Construct a Down-Plunge Profile

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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The above diagram shows a block model of a fold with top, side and end views (the traditional cross-section). We can see that both the traditional cross-section and the map view are oblique to the axis of the fold. Both are actually oblique cross-sections. If the plunge were 45 degrees, both views would look the same. When the plunge is less than 45 degrees, the cross-section provides the truer view. When the plunge is greater than 45 degrees, however, the map view is closer to the true shape of the fold.

The only true view of the shape of the fold is found by looking down the fold axis - that is, down the plunge (top diagram)

We can see that a down-plunge view can be easily obtained by simply compressing the map view by some factor. (Actually, looking a bit ahead, the compression factor is the sine of the plunge.)

There are two very nice features of down-plunge profiles:
  • In contrast to cross-sections, every point on the profile view is derived from data - the map view. We do not interpolate fold shapes or extrapolate dips. We do assume the fold has constant plunge over the area being profiled. Thus profile views show more detail and are better supported than cross sections.
  • Topographic effects that complicate map views (left) disappear in down-plunge profile views (right). The lines that generate the fold shape may intersect the topography in complex ways but all we see when we look down the plunge of the fold is the shape of the fold.
However, topography can complicate matters. The point in red at (x,y,z) would project at a different point on the profile plane than would a point at (x,y,0).

The diagram at left shows the coordinates we will use in developing formulas for down-plunge profiling.

Obviously, x = x'. Distances at right angles to the trend of the fold project true.

Here we develop a formula for taking topography into account. We can see that:
  • When topography is small compared to the map scale, it becomes insignificant
  • When plunge is steep, map coordinates dominate
  • When plunge is shallow, topography can dominate. In the extreme case p = 0, we could look at a vertical cliff and see a true profile, whereas the geology would be all but invisible on a map.

Obviously, y' = y sin p + z cos p. Thus, the coordinates of (x,y,z) in the profile plane are:

  • x' = x
  • y' = y sin p + z cos p

There are two ways to proceed from here. The formulas are easily computerized. We need two files: one with the geology of the map area and one with topography. Using the topography file, we find coordinates (x,y,z). We refer to the geology file to find the rock unit at (x,y), then project that data to (x',y').

If we already have data files, the computer approach is easy. For a very large or complex project it may pay to generate the files. But for a relatively small and simple structure it may still be faster to use a graphical approach.

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Created 18 October 2000, Last Update 20 October 2000
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