Physics-informed Neural Networks (PINNs) for Wave Propagation and Full
Waveform Inversions
Abstract
We propose a new approach to the solution of the wave propagation and
full waveform inversions (FWIs) based on a recent advance in deep
learning called Physics-Informed Neural Networks (PINNs). In this study,
we present an algorithm for PINNs applied to the acoustic wave equation
and test the model with both forward wave propagation and FWIs case
studies. These synthetic case studies are designed to explore the
ability of PINNs to handle varying degrees of structural complexity
using both teleseismic plane waves and seismic point sources. PINNs’
meshless formalism allows for a flexible implementation of the wave
equation and different types of boundary conditions. For instance, our
models demonstrate that PINN automatically satisfies absorbing boundary
conditions, a serious computational challenge for common wave
propagation solvers. Furthermore, a priori knowledge of the
subsurface structure can be seamlessly encoded in PINNs’ formulation. We
find that the current state-of-the-art PINNs provide good results for
the forward model, even though spectral element or finite difference
methods are more efficient and accurate. More importantly, our results
demonstrate that PINNs yield excellent results for inversions on all
cases considered and with limited computational complexity. Using PINNs
as a geophysical inversion solver offers exciting perspectives, not only
for the full waveform seismic inversions, but also when dealing with
other geophysical datasets (e.g., magnetotellurics, gravity) as well as
joint inversions because of its robust framework and simple
implementation.