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A physics‐guided neural network‐based approach to velocity model calibration for microseismic data

The physics‐guided neural network framework combines the effectiveness of data‐driven and physics‐based models, and it is, therefore, becoming increasingly popular in geophysical applications. We present a physics‐guided neural network–based approach to calibrate velocity models for microseismic data. In our implementation, the physics‐guided neural network comprises of a user‐selected number of fully connected layers, a scaling and shifting layer and a forward modelling operator layer. We input the observed P‐ and S‐wave arrival times to the neural network. In the forward pass, the network's output layer produces normalized P‐ and S‐wave velocities for the subsurface model. The scaling and shifting layer converts the normalized output to realistic velocity values. The forward modelling operator (i.e. a ray‐shooting algorithm) layer computes traveltimes using the velocities from the preceding scaling and shifting layer and the known source–receiver locations. We then evaluate a loss function that compares the predicted traveltimes with the input observed arrival times, and update network's weights and bias parameters. We also use a weight‐based saliency measure to evaluate whether the selected network architecture (i.e. number of hidden layers and neurons) is optimal for the model calibration problem. Finally, using synthetic data examples, we demonstrate that our unsupervised physics‐guided neural network–based approach can provide robust velocity model and uncertainty estimates.