f Probabilistic description of geological information

Incorporation of geological information as a priori information in the inversion of seismic data is necessary to improve results and performances of imaging algorithms. In classical inversion theory, incorporation of geological a priori information is done using an a priori model and a metric over the model space, i.e. a norm which measures the distance between the current model and the a priori model. This implies that uncertainties over the a priori model are monomodal, whatever the norm chosen. This is too restrictive to take into account statistical distributions of physical parameters, e.g. , the distribution of P-wave velocities in a sedimentary basin must be multimodal, each mode corresponding to a type of rock (shale, limestone, sandstone etc.).