Bayesian seismic tomography using normalizing flows

Zhao, Xuebin; Curtis, Andrew; Zhang, Xin

doi:10.1093/gji/ggab298

Cited by 55 publications

(54 citation statements)

References 95 publications

(105 reference statements)

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“…For example, the above inversion across the whole survey area took 15 hours using 7,200 CPU cores. We also note that other methods can be used to further improve the computational efficiency, for example, Hamiltonian Monte Carlo [9,12], Langevin Monte Carlo [37,41], variational inference [30,48,49,55,50] and neural network inversion [27,26,11,51].…”

Section: Discussionmentioning

confidence: 99%

Surface wave dispersion inversion using an energy likelihood function

Zhang,

Zheng,

Curtis

2022

Preprint

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Seismic surface wave dispersion inversion is used widely to study the subsurface structure of the Earth. The dispersion property is usually measured by using frequency-phase velocity (f-c) analysis and by picking phase velocities from the obtained f-c spectrum. However, because of potential contamination the f-c spectrum often has multimodalities at each frequency for each mode. These introduce uncertainty and errors in the picked phase velocities, and consequently the obtained shear velocity structure is biased. To overcome this issue, in this study we introduce a new method which directly uses the spectrum as data. We achieve this by solving the inverse problem in a Bayesian framework and define a new likelihood function, the energy likelihood function, which uses the spectrum energy to define data fit. We apply the new method to a land dataset recorded by a dense receiver array, and compare the results to those obtained using the traditional method. The results show that the new method produces more accurate results since they better match independent data from refraction tomography. This real-data application also shows that it can be applied efficiently since it removes the need to pick phase velocities, and with relatively little adjustment to current practice since it uses standard f-c panels to define the likelihood. We therefore recommend using the energy likelihood function rather than explicitly picking phase velocities in surface wave dispersion inversion.

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Section: Discussionmentioning

confidence: 99%

Surface wave dispersion inversion using an energy likelihood function

Zhang,

Zheng,

Curtis

2022

Preprint

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“…In this study, we applied INNs to surface wave dispersion inversion and 2D travel time tomography, which usually do not show strong multimodality when using a fixed parameterization (Zhang & Curtis, 2020a; Zhao et al., 2020). However, we note that theoretically INNs can be applied to predict any posterior distributions, including multimodal distributions.…”

Section: Discussionmentioning

confidence: 99%

Bayesian Geophysical Inversion Using Invertible Neural Networks

Zhang

Curtis

2021

JGR Solid Earth

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Geoscientists build models of the subsurface to understand properties and processes in the Earth's interior. The models are usually parameterized in some way, so to constrain the models, we must solve a parameter estimation problem. Data are recorded which provide constraints, together with prior knowledge. However, since the physical relationships between parameters and data usually predict data given the parameters (known as the forward calculation) but not the reverse, the solution must be found using inverse theory.Geophysical inverse problems usually have nonunique solutions due to noise in the data, to nonlinearity of the physical relationships between model parameters and data, and to fundamentally unconstrained combinations of parameters. Uncertainties in parameter estimates must therefore be quantified to interpret inversion results correctly. Unfortunately, estimating uncertainty in nonlinear inverse problems can be computationally expensive, and the cost increases both with the number of parameters, and with the computational cost of the forward calculation. In this study, we therefore solve two different types of seismic tomography problems which each have fewer than 100 parameters, and have relatively rapid forward functions (each evaluation takes on the order of seconds). This allows us to evaluate solutions sufficiently accurately to thoroughly test a new method of Geophysical inversion.Geophysical inverse problems are traditionally solved by linearizing (approximating) the nonlinear physics, and using optimization methods which seek a model that minimizes the misfit between observed and predicted data (Aki & Lee, 1976;Dziewonski & Woodhouse, 1987;Iyer & Hirahara, 1993). However, despite their wide applications, linearized procedures cannot produce accurate estimates of uncertainty because data uncertainty distributions can deviate substantially from analytic forms of probability such as Gaussians or Uniform distributions that can be propagated through linearized methods efficiently, and since the distribution of possible models post inversion can be strongly affected by nonlinearity in the physics (Bo-

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“…As the preceding example illustrates, they provide opportunities to balance the (assumed) complexity and expressivity of the solution against computational costs. A number of recent studies have therefore explicitly sought to explore their potential in particular applications, including for earthquake hypocentre determination (Smith et al, 2021), seismic tomography Siahkoohi & Herrman, 2021;Zhao et al, 2021) and hydrogeology (Ramgraber et al, 2021). However, given the fairly broad ambit of variational inference, many past studies could also be seen as falling under this umbrella.…”

Section: Geophysical Applicationsmentioning

confidence: 99%

“…Goodfellow et al, 2014;Creswell et al, 2018), 'variational autoencoders' (Kingma & Welling, 2014), and 'normalizing flows' (Rezende & Mohamed, 2015;Kobyzev et al, 2020). A variety of recent studies have explored diverse applications of these concepts within the context of geophysical inversion: examples include Mosser et al (2020), Lopez-Alvis et al (2021 and Zhao et al (2021). We have no doubt that this area will lead to influential developments, although the precise scope of these is not yet clear.…”

Section: Generative Modelsmentioning

confidence: 99%