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Subsurface Detection

The Inverse Problem

Subsurface detection relies on solutions to what is often called the "inverse problem." A particular set of data are observed, and then models are developed which attempt to fit all the data. Sometimes, when a very nice match is made, it is tempting to assume that a particular model is the only model which can fit the data, although this is rarely true.

An example may illustrate this: Imagine that I am trying to figure out the value of the change you have in your pocket. Suppose I have a device which will detect how many coins you have, and it says you have seven. Then I would know that you have at least $0.07 and at most $1.75. Suppose I have another device which tells me that the coins are of two different sizes, with four of them larger than the other three. The big ones might be quarters, leaving a range from $1.03 to $1.30, or they could be nickels, leaving a range from $0.23 to $0.50. Finally, if I were to think about this more carefully, I would see that not all of the values in these ranges are possible. So you could have $1.03, $1.12, $1.15, $1.21, $1.30 if the larger coins are quarters, or $0.23, $0.32, $0.41, $0.50, if the larger coins are nickels. We have reduced the number of possibilities to nine, but there is no way we can use these "subsurface detection" techniques to constrain things further. Because each of these nine possibilities fits the data perfectly, we might find one and erroneously conclude that because it fit the data so well it must be true. Assumptions were built into our conclusions, also; we assumed it is United States currency, and no half dollars or dollar coins. Such assumptions make sense for most pockets we are likely to run into in this country, but are obviously not valid in other countries.

This example illustrates the nature of subsurface detection. Results are usually somewhat ambiguous, depend on assumptions, and do not directly give the answers we seek. Yet they can provide important constraints. I may be able to make some additional assumptions from other data, hunches, or guesses. For instance, I may know you well enough to figure that you would not keep pennies, which would reduce the number of options to three.


Additional topics

Science EncyclopediaScience & Philosophy: Stomium to SwiftsSubsurface Detection - Seismic Reflection, Electric Techniques, Nuclear Survey Methods, Satellite Altimeter Data, The Inverse Problem - Potential field methods