Stochastic simulation of geological data using isometric mapping and multiple-point geostatistics with data incorporation

• This paper further develops ISOMAPSIM with data conditioning.
• Soft data and hard data are integrated to achieve best simulation quality.
• The proposed method has advantages over FILTERSIM and DISPAT.

Constrained by current hardware equipment and techniques, acquisition of geological data sometimes is difficult or even impossible. Stochastic simulation for geological data is helpful to address this issue, providing multiple possible results of geological data for resource prediction and risk evaluation. Multiple-point geostatistics (MPS) being one of the main branches of stochastic simulation can extract the intrinsic features of patterns from training images (TIs) that provide prior information to limit the under-determined simulated results, and then copy them to the simulated regions. Because the generated models from TIs are not always linear, some MPS methods using linear dimensionality reduction are not suitable to deal with nonlinear models of TIs. A new MPS method named ISOMAPSIM was proposed to resolve this issue, which reduces the dimensionality of patterns from TIs using isometric mapping (ISOMAP) and then classifies these low-dimensional patterns for simulation. Since conditional models including hard data and soft data influence the simulated results greatly, this paper further studies ISOMAPSIM using hard data and soft data to obtain more accurate simulations for geological modeling. Stochastic simulation of geological data is processed respectively under several conditions according to different situations of conditional models. The tests show that the proposed method can reproduce the structural characteristics of TIs under all conditions, but the condition using soft data and hard data together performs best in simulation quality; moreover, the proposed method shows its advantages over other MPS methods that use linear dimensionality reduction.