Multiple-point Geostatistics: A New Challenge

• Activity Number: 128
• Type: Invited
• Date/Time: Monday, August 12, 2002 : 2:00 PM to 3:50 PM
• Sponsor: International Association of Mathematicial Geology (IAMG)
• Author(s): Andre Journel*+
• Affiliation(s): Stanford University
• Keywords: stochastic imaging ; sequential simulation ; training images ; conditional probability ; geology ; spatial distribution

Abstract

Until very recently, geostatistics has relied on two-point statistics (covariance) to build models of spatially distributed phenomena. But two-point statistics cannot model the complexity of geological structures. Any curvilinear pattern requires for its modeling multiple-point (mp) statistics involving the joint variability at three or more points over a given geometric template. These mp statistics are borrowed from training images depicting the expected patterns of geological heterogeneities; they are then exported to the media to be modeled where they are anchored to the actual data.

Simulation proceeds on a grid, which nodes are simulated sequentially along a random path. Each node value is drawn from a probability distribution conditioned to the "single" mp data event constituted by neighboring original data and previously simulated values. This probability is obtained by scanning the training image for repeats of similar mp data events. That scanning is done only once, with the results classified in a search tree data base.

A 3D case-study is presented. The method appears general (different training images), flexible (different types of data), and fast.