Wavefield Reconstruction Inversion via Physics-Informed Neural Networks

Abstract

Wavefield reconstruction inversion (WRI) formulates a PDE-constrained optimization problem to reduce cycle skipping in full-waveform inversion (FWI). WRI is often implemented by solving for the frequency-domain representation of the wavefield using the finite-difference method. The approach requires matrix inversions and affords limited flexibility to accommodating irregular model geometries. On the other hand, physics-informed neural network (PINN) uses the underlying physical laws as loss functions to train the neural network (NN) to provide flexible continuous functional approximations of the solutions without matrix inversions. By including a dataconstrained term in the loss function, the trained NN can reconstruct a wavefield that simultaneously fits the recorded data and satisfies the Helmholtz equation for a given initial velocity model. Using the predicted wavefields, we rely on a small-size NN to predict the velocity using the reconstructed wavefield. In this velocity prediction NN, spatial coordinates are used as input data to the network and the scattered Helmholtz equation is used to define the loss function. After we train this network, we are able to predict the velocity in the domain of interest. We develop this PINN-based WRI method and demonstrate its potential using a part of the Sigsbee2A model and a modified Marmousi model. The results show that the PINN-based WRI is able to invert for a reasonable velocity with very limited iterations and frequencies, which can be used in a subsequent FWI application.

Physics‐Informed Neural Networks for Elliptical‐Anisotropy Eikonal Tomography: Application to Data From the Northeastern Tibetan Plateau

“…For forward problems, PINNs have been applied to the eikonal equation for traveltime calculation in isotropic and anisotropic media (Smith et al., 2020; Taufik et al., 2022; Waheed, Alkhalifah, et al., 2021; Waheed et al., 2020; Waheed, Haghighat, et al., 2021) and directly simulate wave equation solutions for acoustic and elastic wave propagation (Alkhalifah et al., 2020; Karimpouli & Tahmasebi, 2020; Moseley, Markham, & Nissen‐Meyer, 2020; Moseley, Nissen‐Meyer, & Markham, 2020; Song & Wang, 2023; Song et al., 2021, 2022). For inverse problems, PINNs have been proposed for exploration‐scale seismic tomography with the factored eikonal equation (Gou et al., 2022; Waheed, Alkhalifah, et al., 2021; Waheed, Haghighat, et al., 2021) and wavefield reconstruction inversion (Song & Alkhalifah, 2021). A PINN algorithm has also been developed for full waveform inversion, as demonstrated through various synthetic case studies (Rasht‐Behesht et al., 2022).…”

Eikonal Tomography With Physics‐Informed Neural Networks: Rayleigh Wave Phase Velocity in the Northeastern Margin of the Tibetan Plateau

“…This idea is highly beneficial to seismic tomography for avoiding the iterative process required by the nonlinearity and can directly extract the predicted parameters (e.g., velocity) for the model. The PINN framework has already shown great potential in solving the seismic forward problem (Moseley et al., 2020; Smith et al., 2020; Song et al., 2021; Waheed, Haghighat, et al., 2021) and seismic inverse problem (Song & Alkhalifah, 2021). Waheed, Alkhalifah, et al.…”

Single Reference Frequency Loss for Multifrequency Wavefield Representation Using Physics-Informed Neural Networks

“…Besides, the complexity of the wave equation in elastic or anisotropic media can considerably add to the computational burden. The recently developed physicsinformed neural network (PINN) for solving the Helmholtz equation showed considerable potential in modeling because of its flexibility, low memory requirement, and no limitations are imposed on the shape of the solution space [1]. However, it is hard to train, admitting less than optimal solutions for practical Xinquan Huang and Tariq Alkhalifah are with the Physical science and engineering division, KAUST e-mail: (xinquan.huang@kaust.edu.sa, tariq.alkhalifah@kaust.edu.sa).…”