Rock Physics guided machine learning for shear sonic log prediction

Shear wave velocity (Vs) is a vital parameter for various petrophysical, geophysical, and geomechanical applications in subsurface characterization. However, obtaining shear sonic log is often challenging since it often costs extra budget and time to acquire. Conventional methods for predicting Vs often rely on empirical relationships and rock physics models. However, these models often fall short in accuracy due to their inability to account for the complex nonlinear factors affecting the relationship between Vs and other parameters. We propose a physics-guided machine learning approach to predict shear sonic log using the various physical parameters (e.g. natural gamma ray, P-wave velocity, density, resistivity) that can be routinely obtained from standard logging suites. Three types of rock physical constraints including the mudrock line, empirical P- and S- wave velocity relationship and multi-parameter regression from the logging data, are combined with three physical guidance strategies including constructing physics-guided pseudo labels, physics-guided loss function and transfer learning, to blind test four wells based on one training well in a clastic reservoir. Compared to pure supervised ML, all the model that incorporates physical constraints significantly improves prediction accuracy and generalization performance, demonstrating the importance of incorporating first-order physical laws into data-driven network training. The multi-parameter regression relationship combined with the strategy of constructing physics-guided pseudo labels gives the best prediction performance, with the average root mean square error (RMSE) of the blind test dropping by 47%.