S-wave velocity prediction of shale reservoirs based on explainable physically-data driven model

The shear wave (S-wave) velocity is a key basis for shale reservoir development, particularly for fracability evaluation. Additionally, S-wave velocity also plays a significant role in prestack seismic inversion and amplitude versus offset (AVO) analysis. However, the actual logging data often lack S-wave velocity data, so it is of significant importance for S-wave velocity prediction. We propose a rapid and precise prediction method for the S-wave velocity in shale reservoirs based on class activation maps (CAM) model combined with physically constrained two-dimensional Convolutional Neural Network (2D-CNN). High sensitivity curves related to S-wave velocity are selected as the foundation. Meanwhile, based on the petrophysical theory of pore medium, the petrophysical model of complex multi-mineral components is established. The dispersion effect is reduced to a certain extent and the results are used to constrain the model. The Adam optimization algorithm is used to construct a 2D-CNN model under the constraint of petrophysical model. The CAM is obtained by replacing the global average pooling (GAP) layer with a fully connected layer, which in turn leads to interpretable results. Then, the model is applied to wells A, B1, and B2 in the southern Songliao Basin. Afterwards, comparisons are made with unconstrained model and petrophysical model. The results show that the correlation coefficients and relative errors in the three test wells are 0.96 and 2.14%, 0.97 and 2.35%, and 0.97 and 2.9%, respectively. The higher prediction accuracy and generalization ability of the new method is confirmed. Finally, we present the defined C-factor as a means of evaluating the extent of concern regarding CAMs in regression problems. The C-factor confirms 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 to assist in proving the importance of constraints.

Keywords: S-wave velocity prediction; Physically constrained 2D-CNN; Petrophysical model; Class activation mapping technique; Explainable results