An information content measure using multiple-point statistics

Multiple-point geostatistics aims at reproducing complex patterns involving many locations at a time, which is much beyond the reach of a two-point variogram model as in traditional geostatistics. In multiple-point geostatistics, sometimes it is necessary to have a quantitative measurement of how informative a data event is with regard to the unknown node, the multiple-point equivalence of a kriging variance. It should be a statistic accounting not only for various possible data configuration and specific data values, but also for the spatial structural information provided by prior geological knowledge. In this paper, we propose two alternative definitions of information content for a multiple-point data event. One is defined as a linear function of the conditional probability, and the other uses entropy for the definition. This information content measure can be widely applied in many occasions in multiple-point simulation. Three applications are presented in the paper. First it is used to rank all unknown nodes to generate a structured path for sequential simulation. Second it is used to decide how to reduce a data event when not enough replicates of it can be found in the training image. Finally it is used to adjust the relative contributions of different data sources in a data integration algorithm. All these applications show an improvement of simulation due to the utilization of this newly defined multiple-point statistic.