Iterative most-squares inversion: application to magnetotelluric data

Abstract

S U M M A R YConventional 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.

Two-Dimensional Magnetotelluric Modelling of Ore Deposits: Improvements in Model Constraints by Inclusion of Borehole Measurements

“…Since Kalscheuer et al's (2010) algorithm employs logarithmic resistivities of the 2D cells, the errors on actual cell resistivities are factors f corresponding to resistivity ranges q=f ; f q ½ . Meju and Hutton (1992), Meju (1994), Kalscheuer and Pedersen (2007) and Kalscheuer et al (2010) demonstrated that verification of linearised model error estimates using nonlinear most-squares inversion is generally desirable.…”

Combined transient electromagnetic and magnetotelluric study of the southern Kenya rift valley

“…The uniqueness of the final solution can be investigated by computing the resolution matrix, or by finding the most extreme parameter values which will produce a response function which is consistent with the observed. The application of such method to MT data has been described by Meju (1988) and Meju and Hutton (1992). There are other techniques for addressing the non-uniqueness inherent in the inversion of MT data (e.g.…”

“…The method is too consumptive of computing time and such a random search can never be exhaustive (Meju and Hutton, 1992). Linearized inversion methods are now widely used in EM data analysis.…”

“…The non-linear nature of the MT problem, the limited bandwidth of measurements, coupled with observational errors, biasing effects both due to cultural noise or lateral effects, along with the "smearing out" of sharp conductivity contrasts or thin layers by the diffusing EM energy, ensure that an infinite set of conductivity structures will satisfy a finite set of EM data (Meju and Hutton, 1992). This property of non-uniqueness forms the major problem in the interpretation of resistivity depth models derived from EM data, and it becomes apparent that additional independent geophysical or geological information concerning one or more of the parameters should be incorporated into the procedure to reduce the range of non-uniqueness.…”

“…A great variety of 1-D modelling and inversion schemes exist (Niblett and SaynWittgenstein, 1960;Wu, 1968;Jupp and Vozoff, 1975;Jones and Hutton, 1979;Parker, 1980;Parker and Whaler, 1981;Fischer et al, 1981;Hobbs, 1982;Constable et al, 1987;Meju, 1988Meju, , 1992Meju and Hutton, 1992).…”