Two‐dimensional magnetotelluric inversion of blocky geoelectrical structures

Abstract

[1] This paper demonstrates that there are alternative approaches to the magnetotelluric (MT) inverse problem solution based on different types of geoelectrical models. The traditional approach uses smooth models to describe the conductivity distribution in underground formations. In this paper, we present a new approach, based on approximating the geology by models with blocky conductivity structures. We can select one or another class of inverse models by choosing between different stabilizing functionals in the regularization method. The final decision, whose approach may be used for the specific MT data set, is made on the basis of available geological information. This paper describes a new way of stabilizing two-dimensional MT inversion using a minimum support functional and shows the improvement that it provides over traditional methods for geoelectrical models with blocky structures. The new method is applied to MT data collected for crustal imaging in the Carrizo Plain in California and to MT data collected for mining exploration by INCO Exploration.

The CAFE Experiment : a joint seismic and MT investigation of the Cascadia Subduction System

“…The argument is that by seeking the smoothest model (again, for a sufficiently large misfit), only structure explicitly required by the data will be resolved (de Groot-Hedlin and Constable, 1990). In nature, sharp geoelectric boundaries do of course exist, and smooth algorithms may not sufficiently resolve these boundaries (Smith et al, 1999, de Groot-Hedlin and Constable, 2004, Mehanee and Zhdanov, 2002.…”

“…In order to address these difficulties, several algorithms have been developed that allow for sharp boundaries by making different global assumptions about the distribution of the modeled parameter in the subsurface, for example by favoring models made up of layers (Smith et al, 1999, de Groot-Hedlin andConstable, 2004) or containing primarily blocky structure (Mehanee and Zhdanov, 2002). Of course, each of these global algorithms present trade-offs, and are effective largely to the extent that the underlying assumptions are accurate throughout the modeled space.…”

“…where d is the observed data and Fm the data predicted by the model, and s(m) is a functional that represents assumptions or a priori information that the worker has chosen to include, with its relative importance determined by the regularization parameter A (Tikhonov and Arsenin, 1977, Parker, 1994, Mehanee and Zhdanov, 2002.…”

“…While several stabilizing functions have been successfully used (least squares, minimum norm of the gradient, distance from an a priori model, etc.) in various geophysical applications (Smith et al, 1999, Mehanee and Zhdanov, 2002, de Groot-Hedlin and Constable, 2004, many magnetotelluric algorithms employ the minimum norm of the Laplacian, which will seek the smoothest model possible that fits the data (for a given misfit). The argument is that by seeking the smoothest model (again, for a sufficiently large misfit), only structure explicitly required by the data will be resolved (de Groot-Hedlin and Constable, 1990).…”

Magnetotellurics in locally-layered random media

“…The resistivity map is then varied iteratively to minimize the objective function, thus giving a trade-off between fitting the data and the assumed nonoscillatory nature of the solution. (Some recent developments in regularization theory have dealt with sharp geoelectric boundaries; see [13], [3], [15].) Paradoxically, it is well known that resistivity does not vary smoothly with depth, but has order one oscillations on very small spatial scales.…”