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Entropy 2011, 13(4), 790-804; doi:10.3390/e13040790
Article

Entropic Regularization to Assist a Geologist in Producing a Geologic Map

1,* , 2
,
2
 and
2
1 Geophysics Department, Observatório Nacional, Rio de Janeiro, 20921-400, Brazil 2 Geophysics Department, Federal University of Pará, Belém, Pará, 66075-110, Brazil
* Author to whom correspondence should be addressed.
Received: 1 February 2011 / Revised: 29 March 2011 / Accepted: 31 March 2011 / Published: 6 April 2011
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Abstract

The gravity and magnetic data measured on the Earth’s surface or above it (collected from an aircraft flying at low altitude) can be used to assist in geologic mapping by estimating the spatial density and magnetization distributions, respectively, presumably confined to the interior of a horizontal slab with known depths to the top and bottom. To estimate density or magnetization distributions we assume a piecewise constant function defined on a user-specified grid of cells and invert the gravity or magnetic data by using the entropic regularization as a stabilizing function that allows estimating abrupt changes in the physical-property distribution. The entropic regularization combines the minimization of the first-order entropy measure with the maximization of the zeroth-order entropy measure of the solution vector. The aim of this approach is to detect sharp-bounded geologic units through the discontinuities in the estimated density or magnetization distributions. Tests conducted with synthetic data show that the entropic regularization can delineate discontinuous geologic units, allowing a better mapping of sharp-bounded (but buried) geologic bodies. We demonstrate the potential of the entropic regularization to assist a geologist in obtaining a geologic map by analyzing the estimated magnetization distributions from field magnetic data over a magnetic skarn in Butte Valley, Nevada, U.S.A. We show that it is an exoskarn where the ion exchange between the intrusive and the host rock occurs along a limited portion of the southern intrusive border.
Keywords: entropic regularization; geologic map; gravity data; magnetic data; inversion; physical-property estimate entropic regularization; geologic map; gravity data; magnetic data; inversion; physical-property estimate
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Barbosa, V.C.; Silva, J.B.; Vasconcelos, S.S.; Oliveira, F.S. Entropic Regularization to Assist a Geologist in Producing a Geologic Map. Entropy 2011, 13, 790-804.

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