Low frequency full waveform seismic inversion within a tree based Bayesian framework

Ray, Anandaroop; Kaplan, Sam T.; Washbourne, John; Albertin, Uwe

doi:10.1093/gji/ggx428

Cited by 56 publications

(30 citation statements)

References 49 publications

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“…For example, variational methods could be applied to 3‐D seismic tomography problems to provide an efficient approximation, which generally demands enormous computational resources using McMC methods (Hawkins & Sambridge, ; Zhang et al, , ). The methods also provide possibilities to perform Bayesian inference for full waveform inversion, which is generally very expensive for McMC (Ray et al, ) and suffers from notorious multimodality in the likelihoods. SVGD provides a possible way to approximate these complex distributions given that theoretically it can approximate arbitrary distributions.…”

Section: Discussionmentioning

confidence: 99%

Seismic Tomography Using Variational Inference Methods

Zhang

Curtis

2020

JGR Solid Earth

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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.

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Section: Discussionmentioning

confidence: 99%

Seismic Tomography Using Variational Inference Methods

Zhang

Curtis

2020

JGR Solid Earth

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“…This is particularly beneficial in cases where forward modeling calculations are computationally expensive so that considerable computing time may be spent on a single Markov chain iteration. Examples of applications of parallel tempering to geophysical inverse problems include the inversion of controlled source electromagnetic data (Ray et al, ), finite fault (Dettmer et al, ) and direct seismogram (Dettmer et al, ) inversion, the inversion of surface wave dispersion and receiver function data (Roy & Romanowicz, ), seismic body wave (Bottero et al, ) and ambient noise (Valentová et al, ) tomography, inversion of airborne electromagnetic data (Hawkins et al, ), and full waveform inversion of marine seismic data (Ray et al, ).…”

Section: Methodsmentioning

confidence: 99%

“…Transdimensional inversion is a relatively new concept in ERT but has previously shown great potential in tackling a number of diverse inverse problems such as regression (Gallagher et al, ), inversion of frequency domain (Minsley, ) and controlled source (Ray et al, ) electromagnetic data, geoacoustic inversion of seabed reflection coefficients (Dettmer et al, ), inversion of surface wave phase and group velocities (Young et al, ) and traveltimes (Bodin & Sambridge, ; Galetti et al, ), joint inversion of surface wave dispersion and receiver function data (Bodin, Sambridge, Tkalcic, et al, ), inversion of DC resistivity sounding curves (Malinverno, ), and full waveform inversion of marine seismic data (Ray et al, ). In addition, Hawkins and Sambridge () recently developed a new class of transdimensional solvers that sample over tree structures, and this sampling approach has successfully been applied in 2‐D to the time domain electromagnetic inverse problem (Hawkins et al, ) and to seismic low‐frequency full waveform inversion (Ray et al, ).…”

Section: Introductionmentioning

confidence: 99%

Transdimensional Electrical Resistivity Tomography

Galetti

Curtis

2018

JGR Solid Earth

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This paper shows that imaging the interior of solid bodies with fully nonlinear physics can be highly beneficial compared to imaging with the equivalent linearized tomographic methods and that this is true for a variety of different types of physics. Including full nonlinearity provides interpretable uncertainties and far greater depth of image penetration into unknown targets such as the Earth's subsurface. We use an adaptively parameterized Monte Carlo method to invert electrical resistivity data for the conductivity structure of the Earth and demonstrate the method on two field data sets. Key results include the observation of directly interpretable uncertainty loops which define possible geometrical variations in the edges of isolated anomalies, hence quantifying the spatial resolution of these boundaries. These topologies of uncertainties are similar to those observed when performing fully nonlinear seismic traveltime tomography. This shows that loop‐like uncertainty topologies are expected in the solutions to a wide variety of tomographic problems, using a variety of data types and hence laws of physics (here the Laplace equation; in previous work the Eikonal or ray equations). We also show that the depth to which we can construct a tomographic image using electrical data is extended by up to a factor of 8 using nonlinear methods compared to linearized inversion using common standard linearized programs. These advantages come at the cost of significantly increased computation. All of these results are illustrated on both synthetic and real data examples.

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“…With choices based on the physics of the problem, well-designed Bayesian algorithms can infer the resolution with which we can 'see' into the earth. Recent geophysical work highlighting the importance of choosing a priori appropriate basis functions in a Bayesian framework can be found in Hawkins and Sambridge (2015); Pasquale and Linde (2016) and Ray et al (2017). In the field of hydrogeophysics, Cordua et al (2012); Lochbuhler et al (2015) and Laloy et al (2017) have used Training Image (TI) based priors for this purpose.…”

Section: Introductionmentioning

confidence: 99%