Geoelectrical inversion for a one-dimensional anisotropic model and inherent non-uniqueness

It has been shown that the inversion of geoelectrical sounding data from an anisotropic underground structure with an isotropic model can strongly distort the image of the resistivity distribution of the Earth. Because of this it is useful to extend the models to include an anisotropic earth. The inverse model used in this paper is a layered earth with general anisotropy, such that a 3 x 3 resistivity tensor is assigned to each layer. This symmetric, positive-definite resistivity tensor is parametrized by three principal resistivities and three Euler angles. Therefore, together with the thickness, seven parameters for each layer of the earth have to be resolved. The Marquardt-Levenberg method is used to invert the Schlumberger resistivity sounding data with an anisotropic model. The inversion results using synthetic data show that for an anisotropic earth, rather than all parameters, only particular parameter combinations can be resolved uniquely. Theoretical investigations support these conclusions and confirm that unlike the general non-uniqueness in geoelectrical inversion resulting from inaccurate, insufficient or inconsistent data, the non-uniqueness of geoelectrical inversion for an anisotropic model is an inherent one, which means that no unique solution can be obtained, even if perfect data are assumed.