# Structure Contours on Non-planar Surfaces

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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Most geologic structures are not ideal planes, and structure contours on these structures are often neither straight nor equally-spaced. In fact, structure contours can violate many of the rules we are familiar with on topographic maps.

• Geologic structures often have overhangs; hence structure contours can cross. Actually the contours themselves do not cross, only their projections on the map.
• Geologic structures often have discontinuities in the form of faults. Structure contours can terminate and not close.

In the example we consider here, we will be concerned only with data that is fairly well-behaved: smooth, with no overhangs or discontinuities. The problem is very similar to contouring topographic data.

## Some Rules for Construction

• Structure contours must still be parallel to the strike of a structure at every point.
• Keep the contours as simple as possible consistent with the data.
• Keep the contours smooth. Do not show abrupt changes in curvature or spacing unless you have sound geologic reasons to do so.
• Interpolate only between nearby points
• If the structure is only gently curved, you may find it useful to approximate the structure as a series of plane segments at first. For each group of three data points, construct structure contours using the three-point method. Make sure the triangles are as nearly equilateral as possible. Once the contours are constructed, draw the final contours as smoothly as possible using the construction as a guide.
• You will often have surface or near-surface data and little or no data at great depth. In such cases, your contours will be little more than guesses to suggest the three-dimensional form of the structure. Such contours are called form lines. In cases like this, you have no choice but to extrapolate surface data to deep levels and use your knowledge of geologic structures as a guide.

## Example

 1. Contour the data shown 2. Interpolate between nearby points. Avoid extremely long-distance interpolations. 3. Sometimes it pays to treat the data as a series of three-point problems. 4. Once you have a clear mental picture of the structure, construct smooth contours to fit the data.

## Additional Notes on the Example

• Note that some of the data are negative. It is perfectly possible to have data points below sea level when analyzing data from deep wells or when drawing form lines on large, deep structures.
• If you treat the data as a series of three-point problems, contours within each triangle must join the corresponding contours in neighboring triangles.
• When drawing the smoothed contours, the contours must be consistent with the data points but need not be perfectly consistent with points estimated by interpolation. A data point at 210 meters elevation must be located on the uphill side of the 200 meter contour. But interpolated points are only estimates of the elevation of the structure. Trying to fit all the interpolated points exactly may result in contours that are overly erratic. Worse yet, it may create the impression of spurious detail - a user of the contour map may be misled into thinking the undulations in the contour are real features of the structure. It's better to draw smooth contours that are as consistent as possible with both the interpolations and with other contours.
• Note that the 0 and -100 contours are extended into areas of no data, based on the overall shape of known contours. We can be fairly sure the -100 contour passes just outside the -97 data point, but elsewhere, there is little control on the exact locations of these contours. These are examples of form lines. We expect them to be roughly correct, but do not expect high precision from them.