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.
Highlights
One of geologists’ objectives is to unravel the geologic history through the knowledge of the geologic processes
Among the numerous estimated physical-property contrast distributions fitting the data with acceptable precision, the entropic regularization favors an estimated physical-property distribution with locally smooth regions separated by abrupt discontinuities
A geologic map is a useful tool in understanding the geologic history of an study area, which in turn is used in studying the environment of orebody emplacement to be incorporated in mine planning and scheduling
Summary
One of geologists’ objectives is to unravel the geologic history through the knowledge of the geologic processes. The standard Tikhonov regularization method [7] is generally used to guarantee a stable solution It consists of formulating a constrained inverse problem, which is solved by the minimization of a function composed by: (1) the data-misfit function that measures a norm of the difference between the observed and predicted data, and (2) the regularizing function defined in the parameter (model) space that imposes physical or geological attributes on a solution. To the magnetic anomaly over Butte Valley, NV, USA, showed an estimated source presenting one of its dimensions much larger than the other This particular shape (which is different from the usual ring-like shape of most skarns) and the available geological information, allowed to infer that the Butte Valley anomaly is produced by an exoskarn where the ion exchange between the intrusive and the host rock occurs along a limited portion of the southern intrusive border. This example illustrates that the physical property-contrast mapping, when integrated with pertinent geological information, may effectively assist the geologist in elaborating a geological map
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