An efficient method of predicting S-wave velocity using sparse Gaussian process regression for a tight sandstone reservoir

The shear wave (S-wave) velocity plays a crucial role in interpreting the lithology in seismic data, identifying fluids and predicting reservoirs. However, S-wave velocity is often unavailable due to the high cost of measurement and technical constraints. Conventional methods exhibit limitations that potentially impact the accuracy or efficiency on predicting S-wave velocity. Moreover, these methods always ignore the uncertainty quantification associated with the predicted results. This paper proposes a sparse Gaussian process regression (SGPR) method to predict the S-wave velocity in tight sandstone reservoirs. SGPR is a highly efficient regression technique that is based on the Gaussian process regression (GPR) method. In the SGPR method, inducing inputs are introduced to approximate the kernel matrix to decrease the computational complexity. A sparse set of inducing inputs and kernel hyperparameters are optimized through minimizing the Kullback-Leibler (KL) divergence between the exact posterior distribution and the approximate one. In this study, we select several types of logging data, which include porosity, water saturation, shale content, lithology and P-wave velocity, as the inputs for the SGPR method to predict S-wave velocity. To validate its effectiveness, we use the SGPR method to predict S-wave velocity in tight sandstone and compare the results with those from the GPR method, the bidirectional long short-term memory (BiLSTM) method and the Xu-White model. Additionally, we conduct cross-validation to demonstrate the robustness of the SGPR method. Our findings indicate that the SGPR method presents better performance and significant advantages about the accuracy and efficiency. Moreover, the SGPR method offers uncertainty quantification for the predicted S-wave velocity.