Rock-physics-guided machine learning for shear sonic log prediction

The S-wave velocity ([Formula: see text]) is a vital parameter for various petrophysical, geophysical, and geomechanical applications in subsurface characterization. Nevertheless, obtaining shear sonic log is frequently challenging because of its high economic, time, and operating costs. Conventional methods for predicting [Formula: see text] rely on empirical relationships and rock-physics models, which often fall short in accuracy due to their inability to account for the complex factors influencing the relationship between [Formula: see text] and other parameters. We develop a physics-guided machine learning (ML) approach to predict the shear sonic log using various physical parameters (e.g., natural gamma ray, P-wave velocity, density, and resistivity) that can be readily obtained from standard logging suites. Three types of rock-physical constraints combined with three guidance strategies form the various physics-guided models. Specifically, the three constraint models include mudrock line, empirical P- and S-wave velocity relationship, and multiparameter regression from the logging data, and the three guidance strategies involve physics-guided pseudolabels, physics-guided loss function, and transfer learning. To assess the model’s generalization ability and simulate the lack of labeled data in real-world applications, a single well is used as a training well, whereas the remaining four wells are used to blind test in a clastic reservoir. Compared with supervised ML without any constraints, all models incorporating physical constraints demonstrate a significant improvement in prediction accuracy and generalization performance. This underscores the importance of integrating the first-order physical laws into the network training for shear sonic log prediction. The most successful approach combines the multiparameter regression relationship with the physics-guided pseudolabels in this case, resulting in a remarkable 47% reduction in the average root-mean-square error during the blind test.