NONLINEAR INVERSION USING GENERAL MEASURES OF DATA MISFIT AND MODEL STRUCTURE

We investigate the use of general, non-l(2), measures of data misfit a nd model structure in the solution of the non-linear inverse problem. Of particular interest are robust measures of data misfit, and measure s of model structure which enable piecewise-constant models to be cons tructed. General measures can be incorporated into traditional lineari zed, iterative solutions to the non-linear problem through the use of an iteratively reweighted least-squares (IRLS) algorithm. We show how such an algorithm can be used to solve the linear inverse problem when general measures of misfit and structure are considered. The magnetic stripe example of Parker (1994) is used as an illustration. This exam ple also emphasizes the benefits of using a robust measure of misfit w hen outliers are present in the data. We then show how the IRLS algori thm can be used within a linearized, iterative solution to the non-lin ear problem. The relevant procedure contains two iterative loops which can be combined in a number of ways. We present two possibilities. Th e first involves a line search to determine the most appropriate value of the trade-off parameter and the complete solution, via the IRLS al gorithm, of the linearized inverse problem for each value of the trade -off parameter. In the second approach, a schedule of prescribed value s for the trade-off parameter is used and the iterations required by t he IRLS algorithm are combined with those for the linearized, iterativ e inversion procedure. These two variations are then applied to the 1- D inversion of both synthetic and field time-domain electromagnetic da ta.