A probability model considers a regionalized variable as the unique realization of a random function Z that must be reconstructed at its best from the available information. Theory shows that in practice, only the spatial behavior of the average and covariance of the unknown random function Z may be objectively reconstructed from experimental data.

This is enough to solve most of the filtering, estimation and simulation issues encountered in signal processing and during the seismic characterization of oil and gas reservoirs.

All probability models are built according to the same fundamentals: Formulating Spatial stationarity assumptions, specifying spatial average and covariance, and operating mathematical estimation or simulation algorithms.