[Paper Review] Time-domain Wavefield Reconstruction Inversion in a TTI medium

Mathias Louboutin, Gabrio Rizzuti+1 more|arXiv (Cornell University)|Apr 15, 2020

Seismic Imaging and Inversion Techniques15 references4 citations

TL;DR

This paper introduces time-domain wavefield reconstruction inversion (TWRI) for tilted transverse isotropy (TTI) media, enabling robust full waveform inversion with improved resilience to cycle skipping and modeling errors. By leveraging a dual formulation with time-domain propagators, TWRI accurately handles anisotropic physics and outperforms conventional FWI even when anisotropy is mismodeled or omitted.

ABSTRACT

We introduce a generalization of time-domain wavefield reconstruction inversion to anisotropic acoustic modeling. Wavefield reconstruction inversion has been extensively researched in recent years for its ability to mitigate cycle skipping. The original method was formulated in the frequency domain with acoustic isotropic physics. However, frequency-domain modeling requires sophisticated iterative solvers that are difficult to scale to industrial-size problems and more realistic physical assumptions, such as tilted transverse isotropy, object of this study. The work presented here is based on a recently proposed dual formulation of wavefield reconstruction inversion, which allows time-domain propagator that are suitable to both large scales and more accurate physics.

Motivation & Objective

• Address the limitations of full waveform inversion (FWI) in complex subsurface structures, particularly cycle skipping due to poor initial models and bandlimited data.
• Overcome the scalability and implementation challenges of frequency-domain wavefield reconstruction inversion (WRI) for anisotropic media.
• Enable robust inversion in transverse tilted isotropy (TTI) media using time-domain modeling, which supports more accurate physics and large-scale problems.
• Demonstrate that TWRI remains effective even when the assumed physics (e.g., anisotropy) does not match the true data, improving robustness over FWI.
• Validate the feasibility and superiority of TWRI in TTI media through numerical experiments on synthetic models with realistic complexities.

Proposed method

• Adopt a dual formulation of wavefield reconstruction inversion (WRI) that reformulates the constrained least-squares problem into a saddle-point problem in the time domain.
• Use conventional time-domain forward and adjoint wavefield propagators, avoiding the need to solve the augmented wave equation directly.
• Formulate the TWRI objective function as a max-min problem involving model parameters and data-space dual variables, enabling efficient optimization.
• Replace the acoustic wave equation operator with a TTI wave equation operator in the forward modeling step, allowing accurate anisotropic physics.
• Compute model updates using a modified Jacobian that accounts for an extended source term derived from the dual variable, ensuring consistent gradient computation.
• Implement the method using Devito, a finite-difference wave solver, to enable high-performance, reproducible simulations on complex models.

Experimental results

Research questions

• RQ1 Can time-domain WRI be successfully extended to TTI anisotropic media, overcoming limitations of frequency-domain approaches?
• RQ2 How does TWRI perform in comparison to FWI when the true medium exhibits TTI anisotropy but the inversion assumes acoustic isotropy?
• RQ3 To what extent can TWRI mitigate cycle skipping and modeling errors in complex geological structures such as velocity kick-back and salt bodies?
• RQ4 Does the time-domain formulation of TWRI maintain robustness and convergence when anisotropic parameters are inaccurately assumed or omitted?
• RQ5 Can TWRI produce accurate initial model updates even with poor initial models and incorrect water layer parameters in realistic subsurface scenarios?

Key findings

• TWRI successfully reconstructs subsurface models in TTI media using time-domain modeling, demonstrating feasibility and robustness on synthetic benchmarks.
• In the Gaussian lens model, TWRI produces gradient updates that align with the true perturbation in sign and structure, while FWI generates flipped gradients due to cycle skipping.
• Even when anisotropy is entirely omitted in the modeling kernel, TWRI still produces a correct update direction, indicating resilience to physics mismatch.
• On the BG Compass model, TWRI accurately captures the velocity kick-back at ~1 km depth—a region where FWI fails due to turning wave trapping—demonstrating superior imaging capability.
• With incorrect water layer parameters, TWRI still generates a correct update direction in the water layer and preserves features like the velocity kick-back, unlike FWI which diverges.
• The time-domain formulation enables efficient, scalable implementation of TTI-WRI using standard time-stepping solvers, avoiding the scalability bottlenecks of frequency-domain iterative solvers.