Remarks on approximate methods in geophysical inverse problems

Abstract

Several remarks are made on well-known methods used in geophysics to analyse inverse problems. Approximate values are given for Backus and Gilbert kernels, together with an integral equation which enables one to derive then from a Dirichlet kernel. Ways to obtain approximate expressions of the Dirichlet kernels are then studied. Consequences of linearizing a nonlinear inverse problem are analysed both in general and with an exactly solvable example. This example shows situations in which the information derived by way of the linear method is irrelevant or misleading. Some simple remarks on the inference of physical constraints conclude the paper.