The purpose of this study is to build efficiently and automatically a three-dimensional geometric model of the stratigraphic units of the Gulf of Lion margin on the basis of geophysical investigations by a network of seismic profiles, using geostatistics. We want to show that geostatistics can produce unbiased maps of the morphology of submarine stratigraphic units, and furthermore that some specific features of these units can be found, that classical manual mapping may ignore. Depth charts of each surface identified by seismic profiling describe the geometry of these units. The geostatistical approach starts with a statistical analysis to determine the type and parameters of the variograms of the variable “depth” of each identified surface. The variograms of these surfaces show that they are mostly non-stationary. We therefore tried the following two non-stationary methods to map the desired surfaces : (i) the method of universal kriging in case the underlying variogram was directly accessible; (ii) the method of increments if the underlying variogram was not directly accessible. After having modelled the variograms of the increments and of the variable itself, we calculated the surfaces by kriging the variable “depth” on a small-mesh estimation grid.
The depth charts of each surface calculated with the geostatistical model are then interpreted in terms of their geological significance, which makes it possible to suggest hypotheses on the influence of major processes, such as tectonics and rivers (Rhône, Hérault, etc.) on the sedimentary structure of the gulf of Lion margin. The added value of geostatistics for this interpretation is emphasized. These unusual geostatistical methods are capable of being widely used in earth sciences for automatic mapping of “non-stationary” geometric surfaces, i.e. surfaces that possess a gradient or a trend developing systematically in space, such as piezometric or concentrations surfaces.