Training image (TI) is a key input of multipoint geostatistical modeling. For modeling sedimentary facies under nonstationary conditions, it is common to first generate nonstationary TIs, then use a partitioned simulation approach, and finally merge the realizations of each subregion. We develop a new method for partitioning nonstationary TIs based on features extracted using a deep network model. The basic idea of the method is to crop a TI with a sliding window to obtain the subblocks of the TI and use the pretrained convolutional neural network model as a fixed feature extractor for the subblocks. We use K-means to cluster the extracted deep features and t-distributed stochastic neighbor embedding to visualize the clustering effect and assign the classification information of all feature points to the subblocks of the TI as its subregion markers. Finally, we stitch the subblocks of the marked TIs by position to obtain the partitioning results of the nonstationary TIs. Experimental results indicate that the classification accuracy of the method reaches 90.53%, and the partition effect is relatively good. Research indicates that the method can reproduce well the spatial variation characteristics of nonstationary TIs and provide a new method for processing the multipoint geostatistical nonstationarity.

An a priori model for multipoint statistics (MPS) modeling approaches is a training image. Before using MPS modeling, it must be determined whether the training images satisfy the spatial statistical stationarity. Modeling can be performed using the regular MPS approach if a training image is stationary. Otherwise, an enhanced method of nonstationary modeling is required. For instance, partition-based nonstationary modeling is an option. This study proposes a nonstationary evaluation metric based on pattern tile distances. It is possible to more accurately quantify the characteristics of the various distributions of spatial structure features in the entire space and achieve the goal of quantitatively evaluating the nonstationary metrics of training images by quantifying the distances of lower-level subpatterns in the pattern. Furthermore, an automatic partitioning approach based on pattern tile discrepancy is proposed for nonstationary training images to avoid the subjective and inefficient issues of manual partitioning when the training images cannot meet the stationary requirement of MPS modeling.