3-D magnetic imaging using conjugate gradients

Abstract

A 3-D inversion approach is outlined that determines a distribution of susceptibility that produces a given magnetic anomaly. The subsurface model consists of a 3-D array of rectangular blocks, each with a constant susceptibility. The inversion incorporates a model norm that allows smoothing and depth‐weighting of the solution. Since the number of parameters can be many thousands, even for small problems, the linear system of equations is inverted using a preconditioned conjugate gradient approach. This reduces memory requirements and avoids large matrix multiplications. The method is used to determine the 3-D susceptibility distribution responsible for the Temagami magnetic anomaly in southern Ontario, Canada.