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 5.

A primary reason is to visualize a 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 large 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 a lot!

Finally, they can be very aesthetically pleasing to create and to see.

The very basic form of data input is typically - x, y, z, where x and y represent position and z is some value of interest.. Since it is a map consideration of your 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 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. The geodetic datum model for the earth is important when 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. In a small area the relative positions of points is not sensitive to the the projection model. The most important thing is to know what coordinate system and geodetic datum model your data is in. If you plot longitude and latitudes associated with one in the other, 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 system.
• 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.
• USGS site on map projections.
• USGS site on UTM.
• USGS site on GPS.

There are many. Below is a partial list.

• topographic.
• subsurface surfaces:
  • groundwater.
  • fault.
  • stratigraphic contact.
• isopachs (thicknesses).
• chemical concentration in soil or water.
• spatial data concentration (e.g. of fracture density).
• geophysical:
  • magnetic anomaly maps.
  • gravity anomaly maps.
  • heat flow.
• fracture density.
• population densities.
• 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 seen on many maps of surfaces. Instead it is a shaded relief map. We will discuss these. 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?

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. 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.

Contouring algorithms: This is a crucial consideration! Different algorithms can produce very different results.

• 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 is 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 is.
• TEST OF GEOSTATISTICAL SOFTWARES WITH SIMULATED AND REAL RADON DATA, Antoine Kies, Jhang Majerus, Sabine Roth, Centre Universitaire, 162a, avenue de la Faïencerie, L-1511 Luxembourg, Tel. + 352 466644 328 ­ Fax + 352 466644 329 ­ E-mail: kies@cu.lu, François Tondeur, Institut Supérieur Industriel de Bruxelles , rue Royale 150, B-1000 Bruxelles, Belgium, Tel. + 32 2 2174540, Fax: + 32 2 21 74609, E-mail: tondeur@isib.be This is an example of an analysis of the significance of the gridding approach used, with a focus on kriging.
• a more intuitive exploration of kriging.
• a more mathematical discussion of ordinary kriging.

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 below.

• 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.

Software platforms:

Exercise 5: Producing contour maps of geoscience data.

Data sets to play and learn with.

• depth to PC in NE Kansas.
• two way travel times to Jurassic on S edge of Loppa High, Barents Shelf.

Copyright by Harmon D. Maher Jr.. This material may be used for non-profit educational purposes if proper attribution is given. Otherwise please contact Harmon D. Maher Jr.. Last modified 9/06