Assessing uncertainties in velocity models and images with a fast nonlinear uncertainty quantification method

Abstract

Seismic imaging is conventionally performed using noisy data and a presumably inexact velocity model. Uncertainties in the input parameters propagate directly into the final image and therefore into any quantity of interest, or qualitative interpretation, obtained from the image. We considered the problem of uncertainty quantification in velocity building and seismic imaging using Bayesian inference. Using a reduced velocity model, a fast field expansion method for simulating recorded wavefields, and the adaptive Metropolis-Hastings algorithm, we efficiently quantify velocity model uncertainty by generating multiple models consistent with low-frequency full-waveform data. A second application of Bayesian inversion to any seismic reflections present in the recorded data reconstructs the corresponding structures’ position along with its associated uncertainty. Our analysis complements rather than replaces traditional imaging because it allows us to assess the reliability of visible image features and to take that into account in subsequent interpretations.

Taming the divergent terms in the scattering series of Born by renormalization

“…Fang et al (2018) presented a method for uncertainty quantification with weak partial-differential-equation constraints. Also, uncertainty assessment in velocity models and images can be found in Ely et al (2018). Recently, made significant progress on the original application of the ensemble-based Kalman filter method to full waveform inversion and demonstrated impressive results on uncertainty estimation with the Marmousi model.…”

“…12 Ely, G., A. Malcolm, and O. V. Poliannikov (2018). Assessing uncertainties in velocity models and images with a fast nonlinear uncertainty quantification method.…”

4D full-waveform metropolis hastings inversion using a local acoustic solver

“…Here, we use a Metropolis Hastings algorithm that doesn't require the computation of p(d), rather than uses the history of the process to tune the proposal distribution (Haario et al, 2001). See (Ely et al, 2018) for a recent application of the Adaptive Metropolis Hastings algorithm in seismic imaging.…”

“…Poliannikov and Malcolm (2015) use a Bayesian framework to quantify uncertainty in migrated images considering the effects of velocity model and picking errors. Ely et al (2018) proposes a bayesian framework with a fast forward solver based on the field expansion method to address uncertainties in seismic images. In (Kotsi and Malcolm, 2017) we studied model uncertainties in different 4D FWI schemes.…”

A workflow for seismic imaging with quantified uncertainty

“…Several works discuss how to express the uncertainty related to velocity-model building and measure the impact on the migration techniques [1,2,3,4,5,6]. Typically, uncertainties are characterized through a probabilistic perspective and expressed as an ensemble of possible realizations of a random variable, making the Monte Carlo (MC) method the standard tool to manage and quantify uncertainties [7, 8, 9, 10, 11? ].…”