First-Arrival Constrained Physics-Informed Recurrent Neural Networks for Initial Model-Insensitive Full Waveform Inversion in Vertical Seismic Profiling

FWI is a nonlinear optimization problem; significant discrepancies between the initial and true velocity models can lead to solutions converging to local optima. To address this issue, we proposed a PIRNN-based FWI method with first-arrival time constraints. Physics-informed recurrent neural networks (PIRNNs) integrate the physical processes of seismic wave propagation into recurrent neural networks, offering a novel approach for full-waveform inversion (FWI). First, the physical processes of seismic wave propagation were embedded into the recurrent neural network, enabling finite-difference solutions of the wave equation through forward propagation. Second, first-arrival time differences between synthetic and observed records were calculated, which then guided the selection of appropriate seismic traces for FWI loss computation. Additionally, the spatiotemporal gradient information recorded during the forward propagation of the recurrent neural network was utilized for backpropagation, enabling nonlinear optimization of FWI. This method avoids the local optima caused by waveform mismatches between the observed and synthetic records resulting from inaccurate initial velocity models. Numerical experiments on the BP and Marmousi velocity models demonstrated that the proposed method accurately reconstructed subsurface velocity structures even when the initial model significantly deviated from the true model, and maintained a degree of reconstruction accuracy in the presence of considerable noise, thereby validating its low sensitivity to the initial model and its robustness against noise.