Method of obtaining an optimal model of a physical characteristic in a heterogeneous medium, and particularly the subsoil

摘要

An optimal model is produced by inverting an existing model of the physical size of heterogeneous subterranean strata that h been generated using seismic data from a preset number of locations. The model correlates the actual physical size data at the locations, the uncertainty of the data in the existing model along the line of the strata. An optimal model is produced by inverting an existing model of the physical size of heterogeneous subterranean strata that been generated using seismic data from a preset number of locations. The optimal model minimizes a cost dependent function of th difference between a theoretical model, the seismic data and the existing model. The model correlates the actual physical size d at the locations, the uncertainty of the data in the existing model along the line of the strata. A covariance model is produced that a covariance term depends only on a difference vector between the data points and a non-stationary covariance point dependi upon the position and distance between the points. The model may calculate a mean covariance based on a stationary exponential m of covariance. The inversion parameters may be selected so they are compatible with a covariance error model.