A new non‐linear least squares algorithm for the seismic inversion problem

Abstract

We describe the problem of simultaneous determination of hypo‐centre locations and velocity structure, using data from microearthquake networks, and briefly discuss some of the techniques which have been proposed for its solution. In particular we examine the method of Thurber, as implemented in his program SIMUL3L, where the problem is formulated as a non‐linear least‐squares problem. A new program SINEW is proposed which is a modification of SIMUL3L in which a somewhat different algorithm is used to solve the underlying least squares problem. At each iteration, the vector of parameter adjustments is calculated inexactly via an iterative scheme which avoids explicit factorization of the (sparse) Jacobian matrix. Copyright © 1986, Wiley Blackwell. All rights reserved