Combining Physics-Based and Data-Driven Models for Microseismic Velocity Inversion

Accurate source localization and source mechanism estimation in microseismic monitoring critically depend on precise subsurface velocity model reconstruction. Recent advances in data-driven approaches, such as neural network models, have demonstrated promising performance in seismic velocity inversion. However, purely data-driven methods are significantly constrained by their reliance on the completeness of the training dataset. Additionally, the performance of current neural network architectures remains suboptimal and requires further improvement. We propose a step-by-step training methodology that integrates the wave equation-based modeling with a modified U-shaped neural network (U-Net). This approach incorporates physical laws of wave propagation to constrain the updating process of the velocity model. The proposed method carries out the purely data-driven procedure first and then incorporates waveform modeling with finite-difference simulations. Besides, the new method defines dynamic weights within the loss function and introduces the Akaike information criterion (AIC) to detect and extract the P and S phases, which reduces the computational expenses as well as alleviates the artifacts in velocity models effectively. We conducted experiments with synthetic fault models and realistic layered models, and the results show that the wave equation-constrained method recovers the velocity model better than the purely data-driven algorithm. The approach leveraging physics-based and data-driven models can be easily adapted to other geophysical inversion tasks.