Constrained resistivity inversion using seismic data

In this paper we describe and apply a method for constraining structure in anisotropic electrical resistivity inversion. Structural constraints are routinely used to achieve improved model inversion. Here, a second-order (curvature-based) regularization tensor (model covariance) is used to build structure in the model. This structure could be obtained from other imaging methods such as seismic tomography, core samples or otherwise known structure in the model. Our method allows the incorporation of existing geophysical data into the inversion, in a general form that does not rely on any one-to-one correlation between data sets or material properties. Ambiguities in the resistivity distribution from electrical inversion, and in particular anisotropic inversion, may be reduced with this approach. To demonstrate the approach we invert a synthetic data set, showing the regularization tensor explicitly in different locations. We then apply the method to field data where we have some knowledge of the subsurface from seismic imaging. Our results show that it is possible to achieve a high level of convergence while using spatially varying structural constraints. Common problems associated with resistivity inversion such as source/receiver effects and false imaging of strongly resistive or conductive zones may also be reduced. As part of the inversion method we show how the magnitude of the constraints in the form of penalty parameters appropriate to an inversion may be estimated, reducing the computational expense of resistivity inversion.