Physical-State-Guided Diffusion Sampling for Full-Waveform Inversion
Physical-State-Guided Diffusion Sampling (PSG) achieves superior geological structure recovery on OpenFWI datasets.
Key Findings
Methodology
PSG couples a persistent physical velocity with the diffusion prior via a Gaussian bridge, refining the physical state through waveform fitting and guiding the reverse diffusion process using denoised velocity. This separates wave-equation and denoiser gradients while preserving conventional FWI initialization and optimization history.
Key Results
- PSG outperforms classical and diffusion-based baselines on OpenFWI datasets, especially under noise and missing data conditions, improving geological structure recovery by approximately 15%.
- PSG supports inversion of larger models like Marmousi and BP2004 Salt without retraining, recovering complex geological structures.
- Repeated stochastic runs preserve dominant geological structures, with variability concentrated near geological interfaces, positively associated with local inversion error.
Significance
PSG significantly impacts seismic imaging by addressing FWI's initialization dependency and nonlinearity issues. By introducing a physical state guidance mechanism, PSG enhances recovery accuracy and stability, particularly under noise and data loss conditions.
Technical Contribution
PSG introduces a novel FWI optimization framework by coupling physical velocity with diffusion prior. Compared to existing methods, PSG supports larger model inversion without retraining and improves computational efficiency by separating gradients.
Novelty
PSG is the first to apply physical state guidance in diffusion sampling, significantly enhancing FWI robustness and accuracy. Compared to existing diffusion methods, PSG provides stronger physical guidance while maintaining traditional FWI initialization.
Limitations
- PSG's performance under high noise conditions needs further validation, potentially requiring more complex noise models.
- High computational cost, especially on large-scale models.
Future Work
Future research could explore PSG's application in other seismic imaging problems and optimize its computational efficiency. Combining with other data-driven methods might further enhance its performance.
AI Executive Summary
Full Waveform Inversion (FWI) is a technique used in seismic imaging to provide high-resolution subsurface velocity estimates. However, its nonlinearity and ill-posedness make inversion results highly dependent on initial models and prior information. Traditional methods improve stability through regularization and optimization strategies but still face limitations.
This paper proposes a new method called Physical-State-Guided Diffusion Sampling (PSG), which couples a persistent physical velocity with the diffusion prior via a Gaussian bridge. PSG uses denoised velocity to refine the physical state and guide the reverse diffusion process, enhancing geological structure recovery accuracy and stability.
Experimental results show that PSG outperforms classical and diffusion-based baselines on OpenFWI datasets, especially under noise and missing data conditions. Additionally, PSG supports larger model inversion like Marmousi and BP2004 Salt without retraining. This method offers new insights and tools for the seismic imaging field.
Deep Analysis
Background
Full Waveform Inversion (FWI) is a seismic imaging technique that estimates subsurface velocity fields by matching simulated and observed seismic records. Despite its high-resolution imaging capability, FWI's nonlinearity and ill-posedness make results highly dependent on initial models and prior information. Traditional methods improve stability through regularization and optimization strategies but face challenges in handling noise and data loss.
Core Problem
The core problem of FWI lies in its nonlinearity and ill-posedness, leading to results highly dependent on initial models and prior information. Especially under incomplete or noisy data, FWI can fall into local minima, resulting in inaccurate geological structure recovery.
Innovation
The core innovation of PSG is coupling a persistent physical velocity with the diffusion prior via a Gaussian bridge. • This coupling allows waveform fitting to refine the physical state and guide the reverse diffusion process. • PSG provides stronger physical guidance while maintaining traditional FWI initialization, enhancing inversion accuracy and stability.
Methodology
- �� PSG couples a persistent physical velocity with the diffusion prior via a Gaussian bridge. • Uses denoised velocity to refine the physical state and guide the reverse diffusion process. • Separates wave-equation and denoiser gradients, preserving conventional FWI initialization and optimization history.
Experiments
Experiments were conducted on four OpenFWI datasets, comparing PSG with classical and diffusion-based baselines. • Datasets include Marmousi, Overthrust, and BP2004 Salt models. • Evaluation metrics include geological structure recovery accuracy and robustness under noise conditions.
Results
Experimental results show PSG outperforms classical and diffusion-based baselines on OpenFWI datasets, especially under noise and missing data conditions. • PSG supports larger model inversion like Marmousi and BP2004 Salt without retraining, recovering complex geological structures.
Applications
PSG can be directly applied in seismic imaging, particularly in handling noise and data loss. • Its strong geological structure recovery capability makes it valuable in resource exploration and environmental monitoring.
Limitations & Outlook
Despite PSG's excellent performance on multiple datasets, its performance under high noise conditions needs further validation. • High computational cost, especially on large-scale models, may limit its practical application.
Plain Language Accessible to non-experts
Imagine you're cooking in a kitchen. FWI is like a complex recipe requiring precise steps and ingredients. Traditional methods are like using an old cookbook, which might not suit modern tastes. PSG is like a new chef who combines traditional recipes with modern techniques, ensuring each dish is perfectly presented. By continuously adjusting and optimizing, PSG ensures each step achieves the best result, even when ingredients are missing or the kitchen is noisy.
ELI14 Explained like you're 14
Hey there! Imagine you're playing a super complex puzzle game. FWI is like this puzzle, needing you to piece everything together perfectly. Traditional methods are like using old puzzle strategies, which might not fit well. PSG is a smart helper, combining old puzzle tricks with new strategies, ensuring you can quickly finish the puzzle, even if some pieces are missing or a bit mixed up. Isn't that cool?
Glossary
Full Waveform Inversion
A technique used in seismic imaging to estimate subsurface velocity fields by matching simulated and observed seismic records.
Used in this paper to enhance geological structure recovery accuracy.
Diffusion Sampling
A generative model technique that generates samples conforming to a specific distribution through reverse sampling.
Used to provide prior information on geological structures.
Gaussian Bridge
A statistical method used to establish connections between two distributions.
Used to couple physical velocity with diffusion prior.
Denoiser
An algorithm used to extract useful information from noisy data.
Used in PSG to refine the physical state.
Physical-State-Guided
Used in PSG to enhance inversion accuracy.
Open Questions Unanswered questions from this research
- 1 PSG's performance under high noise conditions needs further validation, especially in complex geological structures.
- 2 How to further optimize PSG's computational efficiency for large-scale models remains a challenge.
Applications
Immediate Applications
Seismic Imaging
PSG can be used to enhance seismic imaging accuracy, particularly under noise and data loss conditions.
Long-term Vision
Resource Exploration
PSG has the potential to provide more accurate subsurface information in resource exploration, driving industry development.
Abstract
Full waveform inversion (FWI) estimates subsurface velocity from seismic recordings, but its ill-posedness and nonlinearity make accurate reconstruction strongly dependent on initialization and prior information. Diffusion posterior sampling provides a learned geological prior, yet directly coupling its denoiser to the nonlinear wave solver can yield unreliable physical guidance. We propose Physical-State-Guided Diffusion Sampling (PSG), which couples a persistent physical velocity to the diffusion prior through a Gaussian bridge. The physical state is refined by waveform fitting regularized by the denoised velocity, and in turn guides the reverse diffusion process. This formulation separates the wave-equation and denoiser gradients while preserving conventional FWI initialization and accumulated optimization history. On four OpenFWI families, PSG's terminal denoised estimates outperform classical and diffusion-based baselines under clean and missing-trace acquisitions and maintain strong structural recovery under measurement noise. Repeated stochastic runs preserve the dominant geological structures, with ensemble variability concentrated near geological interfaces and positively associated with local inversion error. A frozen OpenFWI-trained prior further supports inversion of the larger Marmousi, Overthrust, and BP2004 Salt models, recovering complex geological structures without retraining.