GPU-accelerated Direct Sampling method for multiple-point statistical simulation

• A GPU-based Direct Sampling algorithm is proposed for multiple point simulation.
• Implementation adopts several parallel algorithms for data-parallel speedup.
• Experimental results show its superiorities in terms of simulation time.
• The concept of the search ellipsoid is combined with the DS algorithm.

Geostatistical simulation techniques have become a widely used tool for the modeling of oil and gas reservoirs and the assessment of uncertainty. The Direct Sampling (DS) algorithm is a recent multiple-point statistical simulation technique. It directly samples the training image (TI) during the simulation process by calculating distances between the TI patterns and the given data events found in the simulation grid (SG). Omitting the prior storage of all the TI patterns in a database, the DS algorithm can be used to simulate categorical, continuous and multivariate variables. Three fundamental input parameters are required for the definition of DS applications: the number of neighbors n, the acceptance threshold t and the fraction of the TI to scan f. For very large grids and complex spatial models with more severe parameter restrictions, the computational costs in terms of simulation time often become the bottleneck of practical applications.This paper focuses on an innovative implementation of the Direct Sampling method which exploits the benefits of graphics processing units (GPUs) to improve computational performance. Parallel schemes are applied to deal with two of the DS input parameters, n and f. Performance tests are carried out with large 3D grid size and the results are compared with those obtained based on the simulations with central processing units (CPU). The comparison indicates that the use of GPUs reduces the computation time by a factor of 10X–100X depending on the input parameters. Moreover, the concept of the search ellipsoid can be conveniently combined with the flexible data template of the DS method, and our experimental results of sand channels reconstruction show that it can improve the reproduction of the long-range connectivity patterns.