Frequency domain full waveform elastic inversion of marine seismic data from the Alba field using a Bayesian trans-dimensional algorithm

Ray, Anandaroop; Sekar, A.; Hoversten, G. Michael; Albertin, Uwe

doi:10.1093/gji/ggw061

Cited by 57 publications

(26 citation statements)

References 71 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fernández-Martínez et al (2014a,b) have theoretically studied the effect of noise and Tikhonov's regularization in linear and nonlinear inverse problems, showing that the noise enters the cost function perturbing the position of the true inverse model and could be interpreted as a kind of regularization. This fact has also been pointed by Brooks andFrazer (2005), Bodin et al (2012), Gunning et al (2010) and Ray et al (2013Ray et al ( , 2016. Besides, the use of regularization does not impede the existence of equivalent models.…”

Section: Introductionsupporting

confidence: 59%

See 1 more Smart Citation

Uncertainty analysis and probabilistic segmentation of electrical resistivity images: the 2D inverse problem

Fernández-Martínez

Sirieix

et al. 2017

Geophysical Prospecting

View full text Add to dashboard Cite

In this paper, we present the uncertainty analysis of the 2D electrical tomography inverse problem using model reduction and performing the sampling via an explorative member of the Particle Swarm Optimization family, called the Regressive‐Regressive Particle Swarm Optimization. The procedure begins with a local inversion to find a good resistivity model located in the nonlinear equivalence region of the set of plausible solutions. The dimension of this geophysical model is then reduced using spectral decomposition, and the uncertainty space is explored via Particle Swarm Optimization. Using this approach, we show that it is possible to sample the uncertainty space of the electrical tomography inverse problem. We illustrate this methodology with the application to a synthetic and a real dataset coming from a karstic geological set‐up. By computing the uncertainty of the inverse solution, it is possible to perform the segmentation of the resistivity images issued from inversion. This segmentation is based on the set of equivalent models that have been sampled, and makes it possible to answer geophysical questions in a probabilistic way, performing risk analysis.

show abstract

Section: Introductionsupporting

confidence: 59%

“…() and Ray et al . (, ). Besides, the use of regularization does not impede the existence of equivalent models.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty analysis and probabilistic segmentation of electrical resistivity images: the 2D inverse problem

Fernández-Martínez

Sirieix

et al. 2017

Geophysical Prospecting

View full text Add to dashboard Cite

show abstract

“…It has been shown that an improper noise level can introduce biases in tomographic results (Bodin & Sambridge, ; Zhang et al, ), so in our example we used the noise level estimated by hierarchical McMC. It can also be estimated by a variety of other methods (Bensen et al, ; Nicolson et al, , ; Weaver et al, ; Yao & Van Der Hilst, ) and maximum likelihood methods (Ray et al, ; Ray & Myer, ; Sambridge, ). In future it might also be possible to include the noise parameters in variational methods in a hierarchical way.…”

Section: Discussionmentioning

confidence: 99%

Seismic Tomography Using Variational Inference Methods

Zhang

Curtis

2020

JGR Solid Earth

View full text Add to dashboard Cite

Seismic tomography is a methodology to image the interior of solid or fluid media and is often used to map properties in the subsurface of the Earth. In order to better interpret the resulting images, it is important to assess imaging uncertainties. Since tomography is significantly nonlinear, Monte Carlo sampling methods are often used for this purpose, but they are generally computationally intractable for large data sets and high-dimensional parameter spaces. To extend uncertainty analysis to larger systems, we use variational inference methods to conduct seismic tomography. In contrast to Monte Carlo sampling, variational methods solve the Bayesian inference problem as an optimization problem yet still provide fully nonlinear, probabilistic results. In this study, we applied two variational methods, automatic differential variational inference and Stein variational gradient descent, to 2-D seismic tomography problems using both synthetic and real data, and we compare the results to those from two different Monte Carlo sampling methods. The results show that automatic differential variational inference provides a biased approximation because of its implicit transformed-Gaussian approximation, and it cannot be used to find generally multimodal posteriors; Stein variational gradient descent produces more accurate approximations to the results of Monte Carlo sampling methods. Both methods estimate the posterior distribution at significantly lower computational cost, provided that gradients of parameters with respect to data can be calculated efficiently. We expect that the methods can be applied fruitfully to many other types of geophysical inverse problems.

show abstract

“…Applications have appeared in inversion of marine CSEM data, Ray and Key (2012), inversion of controlled-source electromagnetic data, Gehrmann et al (2015), and full waveform elastic inversion of marine seismic data Ray et al (2016).…”

Section: Discussionmentioning

confidence: 99%

Taming uncertainty in geophysical inversion

Sambridge

Hawkins

Dettmer

2016

ASEG Extended Abstracts

View full text Add to dashboard Cite

SUMMARYThe concept of uncertainty in geophysical inversion is often confined to quantification of errors in parameters estimated from some data. A broader definition is to include uncertainty arising from the assumptions made in posing the inverse problem in the first place. These may include assumptions about the physics of the relationship between observations and unknowns, the class of parameterisation assumed for the unknowns, and guesses about the statistical character of random noise contaminating the data. Typically these assumptions are required to arrive at a tractable mathematical problem to solve using geophysical inversion methods. In this paper we outline an inversion approach that allows a broader definition of uncertainty which includes each of these classes of assumption. Including uncertainty in the model parametrization or in the nature of the noise statistics can lead to more realistic inversion results, but not always with increased error bars on the model parameters. For example, relaxing rigid assumptions in the nature of the parametrisation, even in simple problems can result in smaller and more realistic model error estimation. Using the data to decide between different classes of parameterization, physical assumptions or observational noise process is often called `model choice' in statistics, an area that is often overlooked in the geosciences. Over the past 5 years the trans-dimensional inversion approach has increasingly found applications across a variety of inference problems in the geosciences, with new applications appearing regularly.

show abstract

Frequency domain full waveform elastic inversion of marine seismic data from the Alba field using a Bayesian trans-dimensional algorithm

Cited by 57 publications

References 71 publications

Uncertainty analysis and probabilistic segmentation of electrical resistivity images: the 2D inverse problem

Uncertainty analysis and probabilistic segmentation of electrical resistivity images: the 2D inverse problem

Seismic Tomography Using Variational Inference Methods

Taming uncertainty in geophysical inversion

Contact Info

Product

Resources

About