Estimation of shear wave velocity via rock physics-constrained KAN transformer

SUMMARY Elastic wave velocities of reservoirs are among the fundamental parameters for logging evaluation, seismic prediction and hydrocarbon exploration. In conventional geophysical logging, shear wave velocity (VS) is derived from array acoustic logs, which are characterized by high-operational costs and time-consuming processes that restrict their widespread application. Therefore, accurate VS estimation has become a significant task in reservoir prediction. The current major methods of estimating VS include rock physics model and machine learning. However, the traditional physical rock models overlook effects of fluid flow, and the existing machine learning models lack physical knowledge constraints. A novel predictive framework of integrating rock physics model (RPM) and Kolmogorov–Arnold Transformers (KAT) is proposed to estimate elastic wave velocities. First, an RPM is established by incorporating multiple wave-induced fluid flow effects, specifically integrating ‘static, microscopic and macroscopic flow’ regimes. Subsequently, a new time-series network, KAT, is constructed by innovatively replacing standard multilayer perceptron layers with Kolmogorov–Arnold network layers within the transformer architecture, which can capture the sequential dependences of logging data and improve model performance. Finally, the constructed KAT is further constrained by the RPM, and the proposed framework is applied to estimate VS in deep tight sandstone formation. Results demonstrate that the framework minimizes prediction error between measured and estimated VS compared to pure data-driven method or physical model-driven method. Overall, the framework exhibits high reliability, consequently facilitating more precise subsurface parameter prediction.