3D wave-equation dispersion inversion of surface waves

Liu, Zhaolun; Li, Jing; Schuster, Gerard T.

doi:10.1190/fwi2017-007

Cited by 4 publications

(5 citation statements)

References 19 publications

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“…(2016) and Liu et al. (2018) found the optimal S‐velocity model by using the dispersion curves associated with the surface waves. A comprehensive introduction to skeletonized inversion is presented in Lu et al.…”

Section: Introductionmentioning

confidence: 99%

“…problem (Virieux & Operto, 2009) and successfully recovers the background information of the model of interests: Schuster (1991a, 1991b) used wavefield correlations to invert the first arrival traveltime for the subsurface background velocity model, while Choi and Alkhalifah (2015) used a space-domain unwrapped phase with exponential damping to mitigate the nonlinearity associated with the reflections. Dutta and Schuster (2016) inverted for the Qp model by minimizing the central/peak frequency differences between the observed and predicted early arrivals; similarly, Li et al (2017) utilized the peak frequency shifts of the surface wave to invert for the Qs model; and Li et al (2016) and Liu et al (2018) found the optimal S-velocity model by using the dispersion curves associated with the surface waves. A comprehensive introduction to skeletonized inversion is presented in Lu et al (2017).…”

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confidence: 99%

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Seismic Inversion by Hybrid Machine Learning

Chen

Saygin

2021

JGR Solid Earth

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We present a hybrid machine learning (HML) inversion method, which uses the latent space (LS) features of a convolutional autoencoder (CAE) to estimate the subsurface velocity model. The LS features are the effective low‐dimensional representation of the high‐dimensional seismic data. However, no equations exist to describe the relationship between the perturbation of an LS feature and the velocity perturbation. To address this problem, we use automatic differentiation (AD) to connect the two terms. Following this step, we use the wave‐equation inversion to invert the LS features for the subsurface velocity model. The HML misfit function measures the LS feature differences between the observed and predicted seismic data in a low‐dimensional space, which is less affected by the cycle‐skipping problem compared to the waveform mismatch in a high‐dimensional space. A low dimensional LS feature mainly contains the kinematic information of seismic data, while a large dimensional LS feature can also preserve the dynamic information of seismic data. Therefore, the HML inversion can recover the subsurface velocity model in a multiscale approach by inverting the LS features with different dimensions. Based on the different ways of utilizing AD to compute the velocity gradient, we propose full‐ and semi‐automatic approaches to solve this problem. These two approaches are mathematically equivalent; the former is easier to implement, while the latter is computationally more efficient. Numerical tests show that the HML inversion method can effectively recover both the low‐ and high‐wavenumber velocity information by inverting the LS features with different dimensions.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Seismic Inversion by Hybrid Machine Learning

Chen

Saygin

2021

JGR Solid Earth

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“…We performed 1D inversions using a plane wave approximation for a 3D strucutre, which may cause some bias in the inverted velocity strucutre in the presence of strong lateral heterogeneities as noted in Wielandt (1993). In such cases a 3D wave-equation based inversion method could be used in future to improve the results (Li et al 2017;Liu et al 2018).…”

Section: Dispersion Inversion Using Energy Likelihood 23mentioning

confidence: 99%

Surface wave dispersion inversion using an energy likelihood function

Zhang

Zheng

Curtis

2022

Geophysical Journal International

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Summary 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 of data recorded on a local array of receivers. The apparent phase velocity at each frequency of the surface waves travelling across the array is that at which the f-c spectrum has maximum amplitude. However, because of potential contamination by other wave arrivals or due to complexities in the velocity structure the f-c spectrum often has multiple maxima at each frequency for each mode. These introduce errors and ambiguity in the picked phase velocities, and consequently the estimated shear velocity structure can be biased, or may not account for the full uncertainty in the data. To overcome this issue we introduce a new method which directly uses the spectrum as the data to be inverted. 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 with relatively little adjustment to current practice since it uses standard f-c panels to define the likelihood, and efficiently since it removes the need to pick phase velocities. We therefore conclude that the energy likelihood function can be a valuable tool for surface wave dispersion inversion in practice.

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“…In the 2D case, the azimuth angles have only two values: 0 • and 180 • , corresponding to the left and right directions, respectively. The gradient γ(x) of ε with respect to the S-wave velocity v s (x) is given in (Liu et al, 2017), which is computed using a weighted zero-lag correlation between the source and backward-extrapolated receiver wavefields.…”

Section: Theorymentioning

confidence: 99%

“…Wave-equation dispersion inversion (WD) of Rayleigh waves uses solutions to the 2D or 3D elastic-wave equation to invert the dispersion curves of surface waves for the S-velocity model (Li and Schuster, 2016;Li et al, 2016Li et al, , 2017aLiu et al, 2017). The advantage of WD over the traditional dispersion inversion method (Haskell, 1953;Xia et al, 1999Xia et al, , 2002Park et al, 1999) is that WD does not assume a layered velocity model and is valid when there are strong lateral gradients in the S-velocity model.…”

Section: Introductionmentioning

confidence: 99%

Multiscale and layer-stripping wave-equation dispersion inversion of Rayleigh waves

Liu

Huang

2019

Geophysical Journal International

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Rayleigh-wave inversion could converge to a local minimum of its objective function for a complex subsurface model. We develop a multiscale strategy and a layer-stripping method to alleviate the local minimum problem of wave-equation dispersion inversion of Rayleigh waves, and improve the inversion robustness. We first invert the high-frequency and near-offset data for the shallow S-velocity model, and gradually incorporate the lower-frequency components of data with longer offsets to reconstruct the deeper regions of the model. We demonstrate the efficacy of this multiscale and layer-stripping method using synthetic and field Rayleigh-wave data.

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3D wave-equation dispersion inversion of surface waves

Cited by 4 publications

References 19 publications

Seismic Inversion by Hybrid Machine Learning

Seismic Inversion by Hybrid Machine Learning

Surface wave dispersion inversion using an energy likelihood function

Multiscale and layer-stripping wave-equation dispersion inversion of Rayleigh waves

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