Choosing a Regularization Parameter in the Problem of Analytical Continuation of Gravitational Fields (Separation of Anomalies Generated by Shallow and Deep Sources)

Abstract

Abstract —We present a filtration tomography technique for isolating components of the gravity field anomalies generated by inhomogeneities of the horizontally layered density model. The filtration algorithm of field separation relies on the solution of the forward and inverse problems of analytical continuation of harmonic functions through the horizontal boundary plane. We applied the regularizing algorithms to analytical continuation of the gravity field “down” to its generating sources. The fields successively recalculated upward and downward relative to preset depths allowed us to partition the initial (total) field as the sum of the fields generated in the layers based on the properly selected adaptive regularization parameter α. For the sake of stability of the inverse problem solution in the analytical continuation of the observed gravity field to a certain depth, we used the Lavrentiev regularization scheme involving the L-curve method (for selecting the adaptive regularization parameter). The smoothing regularization parameter values obtained from the preset successive depth intervals and grid step for the observed field are shown to be optimal for dividing the observed field into components corresponding to different depths. The developed algorithms for massively parallel computing systems and their application to a group of different heights were numerically implemented on the Uran supercomputer.