S-wave velocity prediction using physical model-driven Gaussian process regression: A case study of tight sandstone reservoir

Abstract

Knowing S-wave velocity is critical to characterize the tight sandstone reservoir owing to its insensitive elastic responses. However, it is challenging to precisely acquire S-wave information due to the high cost and technical difficulties. Here, beyond the conventional model- and statistical data-driven methods, we propose a numerical scheme based on Gaussian process regression (GPR) to predict the S-wave velocity with P-wave velocity and lithologic parameters as input. The GPR is a nonparametric kernel-based probabilistic model, which is explicitly defined by the mean and covariance functions. Compared with other machine-learning methods even the deep learning method, the GPR is a small data-based machine learning method, which is significant for geophysical issues. In addition, through training a small data set, the GPR-based scheme not only accurately estimates S-wave velocity but also quantifies the uncertainty of the results. Compared with conventional methods such as the Castagna relations, the comprehensive formula, and the bidirectional long short-term memory, the S-wave velocity predicted by GPR is more accurate in terms of the mean-squared error, root-mean-squared error, average relative error, and correlation coefficient. The field data test demonstrates that the proposed GPR-based scheme is superior and can be satisfactorily implemented for logging data.