Apparent-magnetization mapping using entropic regularization

Abstract

A new apparent-magnetization mapping method on the horizontal plane combines minimization of first-order entropy with maximization of zeroth-order entropy of the estimated magnetization. The interpretation model is a grid of vertical, juxtaposed prisms in both horizontal directions. To estimate the magnetization of the prisms, assume that the top and bottom of the magnetic sources are horizontal. Minimization of the first-order entropy favors solutions with sharp borders, and the maximization of zeroth-order entropy prevents the tendency of the estimated source to become a single prism with large magnetization. Thus, a judicious combination of both constraints can lead to solutions characterized by regions with virtually constant magnetizations separated by sharp discontinuities. This is applied to synthetic data from simulated intrusive bodies in sediments that have horizontal tops. By comparing the results with those obtained with the common Tikhonov regularization (smoothness constraint) method, it is shown that both methods produce good and equivalent locations of the central positions of the sources. However, entropic regularization delineates the boundaries of the bodies with greater detail. Both the proposed and the smoothness constraints are applied to real anomaly data over a magnetic skarn in Butte Valley, Nevada, U.S.A. Entropic regularization produced an estimated magnetization distribution with sharper boundaries, smaller volume, and higher apparent magnetization as compared with results produced by incorporating the smoothness constraint.

Entropic Regularization to Assist a Geologist in Producing a Geologic Map

“…Here, we discuss an interpretation of the magnetic data from Butte Valley Stock, NV, USA shown by Silva et al [18] that compare the estimated magnetization-contrast distribution produced by the entropic regularization method with that produced by the first-order Tikhonov regularization. The Butte Valley Stock is a buried skarn located on the southern border of a nonmagnetic intrusive body emplaced in nonmagnetic sedimentary rock.…”

“…[18]. (c) Estimated magnetization-contrast distribution produced by the entropic regularization with Ȗ 1 = 3,385 and Ȗ 0 = 100 [18]. Figure 6(b,c) shows the estimated magnetization-contrast distributions using, respectively, the first-order Tikhonov regularization and the entropic regularization with Ȗ 1 = 3,385 e Ȗ 0 = 100.…”

“…Each prism is 0.24 km wide in both x-and y-directions, and its top and base are, respectively, 0.8 and 5 km deep. [18]. (c) Estimated magnetization-contrast distribution produced by the entropic regularization with Ȗ 1 = 3,385 and Ȗ 0 = 100 [18].…”

“…The physical and geologic meaning of the entropic regularization has been explained by [17][18][19]. The minimization of the first-order entropy measure favors an estimated physical-property distribution presenting local abrupt discontinuities.…”

Application of Cauchy-type integrals in developing effective methods for depth-to-basement inversion of gravity and gravity gradiometry data

“…Many research papers have been published over the past decade on this subject (e.g., Barbosa et al, 1997Barbosa et al, , 1999aBarbosa et al, , 1999bSilva et al, 2001Silva et al, , 2006Silva et al, , 2007Silva et al, , 2010aSilva et al, , 2010bGallardo-Delgado et al, 2003;Martins et al, 2010Martins et al, , 2011aMartins et al, , 2011b. The conventional approach to solving depth-to-basement gravity inverse problems is based on parameterization of the earth's subsurface, containing the sedimentary pack, into prismatic cells with known horizontal dimensions and known density contrast, and on estimation of the cell's thicknesses.…”