Three‐dimensional inversion without blocks

Abstract

Summary. We propose a method for solving non‐linear inverse problems in the case where the unknown is a function of the spatial coordinates and the data set is discrete and finite. The method is based on a generalized leastsquares criterion, it is defined directly for non‐linear problems (without previous linearization of the forward problem), and in the particular linear case it gives the same results (although slightly more general) than the Backus & Gilbert approach. As an example, we apply the method to the three‐dimensional seismic velocity inverse problem, using as data the arrival times of seismic waves. The following paper (Nercessian et al.) shows some esults obtained using the present method. Copyright © 1984, Wiley Blackwell. All rights reserved