[Paper Review] PINNtomo: Seismic tomography using physics-informed neural networks

Umair bin Waheed, Tariq Alkhalifah+3 more|arXiv (Cornell University)|Apr 4, 2021

Seismic Imaging and Inversion Techniques23 references39 citations

TL;DR

PINNtomo uses physics-informed neural networks to invert for seismic velocity from traveltime data by solving a factored eikonal equation, yielding a mesh-free, initial-model-agnostic tomography method with improved regularization.

ABSTRACT

Seismic traveltime tomography using transmission data is widely used to image the Earth's interior from global to local scales. In seismic imaging, it is used to obtain velocity models for subsequent depth-migration or full-waveform inversion. In addition, cross-hole tomography has been successfully applied for a variety of applications, including mineral exploration, reservoir monitoring, and CO2 injection and sequestration. Conventional tomography techniques suffer from a number of limitations, including the use of a smoothing regularizer that is agnostic to the physics of wave propagation. Here, we propose a novel tomography method to address these challenges using developments in the field of scientific machine learning. Using seismic traveltimes observed at seismic stations covering part of the computational model, we train neural networks to approximate the traveltime factor and the velocity fields, subject to the physics-informed regularizer formed by the factored eikonal equation. This allows us to better compensate for the ill-posedness of the tomography problem compared to conventional methods and results in a number of other attractive features, including computational efficiency. We show the efficacy of the proposed method and its capabilities through synthetic tests for surface seismic and cross-hole geometries. Contrary to conventional techniques, we find the performance of the proposed method to be agnostic to the choice of the initial velocity model.

Motivation & Objective

• Motivate seismic traveltime tomography as a tool for velocity model building across scales.
• Address ill-posedness and regularization issues in conventional tomography by incorporating physics directly into learning.
• Develop a PINN-based framework to jointly estimate traveltime factors and velocity fields.
• Demonstrate robustness to initial velocity models and applicability to surface and cross-hole geometries.

Proposed method

• Formulate the traveltime T(x) via a factored eikonal equation T(x)=T0(x)·τ(x) to manage the source singularity.
• Use two neural networks: one for the traveltime factor τ(x_s, x) and one for the velocity v(x).
• Enforce physics through a loss that combines traveltime misfit, boundary conditions, and the residual of the factored eikonal equation.
• Pass network outputs through sigmoid activations to enforce positivity and scale to physical ranges.
• Train networks jointly by minimizing a single objective that includes data misfit, boundary conditions, and PDE residuals.
• Implement with SciANN (TensorFlow) and optimize with Adam followed by L-BFGS-B.

Experimental results

Research questions

• RQ1 Can PINNs accurately recover long-wavelength velocity structure from traveltime data in cross-hole and surface geometries?
• RQ2 Is the PINNtomo approach robust to the choice of initial velocity model and irregular topography?
• RQ3 Does incorporating the eikonal equation residual as a physics-informed regularizer improve inversion over conventional smoothing-based methods?
• RQ4 What are the computational and memory implications of the PINNtomo framework for typical 2D seismic tomography setups?

Key findings

• The method reliably recovers long-wavelength features of the true velocity model in both cross-hole and surface geometries.
• PINNtomo is agnostic to the initial velocity model and does not require an imposed depth gradient.
• The physics-informed residual of the eikonal equation acts as an effective regularizer beyond conventional smoothing.
• The mesh-free approach accommodates irregular topography and nonuniform source/receiver placements.
• Computational efficiency is favorable, with reported GTX-level hardware solving examples in minutes (e.g., cross-hole ~6 minutes; surface ~20 minutes).