3-D magnetic imaging using conjugate gradients

Abstract

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.