Apparent-magnetization mapping using entropic regularization

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.