Lecture index: Why contour? / Coordinate
systems and map projections. / Types
of 'earth science' surfaces often contoured? / Examples.
/ Contouring algorithms. / Wire
frames and other forms of visualization.
/ Contouring software. / Exercise
Reading: Computer contouring, in Davis, 1986, Statistics and
Data Analysis in Geology, Wiley, p. 353-383. Available as a pdf
A primary reason is to visualize an actual or
theoretical surface, and see patterns or find anomalies, to understand.
Literature exists on learning 'styles' that people naturally have
and can develop. A visual learning style is one of the most common
and contour maps feed into this ability. The literature on scientific
visualization is a significant topic for good reason.
Sometimes there is a more practical reason.
One may want to interpolate values in between points sampled on
a surface to estimate the value for that specific point. For example,
if you wanted to estimate drilling depth to a given horizon at
a new locality based on nearby drill holes. Or you may want to
estimate the volume of oil in a dome. Sometimes
the contour surface may be input for modeling (e.g. contour maps
of groundwater tables yields flow nets).
Contour maps are a very common product of the
environmental, oil and mineral industry. If you aren't producing
them in your career, you will at the very least be using them
Finally, they can be very aesthetically pleasing
to create and to see.
systems and map projections.
A very basic form of data input for surface modeling is typically
- x, y, z, where x and y represent position and z is some value
of interest. When there are geographic coordinates involved the coordinate
system is important. The two most commonly used geographic coordinate
systems used are:
- latitude and longitude: These are positions described by angular relationships
with the earth's rotation axis as a fundamental line of reference,
and typically involve considerable distortion of lengths and
areas, especially for east-west lines. Note that in order to
make things easier you will often want to transform degrees°
minutes' and seconds" into decimal degrees. This is easy
to do. Divide the minutes by 60 and the seconds by 360 and add
both to the degrees.
- UTM (Universal Transverse Mercator): if you want to minimize distortion involved with
representing a curved surface on a flat page, the UTM system
is often used. A projection is the mathematical algorithm by
which points on the curved earth's surface are mapped onto a
flat sheet of paper. One has to quantify the actual earth's shape
as an ellipsoid in order to do this. The geodetic datum
is an attempt to describe its shape with much greater precision.The
earth is also broken up into UTM
zones by longitude and latitude, and for each zone a
position is described by an easting and northing.
The easting is the number of meters east of the lower left reference
corner of that particular UTM zone, and the northing is the number
of meters north of the same reference corner. Note that this
is a conventional x, y coordinate system, with eastings plotted
along the x axis, and northings along the y axis. Below is a map from the USGS site on UTM showing the zones.
- The geodetic
datum model for the earth is important when positional precision is
required. NAD83 is a commonly used geodatum associated
with North America. It differs a bit from WGS84, a widely
used ellipsoid model for the earth.
The most important thing is to know what coordinate system and
geodetic datum model your data is in. If you plot longitude and
latitudes with different projections you will get misplots.
This misplots can easily be 100s of meters, and so can be significant.
If you need to register two data sets of positions with each
other, then they must use the same geodetic datum and projection
- Most GPS units can be set to give either
latitude and longitude or UTM. I find it often advantageous to
record information initially in latitude and longitude. The GPS
system is based on the ellipsoid model in WGS84.
This is also the one that Google Earth uses.
- USGS site on coordinate systems including UTM.
- USGS page specifically on UTM.
- USGS site on map projections - details, all 397 pages of them.
- NOAA site, beta version of lat/long to UTM conversion calculator.
Types of 'earth science' surfaces often contoured?
There are many. Below is a partial list.
- subsurface surfaces:
- stratigraphic contact.
- isopachs (thicknesses).
- chemical concentration in soil or water.
- concentration of a discrete entity in a sampline area (e.g. of fracture
density, population density).
- magnetic anomaly maps.
- gravity anomaly maps.
- heat flow.
- a large variety of possibilities.
- A contour map is a model, an approximation
of the real surface. Always remember this!
An example: Puget Sound Aeromagnetic Maps and Data
By Richard J. Blakely1, Ray E. Wells1, and Craig S. Weaver2, U.S.
Geological Survey Open-File Report 99-514 Version 1.0, 1999.
Note that this USGS map does not show the typical contour lines
as seen on many maps of surfaces. Instead it is a shaded relief map.
We will discuss these more. With the advent of cheap computing power
and software these have become much more common. What patterns
do you see in this map, and why do they exist? One thing to realize with some of these maps is that there is shading based on an illumination point. This point can be changed and the apperance of the map will be somewhat changed. Gradient slopes in some directions can become enhanced and in other directions subdued, which of course can influence subjective visual interpretation.
Above is an example of a strip across
the Cedar Creek 7.5' USGS topographic quad, showing both contour
lines and an underlying shaded relief map. What basic information
is missing from this image that would help make it a more usable
map? What patterns do you see in this topography and why do you
think they exist?
Aeromagnetic contour map of Georgia. Note the very striking linear pattern in the middle of the state - this reflects various faults and geologic belts in the hinterland of Southern Appalachian geology. The use of contour and shaded relief maps to image geophysical data is standard. Image source USGS site: http://pubs.usgs.gov/of/2001/of01-106/
Contour map of Mercury concentrations in Long Island Sound. What conclusions can you draw from this map pattern. How well constrained do you think various aspects of the pattern are (how would additional samples change the pattern? Image source USGS site: http://pubs.usgs.gov/of/2000/of00-304/htmldocs/chap07/index.htm
Contouring by hand can work well, but is much
more subjective. This is one reason computer generated maps are
now preferred. However, expert knowledge can help quite
a bit in producing a contour map if you know the character of
the surface. This might be considered the 'art' behind
the product. A simple example is rounded vs. angular geometries
for a folded surface. If you know the fold style from observation
and/or experience then you can better complete the contours given the discretion one has between control points. Such
expert knowledge helps you draw a better contour map with less
data. A better solution is to have better control, i.e. more
data points, but data costs!! It is also quite important to
use your expert knowledge about what is being mapped to evaluate
the maps that computer programs generate for you.
Surface trend analysis and mathematical
surfaces: This is similar to fitting
a line in 2-D graph space - a plane or some more complex curved
surface can be fit in 3-D. One advantage of such an analysis is
that the surface can then be very efficiently represented or captured
- as an equation. This is a link to a quick
exploration of modeling surfaces
in Excel as a combination of continuous functions and random
fluctuations. One can also get useful information by taking derivatives
of the surfaces. Such derivatives will map slopes and gradients
of change in slope. This is one of the options in Surfer. It can be especially useful if you want to look for anomalies. For example a regional slope can be modeled, and then the difference between that and observed values is the residual, and can be thought of as an anomaly. This is a path often used in gravity modeling in geophysics.
This is a crucial consideration! Different algorithms can produce
very different results. The fewer control points you have the greater the difference can be.
- Triangulation and interpolation between
points is a simple approach, and one that often guides hand
contouring. The point where a contour line should intersect a
line between two constraining data points is interpolated in
some manner. Then lines can be drawn connecting the identified
points at a particular contour level. A linear interpolation
between two points assumes a local planar character, and thus
the model surface is assume to be faceted like a crystal. This
is a first approximation, but the resulting contour lines are
often not realistic looking.
- Gridding and distance weighting functions: Gridding is where values are computed for a grid,
from primary data which is not evenly distributed (the typical
case). This makes calculation of contour line positions, and/or
production of DEMs and digital relief images, much easier. This
can be very complex, but basically the value of a grid point is computed
as a function of the nearest neighbor control points. Obviously,
the farther away a data control point is from a given grid point,
the less influence it should have in the computation for the
surface value for that point. Kriging is a 'magic' word
often used, but in many situations is argued to be one of the
best approaches. Pay close attention
to this in your reading. You will
explore the difference different contouring algorithms make.
Once again, the smaller your data set, the more important this
- Link to direct comparison of different gridding techniques - http://www.spatialanalysisonline.com/output/html/Griddingandinterpolationmethods.html
- More detailed looking at kriging - http://oilandgastraining.org/data/gl61/G3921.asp?Code=23365
Wire frames and other forms of visualization.
In addition to the classic contour lines, many
other ways of representing or visualizing a surface can now be
done easily. Wire
frame diagrams attempt to give a realistic rendering of the surface
from a defined oblique perspective. Shaded relief maps typically
provide a birds view perspective of a obliquely illuminated surface
with a color scheme that reflects z values. Finally, animations
known as fly-through are also popular. Some examples are given
- One example of utility of transect (wire
frame) models - Justin
Covey's thesis - check out the transects.
- DEMs and shaded
relief maps. Digital Elevation Models are computer files
that list elevation values for a spatial grid with a given spacing.
These are becoming more and more common. Surfer can produce shaded
relief maps from a gridded surface. It can also work with shaded
relief images. DEMs for Nebraska 7.4 minute USGS topographic
quads are available from the Department
of Natural Resources, both with a 30 m and 10 m grid spacing.
- fly-through animations (some
examples). This is really good techno-geek stuff, and beyond
the scope of this course.
Image model multiple subsurface geologic layers for basin analysis and petroleum exploration purposes in Alaska. Image source: http://energy.er.usgs.gov/gg/research/modeling.html
Surfer is a commercial software program that works very
well for modeling surfaces. Its major draw back is the cost,
but we are fortunate to have access to it. This is the program
we will use, and it is often used in industry.
Surface 3. This is
contouring software for the Mac available from the Kansas Geological
Survey. It also has some nice online description
of how the program works, discussing different gridding options
and some of the theory. However, it has not been supported with
time and works less and less well (or not at all ) with OS 10
ArcMap also had the ability to contour data, which we will introduce you to later. The contouring routines are to be found in ArcToolbox. This is a topic beyond the scope of this course, but there are a variety of help options available within ArcGIS and out on the web that you can use to teach yourself how to do this.
There are a variety of freeware contouring programs available that can be readily found through the Google search engine. I am unacquainted with them.
Exercise 5: Producing contour maps of geoscience data.
Data sets to play and learn with.
Possible data sources:
- Quality-Assessed Agrichemical Contaminant Database for Nebraska Ground Water.
- Utah Well and Spring Database.
- Google Earth provides interesting possibilities in terms of creating your own data, some of which are listed below (other possibilities definitely exist). You can set Google Earth so that instead of providing latitude and longitude of a cursor point it provides the UTM position. This is very useful because then your x and y are in meters, and the spatial distortion inherent with latitude and longitude is avoided. Simply contouring the existing landscape would not be very interesting, but there are a variety of situations where you can contour something else by obtaining x-y points at its surface expression. You will need 20 to 30 such points at a minimum for the purposes of this lab. Of course your results will only be good as the underlying Google Earth DEM accuracy permits.
- Mapping the groundwater table in the western Sand Hills of Nebraska: There are portions of the Sand Hills where the interdune depressions are filled with lakes. These lakes are the emergent part of a water table that extends under the adjacent dunes. The lakes are at different elevations, and so there is topography on the groundwater table for one to capture. My mapping x and y as the center of the lake and z as the elevation for a number of lakes one can then contour the surface to get an idea of what the regional groundwater flow pattern is like. An exercise like this can also be done where abundant enough sinkhole lakes occur.
- Structural contours on deformed layers: In more mountainous areas where layers are tilted and folded it can be possible to follow a distinctive layer or a distinctive stratigraphic contact up and down across valleys and ridges. By capturing x, y and z points on the surface trace of that distinctive feature one can then make a structure contour map on the layer or surface and better understand the structural geometry.
- Contouring dissected remnant geomorphic surfaces: In some places, such as just east of Broken Bow headward erosion has cut back into an older geomorphic surface, leaving bits of the surface preserved between the various drainage divides. By obtaining x, y, z points on the preserved sections of the remant surface one can contour to build a model of what the morphology of the older surface might have been.
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