surveying & prospection for archaeology & environmental science topographic surveying &...

Surveying & Prospection for Archaeology & Environmental Science

Topographic Surveying & Feature Mapping

Phil Buckland

Contents

•Topographic survey & feature mapping•Equipment - introduction•Coordinates & Trigonometry - the basic maths of triangles

•Surveying in practice•Alternative data acquisition (briefly)

Topographic survey & feature mapping

Topographic survey- create a cartographic representation of landscape features

- coordinate data (x,y,z - or variants of)- detail (scale/resolution) defined by project aims

- end product usually a 2D contour map (but 3D models becoming more common)

- field techniques improve realism/accuracy

Topographic survey & feature mapping

Feature mapping (objects)- site specific, many variations- locate & relate objects/areas spatially- includes attribute data on objects (object type, name etc.) as well as coordinates.This is a key feature of GIS

- end product often a 2D map or 3D model- can overlay on topographic maps

Equipment - introduction

Three groups used (in this course):

- Levels (dumpy level, theodolite)

- Total Stations (EDM - Electronic Distance Measurers)

- GPS (Global Positioning System)

Equipment - introduction

Coordinates

Relate points/objects together in space- in a plane (horizontal)- vertically (height)

Using coordinates (e.g. x,y,z)with the help of angles and distances

Bearing = angle relative to reference direction (e.g. North, grid North...)

Coordinates in a plane

Cartesian coordinates

Perpendicular axesOrigin at (0,0)Coordinates increase right & up of originCoordinates decrease down & left of originDescarte (1637)

(0,0)x +

+

-

-


Cartesian coordinates

Coordinates of point given by bracketed pairs of numbers: (right,up)(0,0)

x

(3,4)x

(-3,-2)x

(x,y)(Easting,Northing)-depending on coordinate system used


Often easier to avoid negative values by increasing origin coordinates

+

+

(1000,1000)x

(1004,1006)x

(1001,1002)x

(998,999)x

NOTE: Some countries (incl. Sweden) use on maps:y=East x=North

Others use opposite (e.g. (England, USA)

We’ll use (Easting,Northing)

Finding Coordinates

p0x

p1x

Find coordinates of p1 in relation to p0

Easting

Nor

thin

g

p0x

p1x

Referencebearing (N)

Measuring in a planeMeasuring in a plane

Instrument

p0 (instrument) has known coordinates

(0,0) for the moment

reference bearing is known (N)

p1 has a unknown coordinates

Finding Coordinates

өNor

thin

g =

d c

os(ө

)

Easting = d sin(ө)

Use instrument to measure:d - (horizontal) distance p0-p1ө - angle between North & bearing of p1 from p0

p0

p1x


ө = bearing from reference

d = distance from p0 to p1

Thetad

with trigonometry...

Polar Coordinates

Finding Coordinates

ө

Nor

thin

g =

d c

os(ө

)

Easting = d sin(ө)p0x

p1x


d 10m

36.87°

Easting = d sin(ө)= 10 sin(36.87)= 10*0.6= 6m

Northing = d cos(ө)= 10 cos(36.87)= 10*0.8= 8m

ө also called the azimuth

Finding Coordinates

ө

Nor

thin

g =

d c

os(ө

)

Easting = d sin(ө)p0x

p1x


d 10m

36.87°

(6,8)

p1(Easting) = p0(Easting) + (d sin(ө))

p1(Northing) = p0(Northing) + (d cos(ө))

So if p0=(1000,1000) then

p1(Easting,Northing) = (1006,1008)

Trigonometry

ө dist

ance

(d)

Hyp

oten

use

Abs

ciss

a

Opposite

hypotenuse

oppositesin

hypotenuse

abscissacos

abscissa

oppositetan

Tip: abscissa = ‘adjacent’

Trigonometry

ө dist

ance

(d)

Hyp

oten

use

Abs

ciss

a

Opposite

ypotenuse

ppositein

ho

s

ypotenuse

bscissaos

ha

c

bscissa

ppositean

ao

t

Tip: abscissa = ‘adjacent’

SOHCAHTOA

Trigonometry - checking

ө dist

ance

(d)

Hyp

oten

use

Abs

ciss

a

OppositeUse Pythagoras theorem:a2+b2=c2

Opposite2+Abscissa2=Hypotenuse2

Trigonometry - checking

ө dist

ance

(d)

Hyp

oten

use

= 10

Abs

ciss

a =

8

Opposite = 6Use Pythagoras theorem:a2+b2=c2

Abscissa2+Opposite2=Hypotenuse2

82+62=102

64+36=100

Measuring height (Level)

Objekt

Instrumentheight (Ih)

Signal height(Sh)

Object height (Z)

= Instrument height - Signal height + Known height

Object height (Z)relative known height

Known height (benchmark)

= Ih - Sh + p0 height

p0 p1

horizontal distance (d)

Remember: Instrument must be able to see base of signal staff.

Measuring height (Total Station)In

stru

men

the

ight

(Ih

)

Signal height(Sh)

Object height (Z)relative known height

Station height (Stn Z)p0

p1horizontal distance (Hd)

angled distance (Ad)

vertical angle (ө)

Surveying in practice

Using levels

Radial method:position instrument centrally to survey points

N

object

topography


Using levels


N

object

topography

Survey points defineresolution/accuracyof final map...


Using levels


N

object

topography

Survey points defineresolution/accuracyof final map...

Can interpolate - i.e. smooth between the pointsAnd extrapolate - i.e. extend beyond the points


Using levels


N

object

topographyCan interpolate - i.e. smooth between the pointsAnd extrapolate - i.e. extend beyond the points

But can never compensate for bad choice of survey points!

GIGO: Garbage In - Garbage Out


Using levels


N

object

topography


Using levels

Traverse:a continuous series of lines of measured distance.angles & distances allow points to be located

p0

N

angles measured relative to previous bearings

angles always clockwise

p1 p2

p3

p4

p5


Using levels

Traverse:a continuous series of lines of measured distance.Use closed traverse for extra accuracy - errors check by trigonometry

p0

Np1 p2

p3

p4

p5

p6


Using levels

Combining methods:Large areas of topography & features can be surveyed using radial, differential levelling & traverse methods together

p1

p3

p4

p5

p6

p3

p0


Using levels

Differential Levelling:determining the difference in elevation between points on a transect.

p0

p1

back

sigh

t

fore

sight

back

sight

fore

sight

back

sight

fore

sight

back

sight

fore

sight

pApB

pC

p0 = known point (benchmark)


Using levels

Differential Levelling:can be used to survey topography (or other) transects

p0

p1



Using levels

Differential Levelling:can be used to survey topography (or other) transects

More efficiently with use of intermediate sights

p0

p1


BS IS IS FS

Useful concepts

Break of slope (break in slope; slope break)

- dramatic change in angle(or tangent of curve)

- usually best place to put staff

1 2 3

Useful concepts




Think in triangles(preferably in 3D)

Useful concepts




Think in triangles(preferably in 3D)ANDPracticalities!

Useful concepts

Different angle measurements

degrees: trigonometry, common usagefull circle = 360°

gradians: surveying, engineeringfull circle = 400 gon (or grad)

radians: mathematics, physics, Excelfull circle = 2π rad

Useful conceptsdegrees: full circle = 360°

0°

45°

90°

135°

180°

225°

270°

315°

gradians: full circle = 400 gon (also called ‘grad’)

0grad

50gon

100gon

150g

on200gon

250gon

300gon

350g

on

radians: full circle = 2π rad0 rad

1.75

π rad

π rad

0.5π rad

0.25π rad

0.75

π rad

1.5π rad

1.25π rad

Useful concepts

Conversion between angle measures:

gon to degrees:

360*400

__deg__

goninanglereesinangle

use DRG► (or DEG etc) button on calculator

*200

____

goninangleradiansinangle

gon to radians:

Useful concepts

Conversion between angle measures:

In Excel:

Excel uses radians in formulae (e.g. =sin(), =cos(), =tan())

=RADIANS(angle_in_degrees)

degrees to radians:

=RADIANS(angle_in_gon/400*360)

gon to radians:

Alternative data acquisition

Orthophotos - geometrically corrected aerial photographs

GPS surveying - varying degrees of accuracy

Satellite data - elevation; infra-red etc.; with image analysis can be used to differentiate land use & more

Existing maps - ordinance survey; historical

All have their uses - can be combined with survey data using GIS software (e.g. ArcGIS) (although corrections may be needed)

Aerial photographs

Alternative data acquisition

Prospection data- spatial sample data

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