Study on S-wave velocity prediction in shale reservoirs based on explainable 2D-CNN under physical constraints

The shear wave (S-wave) velocity is a critical rock elastic parameter in shale reservoirs, especially for evaluating shale fracability. To effectively supplement S-wave velocity under the condition of no actual measurement data, this paper proposes a physically-data driven method for the S-wave velocity prediction in shale reservoirs based on the class activation mapping (CAM) technique combined with a physically constrained two-dimensional Convolutional Neural Network (2D-CNN). High-sensitivity log curves related to S-wave velocity are selected as the basis from the data sensitivity analysis. Then, we establish a petrophysical model of complex multi-mineral components based on the petrophysical properties of porous medium and the Biot-Gassmann equation. This model can help reduce the dispersion effect and constrain the 2D-CNN. In deep learning, the 2D-CNN model is optimized using the Adam, and the class activation maps (CAMs) are obtained by replacing the fully connected layer with the global average pooling (GAP) layer, resulting in explainable results. The model is then applied to wells A, B1, and B2 in the southern Songliao Basin, China and compared with the unconstrained model and the petrophysical model. The results show higher prediction accuracy and generalization ability, as evidenced by correlation coefficients and relative errors of 0.98 and 2.14%, 0.97 and 2.35%, 0.96 and 2.89% in the three test wells, respectively. Finally, we present the defined C-factor as a means of evaluating the extent of concern regarding CAMs in regression problems. When the results of the petrophysical model are added to the 2D feature maps, the C-factor values are significantly increased, indicating that the focus of 2D-CNN can be significantly enhanced by incorporating the petrophysical model, thereby imposing physical constraints on the 2D-CNN. In addition, we establish the SHAP model, and the results of the petrophysical model have the highest average SHAP values across the three test wells. This helps to assist in proving the importance of constraints.