Geological information and the inversion of seismic data

Abstract

The preceding example, even simple, demonstrates the power and utility of Monte-Carlo methods. There is no theoretical limitation for applying this method to a more complicated problem, e.g., incorporation of complex geological information for the model space or, in the data space, introduction of probabilities to characterize the association between phases and paths in the models (see section 2.2).

The main difficulty remains the cost of the resolution of the forward problem. But, it is always possible (if information is available) to reduce the size of the volume of the model space to be investigated (it is unavoidable if the dimension of the model space is too high). A critical point is also to define an appropriate graph in the model space, and an optimal circulation in this graph to make Monte-Carlo methods efficient.

On the other hand, if the a priori information is correctly introduced and the statistics of the uncertainties on the data space are well described, then Monte-Carlo methods enable direct access to the (possibly non-linear) resolution of the inversion solution.