Transcript Surveying & Prospection for Archaeology & Environmental

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
+
-
x
-
(0,0)
Perpendicular axes
Origin at (0,0)
Coordinates increase
right & up of origin
+ Coordinates decrease
down & left of origin
Descarte (1637)
Coordinates in a plane
Cartesian coordinates
x
x
x
(-3,-2)
(0,0)
(3,4)
Coordinates of point
given by bracketed
pairs of numbers:
(right,up)
(x,y)
(Easting,Northing)
-depending on
coordinate system
used
Coordinates in a plane
Often easier to avoid
negative values by
x
(1004,1006) increasing origin
coordinates
+
x
x
(1001,1002)
(1000,1000)
x
(998,999)
+
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
Northing
x
p0 x
Easting
p1
Find coordinates of
p1 in relation to p0
Measuring in a plane
Reference
bearing (N)
x
p1
p1 has a unknown coordinates
p0 (instrument) has known coordinates
(0,0) for the moment
p0 x
Instrument
reference bearing is known (N)
Finding Coordinates
Northing = d cos(ө)
Reference
bearing (N)
p0
Use instrument to measure:
d - (horizontal) distance p0-p1
x
p1 ө - angle between North &
bearing of p1 from p0
d
ө = bearing from
reference
d = distance from
p0 to p1
ө
Easting = d sin(ө)
with trigonometry...
Polar Coordinates
Finding Coordinates
Reference
bearing (N)
Northing = d cos(ө)
x
p1
d 10m
ө
p0 x
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
Easting = d sin(ө)
ө also called the azimuth
Finding Coordinates
Reference
bearing (N)
Northing = d cos(ө)
x
p1 (6,8)
p1(Easting) = p0(Easting) + (d sin(ө))
d 10m
p1(Northing) = p0(Northing) + (d cos(ө))
So if p0=(1000,1000) then
ө
p0 x
36.87°
p1(Easting,Northing) = (1006,1008)
Easting = d sin(ө)
Trigonometry
Opposite
opposite
sin  
hypotenuse
Abscissa
abscissa
cos 
hypotenuse
ө
opposite
tan  
abscissa
Tip: abscissa = ‘adjacent’
Trigonometry
Opposite
opposite
sin 
hypotenuse
Abscissa
abscissa
cos 
hypotenuse
ө
opposite
tan 
abscissa
SOHCAHTOA
Tip: abscissa = ‘adjacent’
Trigonometry - checking
Opposite
Abscissa
Use Pythagoras theorem:
a2+b2=c2
ө
Opposite2+Abscissa2=Hypotenuse2
Trigonometry - checking
Opposite = 6
Abscissa = 8
Use Pythagoras theorem:
a2+b2=c2
ө
Abscissa2+Opposite2=Hypotenuse2
82+62=102
64+36=100
Measuring height (Level)
Object height (Z)
= Instrument height - Signal height + Known height
= Ih - Sh + p0 height
horizontal distance (d)
Signal
height
(Sh)
Instrument
height (Ih)
Objekt
Known height (benchmark)
p0
p1
Object
height (Z)
relative
known
height
Remember: Instrument must be able
to see base of signal staff.
Measuring height (Total Station)
Signal
height
(Sh)
Instrument
height (Ih)
horizontal distance (Hd)
p0
Station height (Stn Z)
p1
Object
height (Z)
relative
known
height
Surveying in practice
Using levels
Radial method:
position instrument
centrally to survey points
object
N
topography
Surveying in practice
Using levels
Radial method:
position instrument
centrally to survey points
object
N
topography
Surveying in practice
Using levels
Radial method:
N
position instrument
centrally to survey points
Survey points define
resolution/accuracy
of final map...
object
topography
Surveying in practice
Using levels
Radial method:
N
position instrument
centrally to survey points
Survey points define
resolution/accuracy
of final map...
object
Can interpolate - i.e.
smooth between the
points
And extrapolate - i.e.
extend beyond the
points
topography
Surveying in practice
Using levels
Radial method:
N
position instrument
centrally to survey points
Survey points define
resolution/accuracy
of final map...
object
Can interpolate - i.e.
smooth between the
points
And extrapolate - i.e.
extend beyond the
points
topography
Surveying in practice
Using levels
Radial method:
N
position instrument
Can interpolate
- i.e.points
centrally
to survey
smooth between the
points
And extrapolate - i.e.
extend beyond the
points
topography
But can never
compensate for
bad choice of
survey points!
object
GIGO: Garbage In - Garbage Out
Surveying in practice
Using levels
Radial method:
position instrument
centrally to survey points
object
N
topography
Surveying in practice
Using levels
Traverse:
a continuous series of lines of measured distance.
angles & distances allow points to be located
angles measured relative to previous bearings
p1
p2
p4
N
p0
p3
p5
angles always clockwise
Surveying in practice
Using levels
Traverse:
a continuous series of lines of measured distance.
Use closed traverse for extra accuracy - errors check by
trigonometry
p1
p2
p4
N
p5
p0
p3
p6
Surveying in practice
Using levels
Combining methods:
Large areas of topography & features can be surveyed using
radial, differential levelling & traverse methods together
p1
p4
p3
p5
p3
p0
p6
p0
Surveying in practice
Using levels
Differential Levelling:
determining the difference in elevation between
points on a transect.
p1
pA
pB
p0 = known point (benchmark)
pC
Surveying in practice
Using levels
Differential Levelling:
can be used to survey topography (or other) transects
p1
p0
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
BS
IS
IS
FS
p1
p0
p0 = known point (benchmark)
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)
AND
Practicalities!
Useful concepts
Different angle measurements
degrees:
trigonometry, common usage
full circle = 360°
gradians:
surveying, engineering
full circle = 400 gon (or grad)
radians:
mathematics, physics, Excel
full circle = 2π rad
Useful concepts
degrees: full circle = 360°
gradians: full circle = 400 gon (also called ‘grad’)
radians: full circle = 2π rad
0 rad
0grad
0°
45°
315°
1.5π rad
300gon
270°
90° 100gon 0.5π rad
225°
135°
180°
200gon
π rad
Useful concepts
Conversion between angle measures:
use DRG► (or DEG etc) button on calculator
gon to degrees:
angle _ in _ gon
angle _ in _ deg rees 
* 360
400
gon to radians:
angle _ in _ gon
angle _ in _ radians 
*
200
Useful concepts
Conversion between angle measures:
Excel uses radians in formulae (e.g. =sin(), =cos(), =tan())
In Excel:
degrees to radians:
=RADIANS(angle_in_degrees)
gon to radians:
=RADIANS(angle_in_gon/400*360)
Alternative data acquisition
Aerial photographs
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)
Alternative data acquisition
Prospection data
- spatial sample data