Iterative most-squares inversion: application to magnetotelluric data

SUMMARY Conventional least-squares inversion of geophysical observational data yields a model that fits the data best or within a specified tolerance. Due to the nature of practical data, bounding values of the optimal model parameters are often sought and routinely calculated from the covariance matrix of the least-squares solution. Jackson (1976) proposed the most-squares method as an alternative approach to determining bounding values in linear inversion. As an extension of Jackson's method, we present a stable iterative scheme for obtaining extreme parameter sets in non-linear inversion. The scheme is hybrid and combines the useful properties of the ridge regression (Marquardt 1970) and most-squares methods to solve the non-linear inverse problem. The observational errors and the inherent nonuniqueness in the inversion process are accounted for using a class of models that is consistent with the data. The method is flexible and the use of Twomey-Tikhonov type constraints also enables us to define and seek a preferred class of smooth models, especially for cases in which the sought subsurface physical properties show gradational changes. It is applied to magnetotelluric depth sounding data to demonstrate its potential as an appraisal tool for conventional least-squares models.