A method and system for calculating seismic wave travel time based on a semi-discrete physical information neural network

Abstract

This invention discloses a method and system for calculating seismic wave travel time based on a semi-discrete physical information neural network, belonging to the field of geophysical imaging technology. It acquires velocity field data and source locations, and generates a spatial collocation set. Then, it constructs a neural network with alternating layers of smooth and non-smooth activation functions to capture gradient discontinuities in the travel time field. The output is processed using a decomposition method and an exponential activation function to eliminate source singularities and ensure non-negativity of the results. A semi-discrete difference scheme based on virtual step size is introduced, and a Hamiltonian loss function with upwind characteristics is constructed. Numerical dissipation is explicitly injected into the training process, forcing the network to converge to a physically correct viscous solution. Finally, the loss function is minimized to achieve high-precision and robust travel time field reconstruction under complex geological models. This invention solves the problems of standard physical information neural networks easily getting trapped in non-physical solutions and failing to characterize singular interfaces, and has the advantages of being meshless, highly flexible, and physically rigorous.

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