Iterative deconvolution and semiblind deconvolution methods in magnetic archaeological prospecting

Abstract

In archaeological magnetic prospecting, most targets can be modeled by a single layer of constant burial depth and thickness. With this assumption, recovery of the magnetization distribution of the buried layer from magnetic surface measurements is a 2D deconvolution problem. Because this problem is ill posed, it requires regularization techniques to be solved. In analogy with image reconstruction, the solution showing the resolved subsoil features can be considered a focused version of the blurred and noisy magnetic image. Exploiting image deconvolution tools, two iterative reconstruction methods are applied to minimize the least-squares functional: the standard projected Landweber method and a proposed modification of the iterative space reconstruction algorithm. Different regularization functionals inject a priori information in the optimization problem, and the split-gradient method modifies the algorithms. Numerical simulations in the case of perfect knowledge of the impulse response functions demonstrate that the edge-preserving, total-variation functionals give the best results. An iterative semiblind deconvolution method to estimate the burial depth of the source layer was used with a real data set to test the effectiveness of the method.