surveying & prospection for archaeology & environmental science topographic surveying &...
TRANSCRIPT
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 +
+
-
-
Coordinates in a plane
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
Coordinates in a plane
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
Referencebearing (N)
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
Referencebearing (N)
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
Referencebearing (N)
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
Surveying in practice
Using levels
Radial method:position instrument centrally to survey points
N
object
topography
Surveying in practice
Using levels
Radial method:position instrument centrally to survey points
N
object
topography
Survey points defineresolution/accuracyof final map...
Surveying in practice
Using levels
Radial method:position instrument centrally to survey points
N
object
topography
Survey points defineresolution/accuracyof final map...
Can interpolate - i.e. smooth between the pointsAnd extrapolate - i.e. extend beyond the points
Surveying in practice
Using levels
Radial method:position instrument centrally to survey points
N
object
topography
Survey points defineresolution/accuracyof final map...
Can interpolate - i.e. smooth between the pointsAnd extrapolate - i.e. extend beyond the points
Surveying in practice
Using levels
Radial method:position instrument centrally to survey points
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
Surveying in practice
Using levels
Radial method:position instrument centrally to survey points
N
object
topography
Surveying in practice
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
Surveying in practice
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
Surveying in practice
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
Surveying in practice
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)
Surveying in practice
Using levels
Differential Levelling:can be used to survey topography (or other) transects
p0
p1
p0 = known point (benchmark)
Surveying in practice
Using levels
Differential Levelling:can be used to survey topography (or other) transects
More efficiently with use of intermediate sights
p0
p1
p0 = known point (benchmark)
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
Break of slope (break in slope; slope break)
- dramatic change in angle(or tangent of curve)
- usually best place to put staff
Think in triangles(preferably in 3D)
Useful concepts
Break of slope (break in slope; slope break)
- dramatic change in angle(or tangent of curve)
- usually best place to put staff
Think in triangles(preferably in 3D)
Useful concepts
Break of slope (break in slope; slope break)
- dramatic change in angle(or tangent of curve)
- usually best place to put staff
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