Physics-Informed Neural Networks (PINNs) for simulating wave propagation, synthetic seismogram generation, and prediction of wavespeed distribution

Abstract

This study investigates the application of Physics-Informed Neural Networks (PINNs) for the forward modeling of seismic wave propagation and inverse modeling to obtain the wavespeed distribution. PINNs are a class of neural networks that incorporate a Partial Differential Equation (PDE), in this case specifically the acoustic wave equation, into their loss function, enabling them to solve PDEs without relying on a discretized mesh. This mesh-free property shows potential for computationally efficient alternatives to traditional seismic imaging methods like Full Waveform Inversion (FWI), while the application of PINNs in computational seismology is non-trivial and requires care.

Building on previous work, the research systematically experiments with various modular components and hyperparameters of the PINN framework. Experiments were conducted using three velocity models: homogeneous, smooth ellipse anomaly, and discontinuous ellipse anomaly. These velocity models represent increasing levels of reconstruction complexity for PINNs. The training data consisted of two synthetic displacement fields at initial times and displacement recordings from a borehole configuration of 20 seismometers.

The experiments explored alternative choices for four key components of the PINN design. (i) Sampling Strategies: The findings indicate that random sampling with resampling each training iteration is the most effective strategy among those tested for selecting collocation points. (ii) Spatial Normalization: The study proposed an alternative spatial normalization approach based on the time duration of seismograms. This method avoids the circular reasoning inherent in older methods that rely on prior knowledge of the background wavespeed, a property the inversion aims to discover. (iii) Network Architecture: The work demonstrated the necessity of a dual-network architecture, one network to output the wavespeed (α) and another for the wave potential (ϕ), for solving the simultaneous forward and inverse problem. A single-network model was found to fail for the inhomogeneous velocity models.

Additionally, the research analyzed the impact of inversion domain size, finding that the domain is limited, as attempting to cover a large area of the initial displacement perturbations led to convergence failure. The study concludes by discussing pathways for future work, including speculations on the vital next step of replacing the unrealistic, hard-to-obtain initial displacement fields with additional seismometer recordings distributed throughout the domain. This would enable larger inversion domains and increase the PINNs potential for practical use on real-world data.