Inversion for shear-tensile focal mechanisms using an unsupervised physics-guided neural network

Hongliang Zhang, Kristopher A. H. Innanen, David W. S. Eaton

We present a novel physics-guided neural network to estimate shear-tensile focal mechanisms for microearthquakes using displacement amplitudes of direct P-wave. Compared with conventional data-driven fully connected (FC) neural networks, our physics-guided neural network is implemented in an unsupervised fashion and avoids the use of training data, which may be incomplete or unavailable. We incorporate three FC layers and a scaling & shifting layer to estimate shear-tensile focal mechanisms for multiple events. Then, a forward modeling layer is added, which generates synthetic amplitude data based on the source mechanisms emerging from the previous layer. The neural network weights are iteratively updated to minimize the mean squared error between observed and modeled normalized P-wave amplitudes. We apply this machine-learning approach to a set of 530 induced events recorded during hydraulic fracture simulation of Duvernay Shale west of Fox Creek, Alberta, yielding results that are consistent with previously reported source mechanisms for the same dataset. A distinct cluster characterized by more complex mechanisms exhibits relatively large Kagan angles (10 - 25) compared with the previously reported best double-couple solutions, mainly due to model simplification of the shear-tensile focal mechanism. Uncertainty tests demonstrate the robustness of the inversion results and high tolerance of our neural network to errors in event locations, velocity model and P-wave amplitudes. Compared with a single-event grid-search algorithm to estimate shear-tensile focal mechanisms, the proposed neural network approach exhibits significantly higher computational efficiency.