Method allowing to obtain an optimum model of a physical characteristic in a heterogeneous medium such as the subsoil

A method for obtaining an optimized model representing an image of a distribution in a subterranean stratified heterogeneous medium of a physical quantity with respect to waves propagating in the medium, comprising:

• obtaining data representing values of the physical quantity by means of measurements, recordings or observations at different points of the medium along strata directions;
• forming an a priori model by kriging with a stationary covariance between the obtained data representing values of the physical quantity known at points of the medium along the strata directions with uncertainties about the values of the physical quantity in the a priori model at any point along the strata directions being described by a covariance including the stationary covariance that depends only on a distance vector between the points and a non-stationary term depending on a position of the points and on the respective distances between the points;
• controlling inversion parameters from characteristics of the covariance including the stationary covariance;
• and
• constructing by inversion the optimized model by iteratively minimizing a cost function depending on differences between the model being sought and the known data considering the a priori model.