Seismic envelope inversion and modulation signal model

Wu, Ru‐Shan; Luo, Jungang; Wu, Bangyu

doi:10.1190/geo2013-0294.1

Cited by 377 publications

(137 citation statements)

References 40 publications

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“…The source and receiver are located at depths of 20 and 3020 m, respectively, and both are located in the middle of the horizontal axis. Figure 5a shows the original wavefield, its envelope (Wu et al, 2014), and the nonlinearly smoothed wavefield. Here, we apply a triangle smoothing filter with a smoothing width of 0.3 s to the absolute value of the original wavefield to obtain the nonlinearly smoothed wavefield.…”

Section: Behavior Of the Objective Function Using The Nonlinearly Smomentioning

confidence: 99%

“…We use the inverted model as a new starting model for a subsequent FWI based on the conventional least-squares misfit function (Figure 7b). For comparison, we also perform envelope FWI (Wu et al, 2014) with p ¼ 1 and corresponding subsequent FWI. Figure 7c and 7d shows the inverted models of envelope FWI and its subsequent FWI, respectively.…”

Section: Marmousi 2 Synthetic Data Testmentioning

confidence: 99%

“…Wu et al (2014) and Chi et al (2014) estimate the envelope of the wavefield and invert the artificial low-frequency components included in the envelope of the wavefield to update the longwavelength components of the model. Li and Demanet (2016) extrapolate the low-frequency information by a phase-tracking method, and they perform FWI using the extrapolated low frequencies to estimate the low-wavenumber model.…”

Section: Introductionmentioning

confidence: 99%

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Full-waveform inversion using a nonlinearly smoothed wavefield

Choi

Alkhalifah

et al. 2018

GEOPHYSICS

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Conventional full-waveform inversion (FWI) based on the least-squares misfit function faces problems in converging to the global minimum when using gradient methods because of the cycle-skipping phenomena. An initial model producing data that are at most a half-cycle away from the observed data is needed for convergence to the global minimum. Low frequencies are helpful in updating low-wavenumber components of the velocity model to avoid cycle skipping. However, low enough frequencies are usually unavailable in field cases. The multiplication of wavefields of slightly different frequencies adds artificial low-frequency components in the data, which can be used for FWI to generate a convergent result and avoid cycle skipping. We generalize this process by multiplying the wavefield with itself and then applying a smoothing operator to the multiplied wavefield or its square to derive the nonlinearly smoothed wavefield, which is rich in low frequencies. The global correlation-norm-based objective function can mitigate the dependence on the amplitude information of the nonlinearly smoothed wavefield. Therefore, we have evaluated the use of this objective function when using the nonlinearly smoothed wavefield. The proposed objective function has much larger convexity than the conventional objective functions. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to that of the conventional FWI except for the adjoint source. We progressively reduce the smoothing width applied to the nonlinear wavefield to naturally adopt the multiscale strategy. Using examples on the Marmousi 2 model, we determine that the proposed FWI helps to generate convergent results without the need for low-frequency information.

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Section: Behavior Of the Objective Function Using The Nonlinearly Smomentioning

confidence: 99%

Section: Marmousi 2 Synthetic Data Testmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Full-waveform inversion using a nonlinearly smoothed wavefield

Choi

Alkhalifah

et al. 2018

GEOPHYSICS

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“…Due to the algorithm's drawback of penetration depth, the complex Laplace-Fourier-domain inversion strategy was proposed (Shin and Cha 2009;Shin 2012, 2013;Hu et al 2015) via a series of low-frequency components within 5 Hz and damping constants, which can enlarge the input energy and improve the penetration depth of subsurface models. Recently, seismic envelope inversion that was performed in the envelope domain to predict the low-frequency background of subsurface velocity by synthesizing the envelope's misfit function has attracted the attention of geophysicists (Wu et al 2014;Luo and Wu 2015;Luo et al 2016). Complex Laplace-domain inversion and envelope inversion are two different representatives of low-frequency estimation methods, but both aim at excavating the low-frequency response from the original data and improving the construction of low-frequency a priori information of the ill-posed inverse problem.…”

Section: Introductionmentioning

confidence: 99%

Bayesian seismic multi-scale inversion in complex Laplace mixed domains

Yin

Zong

2017

Pet. Sci.

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Seismic inversion performed in the time or frequency domain cannot always recover the long-wavelength background of subsurface parameters due to the lack of low-frequency seismic records. Since the low-frequency response becomes much richer in the Laplace mixed domains, one novel Bayesian impedance inversion approach in the complex Laplace mixed domains is established in this study to solve the model dependency problem. The derivation of a Laplace mixed-domain formula of the Robinson convolution is the first step in our work. With this formula, the Laplace seismic spectrum, the wavelet spectrum and time-domain reflectivity are joined together. Next, to improve inversion stability, the object inversion function accompanied by the initial constraint of the linear increment model is launched under a Bayesian framework. The likelihood function and prior probability distribution can be combined together by Bayesian formula to calculate the posterior probability distribution of subsurface parameters. By achieving the optimal solution corresponding to maximum posterior probability distribution, the low-frequency background of subsurface parameters can be obtained successfully. Then, with the regularization constraint of estimated low frequency in the Laplace mixed domains, multi-scale Bayesian inversion in the pure frequency domain is exploited to obtain the absolute model parameters. The effectiveness, anti-noise capability and lateral continuity of Laplace mixed-domain inversion are illustrated by synthetic tests. Furthermore, one field case in the east of China is discussed carefully with different input frequency components and different inversion algorithms. This provides adequate proof to illustrate the reliability improvement in low-frequency estimation and resolution enhancement of subsurface parameters, in comparison with conventional Bayesian inversion in the frequency domain.

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“…Wu and Alkhalifah (2016) constructed the objective function based on the data extension and data selective approach. Wu et al (2014) estimated the envelope of wavefield and inverted the artificial low frequency components included in the envelope of wavefield to update long wavelength components of the model.…”

Section: Introductionmentioning

confidence: 99%

Full Waveform Inversion Using Nonlinearly Smoothed Wavefields

Li¹,

Choi²,

Alkhalifah³

et al. 2017

Proceedings

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SummaryThe lack of low frequency information in the acquired data makes full waveform inversion (FWI) conditionally converge to the accurate solution. An initial velocity model that results in data with events within a half cycle of their location in the observed data was required to converge. The multiplication of wavefields with slightly different frequencies generates artificial low frequency components. This can be effectively utilized by multiplying the wavefield with itself, which is nonlinear operation, followed by a smoothing operator to extract the artificially produced low frequency information. We construct the objective function using the nonlinearly smoothed wavefields with a global-correlation norm to properly handle the energy imbalance in the nonlinearly smoothed wavefield. Similar to the multi-scale strategy, we progressively reduce the smoothing width applied to the multiplied wavefield to welcome higher resolution. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to the conventional FWI except for the adjoint source. Examples on the Marmousi 2 model demonstrate the feasibility of the proposed FWI method to mitigate the cycle-skipping problem in the case of a lack of low frequency information.

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Seismic envelope inversion and modulation signal model

Cited by 377 publications

References 40 publications

Full-waveform inversion using a nonlinearly smoothed wavefield

Full-waveform inversion using a nonlinearly smoothed wavefield

Bayesian seismic multi-scale inversion in complex Laplace mixed domains

Full Waveform Inversion Using Nonlinearly Smoothed Wavefields

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