Shear wave velocity prediction using physical model-driven GPR: a case study of tight sandstone reservoir

Knowing shear wave (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 both P-wave velocity and lithologic parameters as input. The GPR is a non-parametric kernelbasedprobabilistic model, which is explicitly de ned by the mean and covariance functions. Compared with other machine learning method even the deep learning method, the Gaussian process regression is a small data based machine learning method, which is signi ficant for geophysical issues. In addition, through training a small data set, the GPR-based scheme not only accurately estimate S-wave velocity, but also quantifythe uncertainty of the results. Compared with conventional methods including the mudrock line formula, the comprehensive formula and the BiLSTM, the S-wave velocity predicted by GPR are more accurate in terms of the mean squared error, root mean squared error, average relative error and correlation coeffcient. The eld data test demonstrates that the proposed GPR-based scheme is superior and can be satisfactorily implemented for logging data.