002]

651 1 1 2.6 [ 3.7] 6.2 [ 8.7] 0.0002 [0.0003]

652 1 1 9.0 [12.7] 7.9 [11.2] 0.0001 [0.0001]

9001 1 1 6.2 [ 8.8] 6.4 [ 9.1] 0.0001 [0.0001]

9002 1 1 6.6 [ 9.3] 4.1 [ 5.8] 0.0000 [0.0000]

Warnings:

1 has large split in horizontal directions.

IS 1 1.600 107.02508 89.56210 157.9213 .000 TH

IS 1 1.600 287.03041 270.03460 157.9215 .000 TH

517 has large split in vertical directions.

IS 517 1.600 297.20039 88.44130 53.7739 .000 TH

IS 517 1.600 117.20089 271.16019 53.7740 .000 TH


IS 652 1.600 108.33140 270.34106 153.3480 .000 TH

BS 652 1.600 288.33013 89.26006 153.3481 .000 TH

--------------------------------------------------------------------------------


--------------------------------------------------------------------------------



1 1 1 6.2 [ 8.7] 7.1 [10.1] 0.0001 [0.0001]

6 1 1 4.0 [ 5.7] 6.5 [ 9.2] 0.0001 [0.0002]

518 1 1 8.7 [12.3] 6.2 [ 8.7] 0.0001 [0.0001]

650 1 1 7.3 [10.3] 7.4 [10.4] 0.0001 [0.0001]

651 1 1 1.6 [ 2.3] 7.6 [10.8] 0.0001 [0.0001]

652 1 1 9.5 [13.4] 8.4 [11.9] 0.0001 [0.0002]

1001 1 1 4.0 [ 5.6] 6.1 [ 8.6] 0.0001 [0.0001]

1002 1 1 0.6 [ 0.9] 5.2 [ 7.3] 0.0001 [0.0001]

1003 1 1 8.9 [12.6] 6.9 [ 9.8] 0.0001 [0.0001]

1436 2 2 7.0 [12.9] 6.4 [11.7] 0.0001 [0.0002]

Warnings:


IS 518 1.600 302.45587 89.57433 92.5751 .000 TH

IS 518 1.600 122.46110 270.02254 92.5752 .000 TH


IS 652 1.600 103.52102 270.11332 100.5462 .000 TH


BS 652 1.600 283.51568 89.48387 100.5464 .000 TH


IS 1003 1.600 233.05198 90.01083 39.1444 .000 TH

IS 1003 1.600 53.05324 269.59015 39.1445 .000 TH


IS 1436 1.600 112.05228 270.00189 192.3932 .000 TH

IS 1436 1.600 292.05116 89.59528 192.3933 .000 TH

IS 1436 1.600 112.05244 270.00184 192.3934 .000 TH

IS 1436 1.600 292.05115 89.59519 192.3932 .000 TH

--------------------------------------------------------------------------------


--------------------------------------------------------------------------------



6 1 1 3.5 [ 5.0] 4.5 [ 6.4] 0.0001 [0.0001]

517 1 1 7.9 [11.2] 5.1 [ 7.2] 0.0000 [0.0000]

650 1 1 5.4 [ 7.7] 5.7 [ 8.1] 0.0001 [0.0001]

651 1 1 4.2 [ 6.0] 6.8 [ 9.6] 0.0001 [0.0002]

652 1 1 0.6 [ 0.8] 9.3 [13.1] 0.0001 [0.0001]

1004 1 1 7.0 [ 9.9] 6.2 [ 8.7] 0.0001 [0.0001]

1435 1 1 6.9 [ 9.8] 4.9 [ 6.9] 0.0000 [0.0000]

1436 1 1 4.7 [ 6.6] 6.4 [ 9.1] 0.0001 [0.0001]

Warnings:


IS 652 1.600 217.14325 89.31318 32.6704 .000 TH

IS 652 1.600 37.14333 270.28413 32.6705 .000 TH

--------------------------------------------------------------------------------


--------------------------------------------------------------------------------



6 1 1 6.6 [ 9.3] 10.7 [15.2] 0.0005 [0.0007]

518 1 1 2.8 [ 4.0] 9.1 [12.9] 0.0000 [0.0000]

650 1 1 11.5 [16.3] 11.9 [16.8] 0.0001 [0.0001]

651 1 1 6.9 [ 9.7] 12.1 [17.1] 0.0001 [0.0001]

652 1 1 4.4 [ 6.2] 9.8 [13.9] 0.0001 [0.0001]

1436 1 1 1.7 [ 2.4] 9.3 [13.2] 0.0000 [0.0000]

Warnings:


IS 6 1.600 356.50087 90.19404 226.5034 .000 TH

IS 6 1.600 176.50180 269.40348 226.5027 .000 TH


IS 518 1.600 178.06241 269.58308 80.3458 .000 TH

IS 518 1.600 358.06201 90.01421 80.3458 .000 TH




IS 650 1.600 180.00158 270.02508 296.9886 .000 TH

BS 650 1.600 359.59595 89.57260 296.9885 .000 TH


IS 651 1.600 9.30384 90.01084 179.0363 .000 TH

IS 651 1.600 189.30481 269.59087 179.0364 .000 TH


IS 652 1.600 200.49370 270.09411 84.3232 .000 TH

IS 652 1.600 20.49308 89.50328 84.3231 .000 TH


IS 1436 1.600 112.30452 90.07457 39.0998 .000 TH

IS 1436 1.600 292.30476 269.52275 39.0998 .000 TH

--------------------------------------------------------------------------------


--------------------------------------------------------------------------------



6 1 1 0.7 [ 1.0] 8.7 [12.3] 0.0000 [0.0000]

517 1 1 2.8 [ 4.0] 8.5 [12.0] 0.0000 [0.0000]

518 2 1 4.3 [ 7.9] 8.8 [16.0] 0.0001 [0.0001]

650 1 1 3.3 [ 4.6] 7.7 [10.9] 0.0000 [0.0000]

652 1 1 6.1 [ 8.6] 12.3 [17.4] 0.0000 [0.0000]

1435 1 1 7.0 [ 9.9] 9.7 [13.7] 0.0001 [0.0001]

Warnings:


IS 6 1.600 84.18072 91.05290 65.0449 .000 TH

IS 6 1.600 264.18062 268.54433 65.0449 .000 TH


IS 518 1.600 143.08545 270.00292 101.5285 .000 TH

IS 518 1.600 323.08466 89.59468 101.5284 .000 TH

BS 518 1.600 323.08478 89.59450 101.5285 .000 TH


IS 652 1.600 304.23557 89.50114 97.7614 .000 TH

IS 652 1.600 124.24043 270.10060 97.7614 .000 TH


IS 1435 1.600 134.08391 270.01007 179.0371 .000 TH

IS 1435 1.600 314.08292 89.59130 179.0372 .000 TH

--------------------------------------------------------------------------------


--------------------------------------------------------------------------------



6 1 1 5.1 [ 7.2] 8.1 [11.4] 0.0001 [0.0001]

517 1 1 4.2 [ 6.0] 8.8 [12.4] 0.0001 [0.0001]


518 1 1 7.4 [10.5] 10.5 [14.8] 0.0000 [0.0000]

650 1 1 6.8 [ 9.6] 8.6 [12.2] 0.0001 [0.0001]

651 1 1 6.6 [ 9.3] 12.0 [16.9] 0.0001 [0.0001]

1435 1 1 4.0 [ 5.6] 8.8 [12.4] 0.0000 [0.0000]

Warnings:


IS 517 1.600 103.52008 90.11333 100.5466 .000 TH

IS 517 1.600 283.52068 269.48391 100.5465 .000 TH


IS 518 1.600 37.14316 90.28437 32.6708 .000 TH

IS 518 1.600 217.14421 269.31311 32.6708 .000 TH


IS 650 1.600 296.48463 270.00083 220.2231 .000 TH

BS 650 1.600 116.48367 90.00039 220.2232 .000 TH


IS 651 1.600 124.24053 90.10087 97.7617 .000 TH

IS 651 1.600 304.24146 269.50082 97.7618 .000 TH


IS 1435 1.600 145.27401 269.50319 84.3236 .000 TH

IS 1435 1.600 325.27345 90.09405 84.3236 .000 TH

The meaned data follows.

data-meaned.tra


* Observations made on both faces

OCC 650 1.600 CTRL

BS 9002 1.600 104.42145 89.36013 185.7617 .000 TH

IS 1 1.600 87.33322 90.46383 99.9060 .000 TH

IS 6 1.600 314.38381 91.12515 71.9465 .000 TH

IS 517 1.600 307.14557 90.09235 124.2919 .000 TH

IS 518 1.600 305.20046 90.04278 216.7045 .000 TH

IS 651 1.600 290.49426 90.08036 123.9951 .000 TH

IS 652 1.600 296.48297 90.00090 220.2248 .000 TH

IS 1008 1.600 75.54344 91.46124 34.1899 .000 TH

IS 9001 1.600 99.15165 90.21519 218.4588 .000 TH



OCC 6 1.600 CTRL

BS 9002 1.600 112.56204 89.21181 250.6894 .000 TH

IS 1 1.600 107.02476 89.56162 157.9214 .000 TH

IS 517 1.600 297.19548 88.44064 53.7740 .000 TH

IS 518 1.600 300.46142 89.30398 146.1880 .000 TH


IS 650 1.600 134.38423 88.47051 71.9460 .000 TH

IS 651 1.600 264.18106 88.54348 65.0454 .000 TH

IS 652 1.600 288.32544 89.25560 153.3478 .000 TH

IS 9001 1.600 107.48159 89.58232 280.2088 .000 TH



OCC 6 1.600 CTRL

BS 652 1.600 288.33076 89.25550 153.3481 .000 TH

IS 1 1.600 107.02575 89.56175 157.9214 .000 TH

IS 517 1.600 297.20064 88.44055 53.7739 .000 TH

IS 518 1.600 300.46245 89.30383 146.1880 .000 TH

IS 650 1.600 134.39001 88.47048 71.9460 .000 TH

IS 651 1.600 264.18231 88.54339 65.0456 .000 TH

IS 9001 1.600 107.48312 89.58225 280.2088 .000 TH

IS 9002 1.600 112.56347 89.21195 250.6893 .000 TH



OCC 517 1.600 CTRL

BS 652 1.600 283.52035 89.48328 100.5463 .000 TH

IS 1 1.600 109.39170 90.16333 211.0392 .000 TH

IS 6 1.600 117.19557 91.15438 53.7733 .000 TH

IS 518 1.600 302.46049 89.57390 92.5752 .000 TH

IS 650 1.600 127.15059 89.50351 124.2892 .000 TH

IS 651 1.600 208.34073 89.54550 35.4545 .000 TH

IS 1001 1.600 169.58419 90.08313 50.0864 .000 TH

IS 1002 1.600 191.51120 90.09014 39.4038 .000 TH

IS 1003 1.600 233.05261 90.01034 39.1444 .000 TH

IS 1436 1.600 292.05176 89.59469 192.3933 .000 TH



OCC 518 1.600 CTRL

BS 6 1.600 120.46179 90.29229 146.1880 .000 TH

IS 517 1.600 122.45530 90.02249 92.5757 .000 TH

IS 650 1.600 125.20078 89.55406 216.7022 .000 TH

IS 651 1.600 143.08515 90.00258 101.5281 .000 TH

IS 652 1.600 217.14329 89.31253 32.6705 .000 TH

IS 1004 1.600 158.03246 90.01210 63.7635 .000 TH

IS 1435 1.600 302.44099 89.58261 80.3462 .000 TH

IS 1436 1.600 282.29048 90.01416 102.8621 .000 TH



OCC 1435 1.600 CTRL

BS 650 1.600 360.00077 89.57176 296.9886 .000 TH


IS 6 1.600 356.50134 90.19328 226.5031 .000 TH

IS 518 1.600 358.06221 90.01357 80.3458 .000 TH

IS 651 1.600 9.30433 90.00599 179.0364 .000 TH

IS 652 1.600 20.49339 89.50259 84.3231 .000 TH

IS 1436 1.600 112.30464 90.07391 39.0998 .000 TH



OCC 651 1.600 CTRL

BS 518 1.600 323.08506 89.59388 101.5285 .000 TH

IS 6 1.600 84.18067 91.05228 65.0449 .000 TH

IS 517 1.600 28.33510 90.04558 35.4534 .000 TH

IS 650 1.600 110.49470 89.52030 123.9924 .000 TH

IS 652 1.600 304.24000 89.50027 97.7614 .000 TH

IS 1435 1.600 314.08342 89.59062 179.0372 .000 TH



OCC 652 1.600 CTRL

BS 650 1.600 116.48415 89.59578 220.2231 .000 TH

IS 6 1.600 108.33002 90.34057 153.3485 .000 TH

IS 517 1.600 103.52038 90.11271 100.5466 .000 TH

IS 518 1.600 37.14368 90.28363 32.6708 .000 TH

IS 651 1.600 124.24100 90.10003 97.7618 .000 TH

IS 1435 1.600 325.27373 90.09343 84.3236 .000 TH

The TRA data with realistic heights follows.

data-meaned-heights updated.tra



OCC 650 1.600 CTRL

BS 9002 1.600 104.42145 89.36013 185.7617 .000 TH

IS 1 1.600 87.33322 90.46383 99.9060 .000 TH

IS 6 1.600 314.38381 91.12515 71.9465 .000 TH

IS 517 1.600 307.14557 90.09235 124.2919 .000 TH

IS 518 1.600 305.20046 90.04278 216.7045 .000 TH

IS 651 1.600 290.49426 90.08036 123.9951 .000 TH

IS 652 1.600 296.48297 90.00090 220.2248 .000 TH

IS 1008 2.840 75.54344 91.46124 34.1899 .000 TH

IS 9001 1.600 99.15165 90.21519 218.4588 .000 TH




OCC 6 1.600 CTRL

BS 9002 1.600 112.56204 89.21181 250.6894 .000 TH

IS 1 1.600 107.02476 89.56162 157.9214 .000 TH

IS 517 1.600 297.19548 88.44064 53.7740 .000 TH

IS 518 1.600 300.46142 89.30398 146.1880 .000 TH

IS 650 1.600 134.38423 88.47051 71.9460 .000 TH

IS 651 1.600 264.18106 88.54348 65.0454 .000 TH

IS 652 1.600 288.32544 89.25560 153.3478 .000 TH

IS 9001 1.600 107.48159 89.58232 280.2088 .000 TH



OCC 6 1.600 CTRL

BS 652 1.600 288.33076 89.25550 153.3481 .000 TH

IS 1 1.600 107.02575 89.56175 157.9214 .000 TH

IS 517 1.600 297.20064 88.44055 53.7739 .000 TH

IS 518 1.600 300.46245 89.30383 146.1880 .000 TH

IS 650 1.600 134.39001 88.47048 71.9460 .000 TH

IS 651 1.600 264.18231 88.54339 65.0456 .000 TH

IS 9001 1.600 107.48312 89.58225 280.2088 .000 TH

IS 9002 1.600 112.56347 89.21195 250.6893 .000 TH



OCC 517 1.600 CTRL

BS 652 1.600 283.52035 89.48328 100.5463 .000 TH

IS 1 1.600 109.39170 90.16333 211.0392 .000 TH

IS 6 1.600 117.19557 91.15438 53.7733 .000 TH

IS 518 1.600 302.46049 89.57390 92.5752 .000 TH

IS 650 1.600 127.15059 89.50351 124.2892 .000 TH

IS 651 1.600 208.34073 89.54550 35.4545 .000 TH

IS 1001 2.930 169.58419 90.08313 50.0864 .000 TH

IS 1002 2.650 191.51120 90.09014 39.4038 .000 TH

IS 1003 2.730 233.05261 90.01034 39.1444 .000 TH

IS 1436 1.600 292.05176 89.59469 192.3933 .000 TH



OCC 518 1.600 CTRL

BS 6 1.600 120.46179 90.29229 146.1880 .000 TH

IS 517 1.600 122.45530 90.02249 92.5757 .000 TH

IS 650 1.600 125.20078 89.55406 216.7022 .000 TH

IS 651 1.600 143.08515 90.00258 101.5281 .000 TH


IS 652 1.600 217.14329 89.31253 32.6705 .000 TH

IS 1004 2.630 158.03246 90.01210 63.7635 .000 TH

IS 1435 1.600 302.44099 89.58261 80.3462 .000 TH

IS 1436 1.600 282.29048 90.01416 102.8621 .000 TH



OCC 1435 1.600 CTRL

BS 650 1.600 360.00077 89.57176 296.9886 .000 TH

IS 6 1.600 356.50134 90.19328 226.5031 .000 TH

IS 518 1.600 358.06221 90.01357 80.3458 .000 TH

IS 651 1.600 9.30433 90.00599 179.0364 .000 TH

IS 652 1.600 20.49339 89.50259 84.3231 .000 TH

IS 1436 1.600 112.30464 90.07391 39.0998 .000 TH



OCC 651 1.600 CTRL

BS 518 1.600 323.08506 89.59388 101.5285 .000 TH

IS 6 1.600 84.18067 91.05228 65.0449 .000 TH

IS 517 1.600 28.33510 90.04558 35.4534 .000 TH

IS 650 1.600 110.49470 89.52030 123.9924 .000 TH

IS 652 1.600 304.24000 89.50027 97.7614 .000 TH

IS 1435 1.600 314.08342 89.59062 179.0372 .000 TH



OCC 652 1.600 CTRL

BS 650 1.600 116.48415 89.59578 220.2231 .000 TH

IS 6 1.600 108.33002 90.34057 153.3485 .000 TH

IS 517 1.600 103.52038 90.11271 100.5466 .000 TH

IS 518 1.600 37.14368 90.28363 32.6708 .000 TH

IS 651 1.600 124.24100 90.10003 97.7618 .000 TH

IS 1435 1.600 325.27373 90.09343 84.3236 .000 TH


TRA to Network is executed. The Network Observations data follows.

data-meaned-heights updated-net.obs


650-9002 HCR 104.42145 2.143

650-9002 HD 185.75718 0.002135

650-1 HCR 87.33322 3.432

650-1 HD 99.896806 0.001927

650-6 HCR 314.38381 4.742

650-6 HD 71.930343 0.001926

650-517 HCR 307.14557 3.154

650-517 HD 124.29144 0.00213

650-518 HCR 305.20046 1.855

650-518 HD 216.70432 0.002137

650-651 HCR 290.49426 3.162

650-651 HD 123.99476 0.00213

650-652 HCR 296.48297 1.827

650-652 HD 220.2248 0.002138

650-1008 HCR 75.54344 12.88

650-1008 HD 34.173585 0.002355

650-9001 HCR 99.15165 1.841

650-9001 HD 218.45438 0.002138


orient

6-9002 HCR 112.56204 0.9898

6-9002 HD 250.67352 0.001463

6-1 HCR 107.02476 0.8328

6-1 HD 157.92131 0.001134

6-517 HCR 297.19548 4.014

6-517 HD 53.760897 0.001442

6-518 HCR 300.46142 1.548

6-518 HD 146.18268 0.001449

6-650 HCR 134.38423 3.019

6-650 HD 71.929817 0.001443

6-651 HCR 264.18106 3.33

6-651 HD 65.033623 0.001443

6-652 HCR 288.32544 1.483

6-652 HD 153.34027 0.00145

6-9001 HCR 107.48159 0.9132

6-9001 HD 280.20877 0.001468


orient


6-652 HCR 288.33076 1.483

6-652 HD 153.34056 0.00145

6-1 HCR 107.02575 0.8328

6-1 HD 157.92131 0.001134

6-517 HCR 297.20064 4.014

6-517 HD 53.760791 0.001442

6-518 HCR 300.46245 1.548

6-518 HD 146.18267 0.001449

6-650 HCR 134.39001 3.019

6-650 HD 71.929815 0.001443

6-651 HCR 264.18231 3.33

6-651 HD 65.033817 0.001443

6-9001 HCR 107.48312 0.9132

6-9001 HD 280.20877 0.001468

6-9002 HCR 112.56347 0.9898

6-9002 HD 250.67344 0.001463


orient

517-652 HCR 283.52035 3.882

517-652 HD 100.54574 0.002129

517-1 HCR 109.39170 1.683

517-1 HD 211.03675 0.001936

517-6 HCR 117.19557 6.329

517-6 HD 53.760253 0.001925

517-518 HCR 302.46049 4.211

517-518 HD 92.575178 0.002128

517-650 HCR 127.15059 3.154

517-650 HD 124.28873 0.00213

517-651 HCR 208.34073 10.93

517-651 HD 35.454461 0.002127

517-1001 HCR 169.58419 8.88

517-1001 HD 50.086246 0.002374

517-1002 HCR 191.51120 10.95

517-1002 HD 39.403664 0.002317

517-1003 HCR 233.05261 11.12

517-1003 HD 39.144398 0.002333

517-1436 HCR 292.05176 2.073

517-1436 HD 192.3933 0.002135


orient

518-6 HCR 120.46179 2.374

518-6 HD 146.18266 0.00193

518-517 HCR 122.45530 4.211

518-517 HD 92.575677 0.002128


518-650 HCR 125.20078 1.855

518-650 HD 216.70203 0.002137

518-651 HCR 143.08515 3.845

518-651 HD 101.5281 0.002129

518-652 HCR 217.14329 11.86

518-652 HD 32.669371 0.002127

518-1004 HCR 158.03246 6.765

518-1004 HD 63.763495 0.002314

518-1435 HCR 302.44099 4.844

518-1435 HD 80.346192 0.002128

518-1436 HCR 282.29048 3.796

518-1436 HD 102.86209 0.002129


orient

1435-650 HCR 360.00077 1.396

1435-650 HD 296.98851 0.002147

1435-6 HCR 356.50134 1.579

1435-6 HD 226.49944 0.001938

1435-518 HCR 358.06221 4.844

1435-518 HD 80.345791 0.002128

1435-651 HCR 9.30433 2.219

1435-651 HD 179.03639 0.002134

1435-652 HCR 20.49339 4.618

1435-652 HD 84.322773 0.002128

1435-1436 HCR 112.30464 9.913

1435-1436 HD 39.099703 0.002127


orient

651-518 HCR 323.08506 3.845

651-518 HD 101.5285 0.002129

651-6 HCR 84.18067 5.239

651-6 HD 65.033137 0.001926

651-517 HCR 28.33510 10.93

651-517 HD 35.453364 0.002127

651-650 HCR 110.49470 3.162

651-650 HD 123.99207 0.00213

651-652 HCR 304.24000 3.991

651-652 HD 97.76099 0.002129

651-1435 HCR 314.08342 2.219

651-1435 HD 179.03719 0.002134


orient


652-650 HCR 116.48415 1.827

652-650 HD 220.2231 0.002138

652-6 HCR 108.33002 2.268

652-6 HD 153.34096 0.001931

652-517 HCR 103.52038 3.882

652-517 HD 100.54604 0.002129

652-518 HCR 37.14368 11.86

652-518 HD 32.669669 0.002127

652-651 HCR 124.24100 3.991

652-651 HD 97.761386 0.002129

652-1435 HCR 325.27373 4.618

652-1435 HD 84.323273 0.002128

Network Adjustment is executed. A portion of the Network Adjustment Report follows.

Only the statistical tests and the worst outliers are shown. =========================================================================================

Parametric Least Squares Network Adjustment Report

=========================================================================================

Post-Adjustment Scaling by Variance factor of unit weight: ON

=========================================================================================

Statistical Summary

=========================================================================================

Number of Iterations : 2

Number of observations : 122

Number of parameters : 37

Number of degrees of freedom : 85

Variance factor of unit weight : 0.42505

Standard deviation of unit weight : 0.65196

Number of each type of observations:

Horizontal Directions : 61

Distances : 61

Number of instrument stations : 7

Number of observations from each station:

6 : 32

517 : 20

518 : 16

650 : 18


651 : 12

652 : 12

1435 : 12

-----------------------------------------------------------------------------------------

Global Test of Variance Factor of Unit weight

-----------------------------------------------------------------------------------------

Using Chi-squared test


Lower critical value Statistic Upper critical value

61.3888 < 36.1293 < 112.3934

FAILED on lower end.

Possible reason:

Standard deviations of observations may be overly pessimistic.

-----------------------------------------------------------------------------------------

-----------------------------------------------------------------------------------------

Goodness of fit test for normality of standardized residuals

-----------------------------------------------------------------------------------------

Using Kolmogorov-Smirnov test


Statistic Critical value

1.1912 < 0.8950

FAILED. Observational residuals are not normally distributed.

-----------------------------------------------------------------------------------------

-----------------------------------------------------------------------------------------

Local Tests of Standardized Residuals

-----------------------------------------------------------------------------------------

Using Tau test


Largest standardized residual Critical Tau value

4.3182 < 3.5337

FAILED. There are outlier observations.


Observation recommended for removal:

6-1 HCR 107.02476 0.8328

-----------------------------------------------------------------------------------------

=========================================================================================

Adjusted observations

=========================================================================================

Notes:

Residuals (corrections applied to raw observations) are in the same units

as their associated observable's standard deviation.

Observations marked with '?' are suspected outliers.

=========================================================================================

Sorted in descending order by standardized residuals

=========================================================================================

Unadjusted Adjusted Standardized

At To Type Value Std.Dev. Value Std.Dev. Residual Residual

-----------------------------------------------------------------------------------------

6 1 HCR 107.02476 0.5430 107.02461 0.4243 -1.4629 -4.3182 ?

6 1 HCR 107.02575 0.5430 107.02589 0.4243 1.4232 4.2012 ?

6 9001 HCR 107.48159 0.5954 107.48174 0.4473 1.5388 3.9161 ?

518 6 HCR 120.46179 1.5478 120.46129 0.8393 -4.9741 -3.8250 ?

6 9001 HCR 107.48312 0.5954 107.48302 0.4473 -0.9751 -2.4814

518 517 HCR 122.45530 2.7454 122.45589 1.0772 5.9457 2.3545

=========================================================================================

Grouped in observational classes, then

sorted in descending order by standardized residuals

=========================================================================================

-----------------------------------------------------------------------------------------

Distance

-----------------------------------------------------------------------------------------



-----------------------------------------------------------------------------------------

650 517 HD 124.2914 0.0014 124.2895 0.0005 -0.0019 -1.4481

650 518 HD 216.7043 0.0014 216.7025 0.0005 -0.0018 -1.3870

650 651 HD 123.9948 0.0014 123.9931 0.0005 -0.0017 -1.2909

650 652 HD 220.2248 0.0014 220.2233 0.0005 -0.0015 -1.1557

6 650 HD 71.9298 0.0009 71.9308 0.0004 0.0010 1.0932

6 650 HD 71.9298 0.0009 71.9308 0.0004 0.0009 1.0909

-----------------------------------------------------------------------------------------


Horizontal Direction

-----------------------------------------------------------------------------------------



-----------------------------------------------------------------------------------------

6 1 HCR 107.02476 0.5430 107.02461 0.4243 -1.4629 -4.3182 ?

6 1 HCR 107.02575 0.5430 107.02589 0.4243 1.4232 4.2012 ?

6 9001 HCR 107.48159 0.5954 107.48174 0.4473 1.5388 3.9161 ?

518 6 HCR 120.46179 1.5478 120.46129 0.8393 -4.9741 -3.8250 ?

6 9001 HCR 107.48312 0.5954 107.48302 0.4473 -0.9751 -2.4814

518 517 HCR 122.45530 2.7454 122.45589 1.0772 5.9457 2.3545

Note that in the “adjusted observations” section, the units for the angles is sexigesimal-

decimal degrees, the units for the standard deviations and residuals are arcseconds, and

observations marked with '?' are suspected outliers. It is likely that the input standard

deviations of horizontal direction observations may be overly pessimistic, because the largest

standardized residuals for horizontal directions are more than twice those for distances. The

observation recommended for removal is the horizontal direction from point 6 to point 1,

with a value of 107°02’47.6” and an input standard deviation of 0.8328”. The suspected

outlier observation can conveniently be excluded simply by copying the underlined line

above into the outliers.obs file. The outlier observations file now contains this one

observation:

outliers.obs

6-1 HCR 107.02476 0.8328

Network Adjustment is executed. The variance factor is reduced (it is now 0.33576) when

the last observation has been removed. From the new Network Adjustment Report, we find

that all three statistical tests still fail. The observation recommended for removal is “518-6

HCR 120.46179 2.374”. The top 6 outlier observations – overall, and in each class – follow.


=========================================================================================



=========================================================================================



-----------------------------------------------------------------------------------------

518 6 HCR 120.46179 1.3756 120.46130 0.7464 -4.8573 -4.2036 ?

6 9001 HCR 107.48159 0.5291 107.48168 0.4171 0.9253 2.8417

6 518 HCR 300.46142 0.8970 300.46122 0.5284 -2.0219 -2.7895

518 517 HCR 122.45530 2.4400 122.45589 0.9576 5.8658 2.6136

6 650 HCR 134.39001 1.7493 134.38562 0.8247 -3.8568 -2.5000

6 518 HCR 300.46245 0.8970 300.46261 0.5191 1.5940 2.1791

=========================================================================================

Grouped in observational classes, then

sorted in descending order by standardized residuals

=========================================================================================

-----------------------------------------------------------------------------------------

Distance

-----------------------------------------------------------------------------------------



-----------------------------------------------------------------------------------------

650 517 HD 124.2914 0.0012 124.2895 0.0004 -0.0019 -1.6262

650 518 HD 216.7043 0.0012 216.7025 0.0004 -0.0019 -1.5840

650 651 HD 123.9948 0.0012 123.9930 0.0004 -0.0017 -1.4695

650 652 HD 220.2248 0.0012 220.2233 0.0004 -0.0015 -1.3176

650 1 HD 99.8968 0.0011 99.8980 0.0005 0.0012 1.2254

651 517 HD 35.4534 0.0012 35.4548 0.0004 0.0014 1.2133

-----------------------------------------------------------------------------------------

Horizontal Direction

-----------------------------------------------------------------------------------------



-----------------------------------------------------------------------------------------

518 6 HCR 120.46179 1.3756 120.46130 0.7464 -4.8573 -4.2036 ?

6 9001 HCR 107.48159 0.5291 107.48168 0.4171 0.9253 2.8417

6 518 HCR 300.46142 0.8970 300.46122 0.5284 -2.0219 -2.7895

518 517 HCR 122.45530 2.4400 122.45589 0.9576 5.8658 2.6136

6 650 HCR 134.39001 1.7493 134.38562 0.8247 -3.8568 -2.5000

6 518 HCR 300.46245 0.8970 300.46261 0.5191 1.5940 2.1791


We remove the worst outlier by copying the recommendation into the outlier observations

file, which now contains two entries.

outliers.obs

6-1 HCR 107.02476 0.8328

518-6 HCR 120.46179 2.374

Network Adjustment is executed. From the new Network Adjustment Report, we find that

only the local tests pass. There are no more outlier observations in the network. With

removal of the observations mentioned, the computed a posteriori variance factor of unit

weight improves further (to 0.26832), indicating high quality measurements.

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements E-1

Appendix E. Deformation Analysis of a Buried Water Main -

Epoch 2008-08-27 to 2008-10-21


buried water main in section 6.2. The settings and steps are described. The geometrical

deformation analysis of the network between epochs 2008-08-27 and 2008-10-21 follows.

The confidence level is 95%. Recall that each epoch is adjusted with minimal constraints

and outliers are identified in that context before any deformation analysis begins, so these

networks of observations are known to be internally consistent (see Appendix D). The

epochs will be known as epoch 0 (2008-08-27) and epoch 1 (2008-10-21) to allow easier

reuse of the instructions so that further analysis (of other time intervals) can be performed

without settings changes. First the contents of the specifications files are shown.


Adjust Network <

Epochs <

Epoch 0 <

Observations < Minimal Azimuth <> epoch 0 >

Observations to Exclude < epoch 0 outliers >

Point Number Additive < 10000 >

>

Epoch 1 <

Observations < Minimal Azimuth <> epoch 1 >

Observations to Exclude < epoch 1 outliers >


>

>

Coordinates <

Initial Coordinates <>

Network Adjustment-Epochs 0-1-exported coordinates-spaced >


Datum < Datum >

Stable Points < Stable Points >


Report Name < Epochs 0-1 >


Plot Name < Epochs 0-1 >

Show Plot < n >

Approx. Plotting Coordinates < Initial Coordinates >

Export Coordinates <

File < tabbed >

Format <

Fields < P E N H >

Delimiter < tab >

Digits < 5 >

>

>

>

Deformation Analysis.spec

Analyse Network Deformation <

Adjusted < Epoch 0 <> Epoch 1 >

Report < - >



>

Aside from the Network Observations and associated outliers, the other adjustment input is

the coordinates. The file “Initial Coordinates.xyz” is identical to that used in Appendix D, so

it is not repeated here. It supplies initial estimate coordinates for least squares. A datum

definition file, “Datum.fix” contains the fixed- or free-ness for each coordinate of each point

which should not be free. “Minimal Azimuth.obs” contains the azimuth for the minimal

constraint datum. Before a point can be held fixed, correct coordinates must be computed for

it. A point must either be listed with some coordinate fixed in the datum definition file, or

listed in “Stable Points.txt” to be considered as a single point in the adjustment of

observations from multiple epochs. “Stable Points.txt” or “Datum.fix” will most likely be

modified for each analysis iteration. “Stable Points.txt” starts out as an empty file, and the

datum definition files are shown here.

Datum.fix

517 ! ! ?


Minimal Azimuth.obs

518-517 AZ 122.46 0.5

Now that the observations and coordinates are organized and the settings have been checked,

the analysis can be done by executing Network Adjustment followed by Deformation

Analysis. Two Adjusted Survey Network files are generated by Network Adjustment, one

for each epoch. These files are the input for the analysis computations including the

congruency tests. Deformation Analysis is executed. Let us examine the first analysis

report.

================================================================================

Deformation Analysis Report

================================================================================

Pooled variance factor: 0.25956

================================================================================

Horizontal Global Congruency Test


Upper critical value: 1.57

Test statistic: 49.27

49.27 < 1.57

================================================================================

Global congruency test failed.

The horizontal network is suspected of geometrical deformation.


================================================================================

Horizontal Local Congruency Tests



================================================================================

Notes:

For any point's displacement to be considered significant,

the test statistic must exceed the critical value

Points with significant displacement are flagged with an 'X'

--------------------------------------------------------------------------------

Displacement Test Displacement

Point Amount Azimuth Statistic Significant?

--------------------------------------------------------------------------------

1 0.0036 0.00000 9.55

6 0.0034 15.15184 32.58 X

518 0.0014 303.41242 7.13

650 0.0007 171.52116 1.16

651 0.0011 201.48051 5.20

652 0.0010 246.02150 3.33

1001 0.0035 203.37458 4.36

1002 0.0016 240.15184 1.03

1003 0.0006 218.39353 0.15

1004 0.0024 236.58341 2.18

1008 0.0082 346.38232 26.23 X

9001 0.0709 28.00385 1024.87 X

9002 0.0082 22.50012 15.44 X

================================================================================

Error Ellipses of Displacement


================================================================================

Point Semi-Major Semi-Minor Azimuth

Number Axis Axis (D.MMSS)

--------------------------------------------------------------------------------

1 0.0051 0.0020 21.13594

6 0.0021 0.0015 30.37002

518 0.0018 0.0005 122.46000

650 0.0034 0.0018 37.20293

651 0.0020 0.0016 92.23210

652 0.0022 0.0018 171.57505

1001 0.0058 0.0054 169.58402

1002 0.0056 0.0052 11.51095


1003 0.0057 0.0052 53.05203

1004 0.0056 0.0054 124.26378

1008 0.0061 0.0051 41.48424

9001 0.0078 0.0031 20.22459

9002 0.0071 0.0026 24.32367

Points 1, 517, 518, 650, 651, 652, and 1001 through 1004 can now be considered stable.

First, these points are listed as stable between epochs, and their coordinates are estimated by

the current minimal constraint adjustment.

Stable Points.txt

1, 517, 518, 650, 651, 652, 1001, 1002, 1003, 1004

Network Adjustment is executed, but the local test fails for one observation. The possible

outlier observations are listed. Note that the points observed at the first epoch (2008-08-27)

have 10000 added to their point numbers, and those observed at the second epoch (2008-10-

21) have 20000 added.

=========================================================================================


=========================================================================================

Notes:

Residuals (corrections applied to raw observations) are in the same units

as their associated observable's standard deviation.

Observations marked with '?' are suspected outliers.

=========================================================================================


=========================================================================================



-----------------------------------------------------------------------------------------

650 1 HCR 87.33322 2.0759 87.33248 0.8203 -7.4178 -3.8898 ?

651 20006 HCR 84.17570 3.1689 84.18058 1.4272 8.8173 3.1164

10006 1 HCR 107.02575 0.5037 107.02568 0.4286 -0.7475 -2.8243

10006 518 HCR 300.46245 0.9363 300.46267 0.4977 2.2384 2.8223

650 19001 HCR 99.15165 1.1136 99.15141 0.6923 -2.3740 -2.7220

650 1 HCR 87.33276 2.0759 87.33325 0.7888 4.9342 2.5696


The top outlier observation indicates that either point 650 or point 1 is actually unstable.

Referring to the deformation analysis report for the minimal constraint datum when all points

are treated as unstable, point 1 exhibits a coordinate displacement of 3.6 mm, and point 650

only 0.7 mm. The semi-major axis of the error ellipse for the displacement of point 650 is

3.4 mm and the semi-minor axis is 1.9 mm. Clearly, point 650 can be considered stable.

Therefore point 1 should be suspected of being unstable. The next time Network Adjustment

is executed, all the local tests pass. New coordinates have now been computed for the stable

points, and the points 517, 518, 650, 651, 652, 1001, 1002, 1003, and 1004 can now be held

fixed. Since the datum is no longer minimally constrained, the azimuth pseudo observation

is no longer needed. Network Adjustment and Deformation Analysis are executed, and the

deformation analysis report follows.

================================================================================

Deformation Analysis Report

================================================================================

Pooled variance factor: 0.26166

================================================================================

Horizontal Global Congruency Test



Test statistic: 812.68

812.68 < 2.04

================================================================================

Global congruency test failed.

The horizontal network is suspected of geometrical deformation.


================================================================================

Horizontal Local Congruency Tests



================================================================================

Notes:

For any point's displacement to be considered significant,

the test statistic must exceed the critical value.

--------------------------------------------------------------------------------

Displacement Test Displacement

Point Amount Azimuth Statistic Significant?

--------------------------------------------------------------------------------

1 0.0042 4.05082 50.80 Yes

6 0.0040 18.53099 225.07 Yes

1008 0.0089 348.56369 42.06 Yes

9001 0.0716 27.59497 5264.25 Yes

9002 0.0088 23.22088 106.57 Yes

================================================================================

Error Ellipses of Displacement


================================================================================

Point Semi-Major Semi-Minor Azimuth

Number Axis Axis (D.MMSS)

--------------------------------------------------------------------------------

1 0.0018 0.0015 11.14440

6 0.0009 0.0008 122.14323

1008 0.0047 0.0042 84.06501

9001 0.0031 0.0025 11.45486

9002 0.0026 0.0021 18.12218

Bird 2009 Analysis of Survey Point Displacements Using Total Station Measurements F-1

Appendix F. Deformation Analysis for Monitoring

Dangerous Trees


network for tree monitoring in section 6.3. First the settings are shown, then the input data is

presented.

TRA to Network.spec

Centring Method <

ID < Laser Plummet >

Error < 0.6666 >


>

Centring Method <


Error < 0.3333 >


>

Centring Method <

ID < Prism on Tree Top Point >


Error < 0 >

>

Centring Method <

ID < Prism on Tree Bottom Point >


Error < 0 >

>

Survey Instrument <

ID < TCA 2003 >

EDM < 1+1 >

Directional < 0.5 >

Compensator < 0.3 >

>


ID < Tripods >


Sets < 1 >

Instrument <

Re-Level < No >


Re-Centre < No >

Centring < Laser Plummet >


>

Target <



>

>


ID < Tripod to Tree Top Point >

Like < Tripods >

Target <

Centring < Prism on Tree Top Point >


>

>


ID < Tripod to Tree Bottom Point >

Like < Tripods >

Target <

Centring < Prism on Tree Bottom Point >


>

>


ID < Free to Tripod >

Like < Tripods >

Instrument <


Re-Level < No >

Re-Centre < No >

>

>


ID < Free to Tree Top Point >

Like < Tripod to Tree Top Point >

Instrument <


Re-Level < No >

Re-Centre < No >

>

>


ID < Free to Tree Bottom Point >


Like < Tripod to Tree Bottom Point >

Instrument <


Re-Level < No >

Re-Centre < No >

>

>


ID < Tree Monitor >

Default <

Reduction < 3D >

Measurement Scheme < Tripod to Tree Bottom Point >

>

But <

to < 731 >

Reduction < 3D >

Measurement Scheme < Tripod to Tree Top Point >

>

But <

to < 63-64 >

Reduction < 3D >

Measurement Scheme < Tripods >

>

But <

to < 99 >

Reduction < 3D >


>

But <

to < 1-8 >

Reduction < 3D >


>

But <

at < 100-102 >

Reduction < 3D >

Measurement Scheme < Free to Tree Bottom Point >

>

But <

at < 100-102 >

to < 731 >

Reduction < 3D >

Measurement Scheme < Free to Tree Top Point >

>

But <

at < 100-102 >


to < 63-64 >

Reduction < 3D >


>

But <

at < 100-102 >

to < 99 >

Reduction < 3D >


>

But <

at < 100-102 >

to < 1-8 >

Reduction < 3D >


>

>


Input File < 2006-01-19- EN-MONITOR-mini-meaned >

Output File < 2006-01-19-network >

Reduction RuleSet < Tree Monitor >

>


Input File < 2007-10-16 JDH-edit-mini-meaned >

Output File < 2007-10-16-network >

Reduction RuleSet < Tree Monitor >

>


Adjust Network <

Epochs <

Epoch 0 <

Observations < MINIMAL CONSTRAINT AZIMUTH <> 2006-01-19-network

>


>

Epoch 1 <

Observations < MINIMAL CONSTRAINT AZIMUTH <> 2007-10-16-network

>


>

>

Coordinates <

Initial Coordinates <>


Network Adjustment-Epochs 0-1-exported coordinates-spaced >


Datum < Datum >

Stable Points < Stable Points >


Report Name < Epochs 0-1 >

Plot Name < Epochs 0-1 >

Show Plot < y >


Override Ellipse Exaggeration < y >

Ellipse Exaggeration Factor < 50 >

Export Coordinates <

File < spaced >

Format <

Fields < P E N H >

Delimiter < space >

Digits < 5 >

>

>

>

Deformation Analysis.spec

Analyse Network Deformation <

Adjusted <

Epoch 0 <>

Epoch 1 <>

>



Override Ellipse Exaggeration < y >

Ellipse Exaggeration Factor < 50 >

Report < Epoch 0-1 >

>

The input data follows.


1 1487.00900 654.69700 100.08900


2 1499.99937 699.99813 100.00581

3 1490.93665 681.96505 101.15283

4 1496.17670 721.35694 100.67119

5 1513.18346 727.61588 97.95537

6 1516.20114 720.10284 97.30891

7 1517.93943 697.79131 96.63243

8 1524.49101 676.30824 96.57089

37 1493.43531 689.54922 110.24611

64 1488.29988 666.70747 100.71297

99 1497.21543 656.68165 97.18629

721 1502.59505 667.89133 98.51880

723 1497.70732 668.94493 100.47919

731 1503.58467 666.07680 110.58097

Datum.fix

1 ! ! !

2 ! ? ?

MINIMAL CONSTRAINT AZIMUTH.obs

1-2 AZ 16.0002 1

2006-01-19- EN-MONITOR-mini-meaned.tra

* Doubled observations made on both faces


OCC 1 1.509 CTRL

BS 2 1.616 16.00057 89.58069 47.1259 .000 TH

IS 3 1.300 8.11372 88.13209 27.5634 .000 TH

IS 64 0.200 6.08012 93.14006 12.0982 .000 TH

IS 99 0.200 78.59467 112.02107 11.2180 .000 TH

IS 731 0.000 55.31380 65.55345 22.0215 .000 TH

* One faced observations made on face left


OCC 1 1.509 CTRL

BS 2 1.616 16.00028 89.58144 47.1259 .000 TH

IS 721 0.000 49.44545 98.34294 20.6518 .000 TH

* Doubled observations made on both faces


OCC 64 1.537 CTRL

BS 2 1.616 19.21532 91.01027 35.2909 .000 TH

IS 1 1.508 186.08254 93.05143 12.0959 .000 TH



OCC 64 1.537 CTRL


BS 2 1.616 19.21465 91.01126 35.2909 .000 TH

IS 3 0.200 9.48372 93.18490 15.5099 .000 TH

IS 99 0.200 138.21133 109.54537 14.2703 .000 TH



OCC 99 1.505 CTRL

BS 64 1.535 318.20496 75.08123 13.8804 .000 TH

IS 1 1.300 258.58478 75.25467 10.7423 .000 TH



OCC 3 1.622 CTRL

BS 2 1.616 26.39587 93.16094 20.2123 .000 TH

IS 1 1.300 188.10404 92.52381 27.5833 .000 TH

IS 37 0.000 18.13099 46.54153 10.9354 .000 TH

IS 64 0.200 189.47346 96.50562 15.5959 .000 TH

IS 723 0.000 152.30341 98.53263 14.8538 .000 TH

2007-10-16 JDH-edit-mini-meaned.tra



OCC 101 1.750 CTRL

BS 1 0.200 188.06224 95.55436 24.5496 .000 TH

IS 2 1.300 24.19186 93.45252 23.2370 .000 TH

IS 3 0.520 8.49204 110.16484 3.3368 .000 TH

IS 37 0.000 15.37117 56.13254 13.3419 .000 TH

IS 64 0.200 190.02067 98.48010 12.4973 .000 TH

IS 723 0.000 143.49417 100.46045 12.5236 .000 TH



OCC 102 1.750 CTRL

BS 99 0.200 137.51079 114.17072 11.5357 .000 TH

IS 1 0.200 197.50500 100.10262 10.4357 .000 TH

IS 3 1.300 2.33135 88.57371 17.5110 .000 TH

IS 64 0.200 320.16587 112.46159 3.1487 .000 TH

IS 721 0.000 74.41467 105.38369 13.3966 .000 TH



OCC 1 1.572 CTRL

BS 64 0.200 6.08317 93.32025 12.1044 .000 TH

IS 731 0.000 55.50006 66.05235 21.9727 .000 TH

analysis of survey point displacements using total station...

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