Two - dimensional magnetotelluric inversion of blocky geoelectrical structures

of the traditional smooth inversion this information is provided as [2J The two-dimensional (2-D) magnetotelluric inverse problem an assumption that the solution, the geoelectrical model in the MT has been addressed by several authors. The most well-known case, should be represented by smooth functions. At the same time, approaches are the search for a smooth model [de Groot-Hedlin in some geological situations it can be useful to consider other and Constable, 1990; de Lugao et al., 1997; Mackie et aI., 1997; assumptions in selecting the class of possible solutions. For Rodi and Mackie, 2001] and the rapid relaxation inversion (RRI) example, the traditional smooth inversion algorithms have difficul­ [Smith and Booker, 1991). The majority of existing algorithms are ties in describing the sharp geoelectrical boundaries between differ­ based on the minimum norm or maximum smoothness criteria used ent geological formations, while in actual geological situations, for stable inversion of magnetotelluric data. The RRI method is sharp boundaries may constitute an important goal of interpretation. also based on approximate calculation of the Frechet derivatives This problem arises in inversion for a local conductive target with a under the assumption that horizontal variations in conductivity are sharp boundary embedded in a resistive host rock, which is a typical much smaller than vertical ones. model in mining exploration. Another example is a marine MT [3J The magnetotelluric (MT) inverse problem, as almost any survey to map the salt dome structures in sea bottom geological inverse problem in geophysics, is ill-posed and therefore unstable. formations [Hoversten et al., 1998). Even in general cases of It means that one can find several very different geoelectrical regional geological studies we may be interested in determining models fitting the observed data with the same accuracy. The stable large regions with blocky structures. In these situations it can be solution of an ill-posed inverse problem can be obtained by using useful to search for a stable solution within the class of inverse the corresponding regularization methods [Tikhonov and Arsenin, models with blocky geoelectrical structures . The mathematical 1977J. The regularization is based on a simple idea ofsearching for technique for solving this problem was developed by Portniaguine a solution within the specific class of selected models. Note that the and Zhdanov [1999a). It is based on introducing a new type of traditional way to implement regularization in inverse problem stabilizing functional in inverse problem solution, a so-called solution is based on considering the class of inverse models with minimum support functional. We call this technique a focusing smooth distribution of model parameters. Within the framework of regularized inversion to distinguish it from the traditional smooth the classical Tikhonov regularization, one can select the smooth regularized inversion. solution by introducing the corresponding minimum norm, or [5J This technique was successfully applied to the inversion of " smoothing" stabilizing functionals. This approach is widely used gravity data [Last and Kubik, 1983; Portniaguine and Zhdanov, in geophysics and has been proved to be a powerful tool for stable 1999aJ to generate a focused and resolved inverse image of the inversion of geophysical data. Note that practically all traditional density distribution in a geological cross section. This idea was MT inversion methods use the same approach and therefore they also implemented in inversion of three-dimensional (3-D) con­ produce a smooth image of geoelectrical structures, which in some trolled-source MT (CSMT) data over the structures with sharp cases may not describe the geology properly. geoelectrical boundaries [Portniaguine and Zhdanov, 1999b; Zhda­ [4] It is important to emphasize, however, that regularization nov and Hursan, 2000]. In this paper we demonstrate that this does not necessarily mean a smoothing of the solution. The main approach helps to generate much more "focused" and resolved basis for regularization is the implementation ofa priori information images of blocky geoelectrical structures than conventional MT inversion methods.