A Physically Regularized Neural Network-Based Full Waveform Inversion Method

doi:10.1007/s11770-025-1264-2

A Physically Regularized Neural Network-Based Full Waveform Inversion Method

2025-10-01

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DOI：10.1007/s11770-025-1264-2

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Full waveform inversion (FWI) is an imaging method that uses all the information in the seismic record to reconstruct the parameters of the subsurface medium with high accuracy, and is widely used in geophysical exploration. However, the traditional FWI method faces challenges such as high computational cost, strong dependence on the initial model, and the tendency to fall into local optimality. To this end, this paper proposes a full waveform inversion method based on Physically Regularized Neural Network for FWI (PRNN-FWI), which integrates the nonlinear modelling capability of neural networks with the physical constraints of fluctuation equations in order to construct an end-to-end inversion framework. The method takes the seismic source record as input, generates a velocity model by neural network, and generates a synthetic seismic record by finite-difference orthogonal module, which is then used for residual computation with the observed data. During the inversion process, an automatic differentiation mechanism is used to update the network parameters in reverse, thus continuously optimising the velocity model. In this paper, a physical regularisation term is introduced into the loss function to explicitly strengthen the fluctuation equation constraints and improve the physical consistency and generalisation ability of the model. Experimental results show that PRNN-FWI can still effectively reconstruct the real velocity structure without the need to provide an initial velocity model. Compared with the traditional FWI method, the method in this paper greatly reduces the dependence on the initial model, and the computational cost of the inversion can be significantly reduced by replacing the model gradient update of the traditional method with the neural network approximation. The inversion test results under the complex construction model also show that the method in this paper has better imaging effect and application potential.

Keywords:

Physically Regularized Neural Network

Velocity Modeling

Wave equation

Full Waveform Inversion

A Physically Regularized Neural Network-Based Full Waveform Inversion Method

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