Fuzzy Geological Model

The problem considered is a 3D Earth Model property prediction by well (and seismic) data. It is shown, that multimodal fuzzy presentation of the parameter (porosity) value in each elementary volume is quite adequate, when we deal with geological medium. After the region of parameter values is subdivided into n categories (n is no more than 20), the membership function f is represented by n number of discrete values f1, f2 ... fn. Presentation, when parameter value in each elementary volume is specified by a set of f1, f2 ... fn, is called a fuzzy model. <br><br>Values f1, f2 ... fn are treated as evidences in favor of different parameter categories. They can be obtained using the next three procedures: (1) fuzzy transformation of well data; (2) fuzzy transformation of seismic attributes; (3) fuzzy evidence summation by Dempster’s rule. Analytical comparison with geostatistics is done in two point example. As shown, a fuzzy model uncertainty is dependent on data contrast. A case study with 93 wells is also considered. Thanks to economic uncertainty distribution, fuzzy model realizations look like a set of deterministic models.<br>