Magnetization Vector Inversion Equations and Forword and Inversed 2‐D Model Study

Abstract

AbstractWe derive magnetization vector tomography imaging equations and compare them with the magnetization scalar tomography imaging equation. The derived equations are applicable to 3‐D and 2‐D magnetization vector inversion problems, vertical component magnetic field data and total intensity of magnetic field data. In the inversion process, an improved Gauss‐Sadel iterative method with a weight coefficient determined by magnetic prism's buried depth is introduced. 2‐D model forward and inversed studies show that when the model consists of two layers, each has 51 prisms, the inversed vertical and horizontal magnetization components with the zero magnetization initial model are consistent well with the model parameters, except the edge effect near the boundary. When the model consists of five layers, and each has 51 prisms, the inversed vertical and horizontal magnetization components can be obtained with a homogeneous initial magnetization model instead of zero initial magnetization one, and the boundary effect also exists. Up to now, we cannot get much more details of fine magnetization structures from the inversion results. This aim will be reached by further work in the future.