when we use the equivalent source method for the processing of potential field data , how we can choose the value of the depth to the equivalent layer ?
Can we use an average of the the depth solutions obtained from the diffrent semi-automated methods?
The bad selection of the value of the depth, how it affects on the obtained model? Does it give a bad model or just it take more time to obtain a good solution?
Adrien's answer (above) is pretty much complete, if you work thought the references he supplies.
A short answer might be: The depth of the layer sets the extent to which you fit the detail in the observations. If its deep, the layer has no way to "fit" detail, so it'll smooth it. That's an implicit low-pass filter but it can be quite useful, as long as you use it intelligently.
To fit the data perfectly, the layer needs to be between all sources and the observation surface, and finely gridded enough to be able to fit all wavelengths in the data.
Interpretation is an iterative process. Therefore, a longer answer might be: For a first pass one should set the depth of the layer deep, then revise the layer to a shallower depth. This should allow you to "fit" both the "regional" and the "residual" detail within your data. As long as you use this approach intelligently you should improve the speed and accuracy of your interpretations.
Mahmoud, the paper of Dampney (1969) was mainly intended to perform the upward continuation of an unevenly spaced gravity anomaly to a horizontal datum. Actually, there are more advanced techniques to do that. In such methods, the so-called "equivalent layer" is just the topographic surface. However, keep in mind that this concept of "equivalent layer" is just a result from the so-called Dirichlet integral (see Grant & West text book) in the gravity case. But the same Dirichlet integral (or its developments) should be also used for magnetic anomalies, when the analogy existing in the case of gravity data is no longer valid.
The equivalent layer concept can still be used in work on magnetic fields. A really good example of that is published in GUNN, P J, 1975. Linear transformations of gravity and magnetic fields.. Geophys. Prosp., v. 23, p. 300 312.
He gives all the operators like pole reduction, continuation, gradient extraction and the like, but if you look at the mathematical development, its all based on an equivalent layer concept.
Hi,
You can also see the paper by Sharma, 2012, Computers and Geosciences, VFSARES—a very fast simulated annealing FORTRAN program for interpretation of 1-D DC resistivity sounding data from various electrode arrays.
Do you use equivalent sources to transform the field? Best of all, you should choose the depth one to two spaces between nodes if you use the grid. The simplest case is one equivalent layer and point sources. There can be too smooth solution if you choose the depth more than 2 spaces, and there can be false anomalies between nodes if you choose the depth less than 1 space. If you have strongly nonuniform distribution of potential field data you should use the multylevel approximation. In that case, sources locate on several levels. Usually, the deepest from them has the depth no more than half of the size of the least side of studied area, but the better is no more than 1/3. The nearest layer to the Earth's surface should have the depth one to two of average spaces between observation points. The other layers are between the deepest and the shallowest. But the nonuniform case demands of the application of any special techniques of the source location on each layer. May be these techniques are given in the above-mentioned articles. I don't know, because I have no time to read them now. If not, I have a few articles in Russian, but I will try to translate them in English soon and download for free. One of them has already published on my page.
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