# Uncertainty quantification in imaging and automatic horizon tracking: a Bayesian deep-prior based approach

arXiv: https://arxiv.org/abs/2004.00227 · HTML: https://mlsanity.com/paper/2004.00227/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2020.

## Built on by (most cited first, 7 of 7)

- [Reliable amortized variational inference with physics-based latent distribution correction](https://mlsanity.com/paper/2207.11640/) (2022)
- [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)
- [Learned multiphysics inversion with differentiable programming and machine learning](https://mlsanity.com/paper/2304.05592/) (2023)
- [Velocity continuation with Fourier neural operators for accelerated uncertainty quantification](https://mlsanity.com/paper/2203.14386/) (2022)
- [Dual-space posterior sampling for Bayesian inference in constrained inverse problems](https://mlsanity.com/paper/2603.00393/) (2026)
- [Posterior sampling with CNN-based, Plug-and-Play regularization with applications to Post-Stack Seismic Inversion](https://mlsanity.com/paper/2212.14595/) (2022)

## Abstract (arXiv)

In inverse problems, uncertainty quantification (UQ) deals with a probabilistic description of the solution nonuniqueness and data noise sensitivity. Setting seismic imaging into a Bayesian framework allows for a principled way of studying uncertainty by solving for the model posterior distribution. Imaging, however, typically constitutes only the first stage of a sequential workflow, and UQ becomes even more relevant when applied to subsequent tasks that are highly sensitive to the inversion outcome. In this paper, we focus on how UQ trickles down to horizon tracking for the determination of stratigraphic models and investigate its sensitivity with respect to the imaging result. As such, the main contribution of this work consists in a data-guided approach to horizon tracking uncertainty analysis. This work is fundamentally based on a special reparameterization of reflectivity, known as "deep prior". Feasible models are restricted to the output of a convolutional neural network with a fixed input, while weights and biases are Gaussian random variables. Given a deep prior model, the network parameters are sampled from the posterior distribution via a Markov chain Monte Carlo method, from which the conditional mean and point-wise standard deviation of the inferred reflectivities are approximated. For each sample of the posterior distribution, a reflectivity is generated, and the horizons are tracked automatically. In this way, uncertainty on model parameters naturally translates to horizon tracking. As part of the validation for the proposed approach, we verified that the estimated confidence intervals for the horizon tracking coincide with geologically complex regions, such as faults.