f Inverse Methods to Combine Geology, Geostatistics and Multiphysic Data

Inverse methods are used to infer model parameters from observed data that are related via random or deterministic functions. Their application to Earth Sciences has expanded more recently to encompass the problem of data and information integration considering the combination of multiple geophysical data surveys, information of multiple properties distributed in space, their relationships, embedded object structure and scale issues. Modelling the complexity related with the multiple parameter subspaces and functions across them is priced by the coherency of the estimated results with the available information and the simplification of the posterior information due to modes and uncertainty reduction. The formulation of this problem is based on modelling the posterior probability density that combines the various components of the available information and data. Appraisal of the posterior information can be obtained parameter wise with calculation of probability distributions describing the posterior uncertainty, or globally via full model configurations corresponding to maximum posterior probability configurations or realizations from the posterior probability. We present examples of the applications of these methods to various problems in Earth Sciences, ranging from the description of the lithospheric structure of interacting plate boundaries to the characterization of hydrocarbon reservoirs.