# Velocity continuation with Fourier neural operators for accelerated uncertainty quantification

arXiv: https://arxiv.org/abs/2203.14386 · HTML: https://mlsanity.com/paper/2203.14386/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 27 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Deep Bayesian inference for seismic imaging with tasks](https://mlsanity.com/paper/2110.04825/) (2021)
- [Learning by example: fast reliability-aware seismic imaging with normalizing flows](https://mlsanity.com/paper/2104.06255/) (2021)
- [A deep-learning based Bayesian approach to seismic imaging and uncertainty quantification](https://mlsanity.com/paper/2001.04567/) (2020)
- [Learned imaging with constraints and uncertainty quantification](https://mlsanity.com/paper/1909.06473/) (2019)
- [Uncertainty quantification in imaging and automatic horizon tracking: a Bayesian deep-prior based approach](https://mlsanity.com/paper/2004.00227/) (2020)
- [Deep learning approaches to surrogates for solving the diffusion equation for mechanistic real-world simulations](https://mlsanity.com/paper/2102.05527/) (2021)

## Built on by (most cited first, 2 of 2)

- [Reliable amortized variational inference with physics-based latent distribution correction](https://mlsanity.com/paper/2207.11640/) (2022)
- [WISE: full-Waveform variational Inference via Subsurface Extensions](https://mlsanity.com/paper/2401.06230/) (2023)

## Abstract (arXiv)

Seismic imaging is an ill-posed inverse problem that is challenged by noisy data and modeling inaccuracies -- due to errors in the background squared-slowness model. Uncertainty quantification is essential for determining how variability in the background models affects seismic imaging. Due to the costs associated with the forward Born modeling operator as well as the high dimensionality of seismic images, quantification of uncertainty is computationally expensive. As such, the main contribution of this work is a survey-specific Fourier neural operator surrogate to velocity continuation that maps seismic images associated with one background model to another virtually for free. While being trained with only 200 background and seismic image pairs, this surrogate is able to accurately predict seismic images associated with new background models, thus accelerating seismic imaging uncertainty quantification. We support our method with a realistic data example in which we quantify seismic imaging uncertainties using a Fourier neural operator surrogate, illustrating how variations in background models affect the position of reflectors in a seismic image.