Estimation of depth and magnetization of magnetic sources from magnetic data: The linearized continuous inverse problem for 21/2D structures

The estimation of the depth to the top and bottom of a magnetic source from magnetic data defines a nonlinear inverse problem, while the evaluation of the distribution of magnetization determines a linear inverse problem. In this paper, these interpretation problems are resolved in the continuous case of 21/2D magnetized bodies with lateral magnetization variations. A formulation of the magnetic problem accounting for different directions of remanent and total magnetization vectors and including a more general definition of apparent susceptibility is presented. Differences between 2D and 21/2D formulations are stressed, as regards the anomaly amplitude, shape and zero-level. In order to utilize well-known continuous linear inverse methods, Fréchet derivatives of the data functionals with respect to the depth of the source top and bottom, are analytically described. Thus, using the spectral expansion inverse method (Parker, 1977) and linearizing the problem at several steps of an iterative process, the source depth is obtained within a few iterations, although the starting model is distant from the final solution. The interpretation of an anomaly in the Italian region shows the usefulness of the method. © 1990 Birkhäuser Verlag.