Avoiding External Training Image in Direct Sampling: A Synthetic Case Study on Leveraging Extensive Hard Data

Abstract Extensive hard data could potentially replace the training image in doing Multi-Point Geostatistics (MPS). However, direct use of the standard MPS Direct Sampling algorithm will typically not produce proper results, owing to the absence (or at least, sufficient replication) of enough data patterns in the data set to warrant sufficient reproduction of the underlying random process. As a result, during the step of training image scanning, there will be a reduction of the conditional data neighbourhood in the simulation grid data event, generating inconsistencies of neighbourhood size in simulating each point. Here, we propose to use a spatial tolerance in extracting the training image data events. This framework can also be extended to MPS for the purpose of estimation rather than simulation. Additionally, we compared the proposed method with Sequential Indicator Simulation, where it outperformed the two-point geostatistics method.