Publikationsrepositorium - Helmholtz-Zentrum Dresden-Rossendorf

Extensive hard data could potentially replace the training image in doing MPS. However, direct use of the the standard MPS Direct Sampling algorithm will typically not produce proper results, owing to the absence (or at least, sufficient replication) of every necessary data pattern in the data set. 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 has long been used to obtain experimental variogram in two-point geostatistics, and is also common in high-order cumulant based methods.

A synthetic case study of a fluvial depositional environment will be presented, together with a comparison of the usage of various types of training images (e.g. hard data, complete training image, multiple training images). This framework can also be extended to MPS for the purpose of estimation rather than simulation.
This is achieved by obtaining marginal
conditional probabilities by storing potential simulated values during the training image scan-
ning step for each grid cell, conditioning only to hard data. This could be a time saver for
users interested only in the point-wise statistics of the realizations without having to generate
multiple realizations.