Stochastic Inverse Modelling Under Realistic Prior Model Constraints With Multiple-Point Geostatistics
Monday, January 7, 2002 - 11:00am - 12:00pm
In geostatistics spatial variability is traditionally quantified using an autocorrelation function (variogram). Stochastic simulations are intended to generate 3D models that honor this statistic as well as any hard (direct measurements) and soft data (indirect, geophysical measurements. Two severe limitations currently exist in this field: (1) the variogram is often not a good quantifier of spatial heterogeneity, it fails at capturing strongly connected bodies or curvi-linear structures such as channels, (2) information gathered from strongly non-linear subsurface processes (such as multiphase flow data) cannot be directly integrated. The latter essentially consists of solving a spatial inverse problem. In this presentation, I will introduce the field of multiple-point geostatistics and a practical methodology for solving large spatial inverse problems under virtually any prior geological model constraints. Multiple-point geostatistics allows to model prior geological information based on so-called training images. Training images are conceptual but explicit quantifications of geological patterns present in the subsurface. Multiple-point geostatistics allows to model these patterns, then anchor them to subsurface hard data. In this paper I demonstrate how information gathered from subsurface process data, such as flow, can be integrated into these geostatistical models by means of a simple Markov chain process, while at the same time honoring prior geological information depicted in the training image.