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.
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
ABSTRACT. There is a growing interest in the inversion of self-potential (SP) anomalies, in terms of their current sources, as a way to obtain qualitative and quantitative information about dynamical Earth’s subsurface processes. For anomalies interpretation based on geobattery models (as in mineral prospecting and contaminated sites characterization), current polarity indicates terminal anodic-cathodic reactions and current strength gives information on their rate, both important parameters in characterizing the spatial distribution of related redox systems. For investigations in hydrogeophysics, current polarity indicates infiltration/exudation points or interfaces with contrasting physical properties and current strength can be associated to seepage velocity, important parameters to remotely access groundwater hydrology. Actually, promising rewards from SP inversion for current sources deeply rely on the reliability in which polarity and strength for a current distribution can be determined from inverting a data set, considering the uncertainty of the inverse problem and noise level found. In this paper we combine existing regularizing procedures to verify in what conditions a single bipolar, man-made current source can be mapped from a tank experiment data set. As a result, we outline a procedure that can be applied in field conditions to tune data inversion parameters in mapping a subsurface current distribution.Keywords: spontaneous potential, mineral prospecting, contaminated sites characterization, applied geophysics, data inversion. Vínculo para mapeamento de fontes de corrente em subsuperfícieRESUMO. Há um interesse crescente na inversão de anomalias de Potencial Espontâneo (SP), em termos de suas fontes de corrente, como forma de obter informações qualitativas e quantitativas sobre processos dinâmicos sub- superficiais da Terra. Para interpretações de anomalias baseadas no modelo de geobateria (como na prospecção mineral e caracterização de áreas contaminadas), a polaridade das correntes indica terminais de reações anódico- catódicas e a intensidade das correntes assinala sua taxa, parâmetros importantes na caracterização de sistemas redox. Para investigações hidrogeofísicas, a polaridade da corrente indica pontos de infiltração/exsudação ou interfaces com propriedades físicas contrastantes e a intensidade da corrente associa-se à velocidade de infiltração, parâmetros importantes para acessar remotamente a hidrologia subterrânea. Inversões bem-sucedidas de SP para fontes de corrente dependem da confiabilidade em que a polaridade e a intensidade da distribuição de correntes podem ser determinadas, considerando a incerteza do problema inverso e o nível de ruído. Neste artigo, combinamos procedimentos de regularização existentes para verificar em que condições uma única fonte de corrente artificial bipolar pode ser mapeada, a partir de um conjunto de dados de experimentos em tanque. Como resultado, delineamos um procedimento aplicável em condições de campo para o mapeamento de uma distribuição de corrente subterrânea.Palavras-chave: potencial espontâneo, prospecção mineral, áreas contaminadas, geofísica aplicada; inversão de dados
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