Impact of geostatistical nonstationarity on convolutional neural network predictions

Convolutional neural networks (CNNs) are gaining tremendous attention in subsurface studies due to their ability to learn from spatial image data. However, most deep learning studies in spatial context do not consider the impact of geostatistical nonstationarity, which is commonly encountered within the subsurface phenomenon. We demonstrate the impact of geostatistical nonstationarity on CNN prediction performance. We propose a CNN model to predict the variogram range of sequential Gaussian simulation (SGS) realizations. Model performance is evaluated for stationarity and three common forms of geostatistical nonstationarity: (1) large relative variogram range-related nonstationarity, (2) additive trend and residual model-related nonstationarity, and (3) mixture population model-related nonstationarity. Our CNN model prediction accuracy decreases in the presence of large relative variogram range-related nonstationarity, for the additive trend and residual model-related nonstationarity, the relative prediction errors increase for high trend variance proportions with a decrease in variogram range; regarding the mixture population model-related nonstationarity, the predictions are closer to the smaller variogram range. Common forms of geostatistical nonstationarity may impact CNN predictions, as with geostatistical estimation methods, trend removal and workflows with stationary residuals are recommended.