Estimating the Depth of Stratigraphic Units from Marine Seismic Profiles Using Nonstationary Geostatistics

The object of this study is to build a three-dimensional (3D) geometric model of the stratigraphicunits of the margin of the Rhone River on the basis of geophysical investigations by a networkof seismic profiles at sea. The geometry of these units is described by depth charts of eachsurface identified by seismic profiling, which is done by geostatistics. The modeling starts bya statistical analysis by which we determine the parameters that enable us to calculate thevariograms of the identified surfaces. After having determined the statistical parameters, wecalculate the variograms of the variable Depth. By analyzing the behavior of the variogramwe then can deduce whether the situation is stationary and if the variable has an anisotropicbehavior. We tried the following two nonstationary methods to obtain our estimates: (a) Themethod of universal kriging if the underlying variogram was directly accessible. (b) Themethod of increments if the underlying variogram was not directly accessible. After havingmodeled the variograms of the increments and of the variable itself, we calculated the surfacesby kriging the variable Depth on a small-mesh estimation grid. The two methods then arecompared and their respective advantages and disadvantages are discussed, as well as theirfields of application. These methods are capable of being used widely in earthsciences forautomatic mapping of geometric surfaces or for variables such as a piezometricsurface or aconcentration, which are not stationary, that is, essentially, possess a gradient or a tendencyto develop systematically in space.