Physics-Informed Neural Networks for Viscoacoustic Wave Propagation: Forward Modelling, Inversion and Discretization Sensitivity

TL;DR

This paper presents a physics-informed neural network (PINN) framework for viscoacoustic forward modeling and parameter inversion, embedding the viscoacoustic PDE into the loss to enforce physical constraints. The authors introduce a modular architecture with separate nets for pressure, velocity, and absorption, using open boundary conditions and early-time FDM-derived constraints to circumvent point-source singularities and reflections. They demonstrate that PINNs reproduce attenuative wavefields and enable simultaneous recovery of velocity and attenuation from sparse observations, even in layered media, while showing greater robustness to coarse discretization than finite-difference methods. The work suggests PINNs as a data-efficient, physically consistent alternative for high-resolution seismic modeling and inversion in attenuative media, with implications for seismic imaging and hazard assessment.

Abstract

Seismic wave forward and inverse modeling are fundamental tools for subsurface imaging and geological hazard assessment. Conventional grid-based numerical methods, such as finite-difference and finite-element approaches, often require dense discretization and repeated forward simulations, leading to high computational cost in inverse problems. Although deep learning has shown promise in seismic applications, its performance is commonly limited by the need for large labeled datasets and weak enforcement of physical constraints. In this study, we propose a unified physics-informed neural network (PINN) framework for forward modeling and parameter inversion of viscoacoustic wave propagation. By embedding the viscoacoustic wave equation into the learning process, the proposed framework accurately reproduces wavefields, attenuation, and phase characteristics, while enabling the simultaneous inversion of velocity and attenuation parameters from temporally sparse observations. Numerical experiments demonstrate that the PINN approach achieves stable and reliable accuracy compared with finite-difference solutions, while exhibiting reduced sensitivity to spatial discretization. These results highlight the potential of PINNs as a data-efficient and physically consistent alternative for high-resolution seismic modeling and inversion in attenuative media.

Figures (12)

• Figure 1: Overview of the proposed PINN framework for viscoacoustic wave propagation, including the network architecture and the constraint of physical laws. Three separate DNNs are used to approximate the pressure P, velocity v, and absorption coefficient g, respectively. Note that v-Net and g-Net are only activated in inversion mode. Automatic differentiation is exploited for obtaining the derivative terms and further constructing the loss function.
• Figure 2: The spatial domain in case 1. Open boundary conditions are applied at four boundaries.
• Figure 3: The results of pressure field distributions obtained from our proposed PINN and FDM in Case 1. We select three representative snapshots (i.e., t “ 0.35, 0.65, 0.95s) for comparison.
• Figure 4: Comparison of amplitude decay rate for PINNs (red) and FDM(blue) in case 1
• Figure 5: $\boldsymbol{\alpha}$--$f$ curves by PINNs, FDM, and the analytical solution.