Full-waveform inversion via source-receiver extension

Huang, Guanghui; Nammour, Rami; Symes, William W.

doi:10.1190/geo2016-0301.1

Cited by 51 publications

(24 citation statements)

References 49 publications

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“…The cycle-skipping problem 106,117,118 , in which observed and simulated waveforms are misaligned by one cycle or more, renders incorrect misfit measurements and hinders convergence. This issue has motivated reformulations of the inverse problem that are less sensitive to cycle skipping, including adaptive waveform inversion 117 , source-receiver extension 119 , extension through time lag 120 , the use of optimal transport distance 106,121-123 and wavefield-reconstruction inversion 124,125 .…”

Section: Adjoint Simulationsmentioning

confidence: 99%

Seismic wavefield imaging of Earth’s interior across scales

Tromp

2019

Nat Rev Earth Environ

113

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Seismic full-waveform inversion (FWI) for imaging Earth's interior was introduced in the late 1970s. Its ultimate goal is to use all of the information in a seismogram to understand the structure and dynamics of Earth, such as hydrocarbon reservoirs, the nature of hotspots and the forces behind plate motions and earthquakes. Thanks to developments in high-performance computing and advances in modern numerical methods in the past 10 years, 3D FWI has become feasible for a wide range of applications and is currently used across nine orders of magnitude in frequency and wavelength. A typical FWI workflow includes selecting seismic sources and a starting model, conducting forward simulations, calculating and evaluating the misfit, and optimizing the simulated model until the observed and modelled seismograms converge on a single model. This method has revealed Pleistocene ice scrapes beneath a gas cloud in the Valhall oil field, overthrusted Iberian crust in the western Pyrenees mountains, deep slabs in subduction zones throughout the world and the shape of the African superplume. The increased use of multi-parameter inversions, improved computational and algorithmic efficiency , and the inclusion of Bayesian statistics in the optimization process all stand to substantially improve FWI, overcoming current computational or data-quality constraints. In this Technical Review, FWI methods and applications in controlled-source and earthquake seismology are discussed, followed by a perspective on the future of FWI, which will ultimately result in increased insight into the physics and chemistry of Earth's interior.

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Section: Adjoint Simulationsmentioning

confidence: 99%

Seismic wavefield imaging of Earth’s interior across scales

Tromp

2019

Nat Rev Earth Environ

113

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“…If the velocity is correct, the resulting matching filter should resemble Dirac Delta function with energy focussed at zero time lag. We can design a misfit function by applying a penalty on the time lag (Luo and Sava, 2011;Huang et al, 2017) or with an additional normalization term to gain better convexity (Warner and Guasch, 2016). In principle, all those approaches try to measure the departure of the matching filter from a Dirac Delta function.…”

Section: Introductionmentioning

confidence: 99%

The application of an optimal transport to a preconditioned data matching function for robust waveform inversion

Sun

Alkhalifah

2019

GEOPHYSICS

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Full-waveform inversion (FWI) promises a high-resolution model of the earth. It is, however, a highly nonlinear inverse problem; thus, we iteratively update the subsurface model by minimizing a misfit function that measures the difference between the measured and the predicted data. The conventional [Formula: see text]-norm misfit function is widely used because it provides a simple, high-resolution misfit function with a sample-by-sample comparison. However, it is susceptible to local minima if the low-wavenumber components of the initial model are not accurate. Deconvolution of the predicted and measured data offers an extended space comparison, which is more global. The matching filter calculated from the deconvolution has energy focused at zero lag, like an approximated Dirac delta function, when the predicted data matches the measured one. We have introduced a framework for designing misfit functions by measuring the distance between the matching filter and a representation of the Dirac delta function using optimal transport theory. We have used the Wasserstein [Formula: see text] distance, which provides us with the optimal transport between two probability distribution functions. Unlike data, the matching filter can be easily transformed to a probability distribution satisfying the requirement of the optimal transport theory. Though in one form, it admits the conventional normalized penalty applied to the nonzero-lag energy in the matching filter, the proposed misfit function is metric and extracts its form from solid mathematical foundations based on optimal transport theory. Explicitly, we can derive the adaptive waveform inversion (AWI) misfit function based on our framework, and the critical “normalization” for AWI occurs naturally per the requirement of a probability distribution. We use a modified Marmousi model and the BP salt model to verify the features of the proposed method in avoiding cycle skipping. We use the Chevron 2014 FWI benchmark data set to further highlight the effectiveness of the proposed approach.

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“…If the velocity used in modeling is correct, the resulting matching filter would focus energy mainly at zero lag, providing a band limited Dirac delta function. Otherwise, by penalizing the coefficients at non zero-time lag, we can formulate an optimization problem (Luo and Sava, 2011;Huang et al, 2017;Warner and Guasch, 2016). In principle, all those approaches try to measure the departure of the matching filter from a Dirac delta function.…”

Section: Introductionmentioning

confidence: 99%

A robust waveform inversion using a global comparison of modeled and observed data

Sun

Alkhalifah

2019

The Leading Edge

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A high-resolution model of the subsurface is the product of a successful full-waveform inversion (FWI) application. However, this optimization problem is highly nonlinear, and thus, we iteratively update the subsurface model by minimizing a misfit function that measures the difference between observed and modeled data. The L2-norm misfit function provides a simple, sample-by-sample comparison between the observed and modeled data. However, it is susceptible to local minima in the objective function if the low-wavenumber components of the initial model are not accurate enough. We review an alternative formulation of FWI based on a more global comparison. A combination of Radon transform and utilizing a matching filter allows for comparisons beyond sample to sample. We combine two recent developments to suggest the following algorithm for optimal inversion: (1) we compute the matching filter between the observed and modeled data in the Radon domain, which helps reduce the crosstalk introduced in the deconvolution step of computing the matching filter, and (2) we use Wasserstein distance to measure the distance between the resulting matching filter in the Radon domain and a representation of the Dirac delta function, which provides us with the optimal transport between the two distribution functions. We use a modified Marmousi model to show how this Radon-domain optimal-transport-based matching-filter approach can mitigate cycle skipping. Starting from a rather simplified v(z) media as the initial model, the proposed method can invert for the Marmousi model with considerable accuracy, while standard L2-norm formulation is trapped in a local minimum. Application of the proposed method to an offshore data set further demonstrates its robustness and effectiveness.

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Full-waveform inversion via source-receiver extension

Cited by 51 publications

References 49 publications

Seismic wavefield imaging of Earth’s interior across scales

Seismic wavefield imaging of Earth’s interior across scales

The application of an optimal transport to a preconditioned data matching function for robust waveform inversion

A robust waveform inversion using a global comparison of modeled and observed data

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