Combining Gaussian Fields and Fibre Processes for Modelling of Sequence Stratigraphic Bounding Surfaces

The application of sequence stratigraphy concepts to reservoir de scription involves the correlation of different types of (bounding) surfaces from well to well to produce a high resolution reservoir zonation. A stochastic model has been developed for describing the geometry of different types of surfaces, and a reservoir zonation is constructed by simulating a number of surfaces from the base of the reservoir upwards. The surfaces are modelled as transformed Gaussian random fields. Conditioning on observed depths is performed by kriging, including inequality constraints for surfaces not observed in a well due to subsequent erosion. This paper focusses on the stochastic model for a particular type of surface containing erosional valleys. The valleys are modelled by fibre processes and correlated Gaussian random functions. Prior distributions for valley location and geometry are defined and updated to posterior distributions by simulating from the prior model conditioned on the observations. Information such as the depth of the boundaries observed in the wells, and the well pattern with respect to valley orientation, width and sinuosity, is thus utilized in the parameter inference.