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1. New likelihood functions and level-set prior for Bayesian full-waveform inversion

   https://doi.org/10.1190/segam2020-3428223.1  

   Dunlop, Matt; Yang, Yunan (September 2020, SEG Technical Program Expanded Abstracts 2020)

   null (Ed.)

   Seismic full-waveform inversion aims to reconstruct subsurface medium parameters from recorded seismic data. It is solved as a constrained optimization problem in the deterministic approach. Many different objective functions have been proposed to tackle the nonconvexity that originated from the cycle-skipping issues. The analogy between objective functions in the deterministic inversion and likelihood functions in Bayesian inversion motivates us to analyze the noise model each objective function accounts for under the Bayesian inference setting. We also show the existence and wellposedness of their corresponding posterior measures. In particular, the theorem shows that theWasserstein-type likelihood offers better stability with respect to the noise in the recorded data. Together with an application of the level-set prior, we demonstrate by numerical examples the successful reconstruction from Bayesian full-waveform inversion under the proper choices of the likelihood function and the prior distribution. 

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2. Resolution and trade-offs in global anelastic full-waveform inversion

   https://doi.org/10.1093/gji/ggad462  

   Espindola-Carmona, Armando; Örsvuran, Rıdvan; Mai, P. Martin; Bozdağ, Ebru; Peter, Daniel B. (November 2023, Geophysical Journal International)

   SUMMARY Improving the resolution of seismic anelastic models is critical for a better understanding of the Earth’s subsurface structure and dynamics. Seismic attenuation plays a crucial role in estimating water content, partial melting and temperature variations in the Earth’s crust and mantle. However, compared to seismic wave-speed models, seismic attenuation tomography models tend to be less resolved. This is due to the complexity of amplitude measurements and the challenge of isolating the effect of attenuation in the data from other parameters. Physical dispersion caused by attenuation also affects seismic wave speeds, and neglecting scattering/defocusing effects in classical anelastic models can lead to biased results. To overcome these challenges, it is essential to account for the full 3-D complexity of seismic wave propagation. Although various synthetic tests have been conducted to validate anelastic full-waveform inversion (FWI), there is still a lack of understanding regarding the trade-off between elastic and anelastic parameters, as well as the variable influence of different parameter classes on the data. In this context, we present a synthetic study to explore different strategies for global anelastic inversions. To assess the resolution and sensitivity for different misfit functions, we first perform mono-parameter inversions by inverting only for attenuation. Then, to study trade-offs between parameters and resolution, we test two different inversion strategies (simultaneous and sequential) to jointly constrain the elastic and anelastic parameters. We found that a sequential inversion strategy performs better for imaging attenuation than a simultaneous inversion. We also demonstrate the dominance of seismic wave speeds over attenuation, underscoring the importance of determining a good approximation of the Hessian matrix and suitable damping factors for each parameter class. 

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3. Ambient Noise Full Waveform Inversion With Neural Operators

   https://doi.org/10.1029/2025JB031624  

   Zou, Caifeng; Ross, Zachary E; Clayton, Robert W; Lin, Fan‐Chi; Azizzadenesheli, Kamyar (November 2025, Journal of Geophysical Research: Solid Earth)

   Abstract Numerical simulations of seismic wave propagation are crucial for investigating velocity structures and improving seismic hazard assessment. However, standard methods such as finite difference or finite element are computationally expensive. Recent studies have shown that a new class of machine learning models, called neural operators, can solve the elastodynamic wave equation orders of magnitude faster than conventional methods. Full waveform inversion is a prime beneficiary of the accelerated simulations. Neural operators, as end‐to‐end differentiable operators, combined with automatic differentiation, provide an alternative approach to the adjoint‐state method. State‐of‐the‐art optimization techniques built into PyTorch provide neural operators with greater flexibility to improve the optimization dynamics of full waveform inversion, thereby mitigating cycle‐skipping problems. In this study, we demonstrate the first application of neural operators for full waveform inversion on a real seismic data set, which consists of several nodal transects collected across the San Gabriel, Chino, and San Bernardino basins in the Los Angeles metropolitan area. 

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4. Using convolutional neural networks to develop starting models for near-surface 2-D full waveform inversion

   https://doi.org/10.1093/gji/ggac179  

   Vantassel, Joseph P.; Kumar, Krishna; Cox, Brady R. (May 2022, Geophysical Journal International)

   SUMMARY Non-invasive subsurface imaging using full waveform inversion (FWI) has the potential to fundamentally change near-surface (<30 m) site characterization by enabling the recovery of high-resolution (metre-scale) 2-D/3-D maps of subsurface elastic material properties. Yet, FWI results are quite sensitive to their starting model due to their dependence on local-search optimization techniques and inversion non-uniqueness. Starting model dependence is particularly problematic for near-surface FWI due to the complexity of the recorded seismic wavefield (e.g. dominant surface waves intermixed with body waves) and the potential for significant spatial variability over short distances. In response, convolutional neural networks (CNNs) are investigated as a potential tool for developing starting models for near-surface 2-D elastic FWI. Specifically, 100 000 subsurface models were generated to be representative of a classic near-surface geophysics problem; namely, imaging a two-layer, undulating, soil-over-bedrock interface. A CNN has been developed from these synthetic models that is capable of transforming an experimental wavefield acquired using a seismic source located at the centre of a linear array of 24 closely spaced surface sensors directly into a robust starting model for FWI. The CNN approach was able to produce 2-D starting models with seismic image misfits that were significantly less than the misfits from other common starting model approaches, and in many cases even less than the misfits obtained by FWI with inferior starting models. The ability of the CNN to generalize outside its two-layered training set was assessed using a more complex, three-layered, soil-over-bedrock formation. While the predictive ability of the CNN was slightly reduced for this more complex case, it was still able to achieve seismic image and waveform misfits that were comparable to other commonly used starting models, despite not being trained on any three-layered models. As such, CNNs show great potential as tools for rapidly developing robust, site-specific starting models for near-surface elastic FWI. 

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5. A gradient-based Markov chain Monte Carlo method for full-waveform inversion and uncertainty analysis

   https://doi.org/10.1190/geo2019-0585.1  

   Zhao, Z; Sen, M. K. (January 2021, Geophysics)

   null (Ed.)

   Traditional full-waveform inversion (FWI) methods only render a “best-fit” model that cannot account for uncertainties of the ill-posed inverse problem. Additionally, local optimization-based FWI methods cannot always converge to a geologically meaningful solution unless the inversion starts with an accurate background model. We seek the solution for FWI in the Bayesian inference framework to address those two issues. In Bayesian inference, the model space is directly probed by sampling methods such that we obtain a reliable uncertainty appraisal, determine optimal models, and avoid entrapment in a small local region of the model space. The solution of such a statistical inverse method is completely described by the posterior distribution, which quantifies the distributions for parameters and inversion uncertainties. 

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