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

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 Swave 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 meanand can be satisfactorily implemented for logging data.