Stochastic structure-constrained image-guided inversion of geophysical data

Inverse modeling of geophysical data involves the recovery of a subsurface structural model and the distribution of petrophysical properties. Independent information regarding the subsurface structure is usually available, with some uncertainty, from the expertise of a geologist and possibly accounting for sedimentary and tectonic processes. We have used the available structural information to construct a model covariance matrix and to perform a structure-constrained inversion of the geophysical data to obtain a geophysical tomogram m We have considered that the geologic models y were built from random variables and were described with a priori probability density function in the Bayesian framework. We have explored for the a posteriori probability density of the geologic models (i.e., the structure of the guiding image) with the Markov-chain Monte Carlo method, and we inverted at the same time, in a deterministic framework, the geophysical data. The sampling of the geologic models was performed in a stochastic framework, and each geologic model y was used to invert the geophysical model m using image-guided inversion. The adaptive metropolis algorithm was used to find the proposal distributions of y reproducing the geophysical data and the geophysical information. In other words, we have tried to find a compromise between the a priori geologic information and the geophysical data to get, as end products, an updated geologic model and a geophysical tomogram. To demonstrate our approach, we used here electrical resistivity tomography as a technique to identify a correct geologic model and its a posteriori probability density. The approach was tested using one synthetic example (with three horizontal layers displaced by a normal fault) and one field case corresponding to a sinkhole in a three-layer structure. In both cases, we were able to select the most plausible geologic models that agreed with a priori information and the geophysical data.