A Review of Least‐squares Inversion and Its Application to Geophysical Problems*

A bstract Geophysical inversion involves the estimation of the parameters of a postulated earth model from a set of observations. Since the associated model responses can be nonlinear functions of the model parameters, nonlinear least‐squares techniques prove to be useful for performing the inversion. A common type of inversion applies iterative damped linear least squares through use of the Marquardt‐Levenberg method. Traditionally, this method has been implemented by solving the associated normal equations in conventional ways. However, Singular Value Decomposition (SVD) produces significant improvements in computational precision when applied to the same system of normal equations. Iterative least‐squares modeling finds application in a wide variety of geophysical problems. Two examples illustrate the approach: (1) seismic wavelet deconvolution, and (2) the location of a buried wedge from surface gravity data. More generally, nonlinear least‐squares inversion can be used to estimate earth models for any set of geophysical observations for which an appropriate mathematical description is available.