Some applications of statistical modelling to solve inverse problems in geophysics

A simple algorithm to solve inverse geophysical problems is presented. It uses a statistical modelling of the forward problem in the presence of an unknown disturbing parameter vector with nonlinear dependence between their components and the model field. The nonlinear dependence is investigated directly in the parameter space and a particular linear approximation is made. Thus, a nearly optimal solution is obtained. The quality of the estimates is statistically predicted, this allows a rational selection of the most informative observation points. The method is especially suitable for many typical inverse problems in geophysical prospecting. A gravity exploration example is presented.