Seismic envelope inversion and renormalization group theory: Nonlinear scale separation and slow dynamics

Wu, Ru‐Shan; Luo, Jungang; Chen, Guoxin

doi:10.1190/segam2016-13962956.1

Cited by 9 publications

(2 citation statements)

References 23 publications

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“…The performance of the conventional EI and FWI on the salt model in numerical experiments also verified this inference. Based on the above analysis, a new direct envelope Fréchet derivative was proposed (Chen, ; Chen & Wu, ; Chen, Wu, & Chen, , ; Chen, Wu, Wang, & Chen, ; Wu & Chen, , , ; Wu et al, ) to derive the sensitivity operator of the EI using the WAE

\begin{matrix} lefttrue \\ \frac{\partial σ_{W}}{\partial v} = \sum_{italicSRT} r_{W} (t) \frac{\partial r_{W}}{\partial e_{W} (t)} \frac{\partial e_{W_{syn}} (t)}{\partial v}, \\ = \sum_{italicSRT} r_{W} (t) \frac{1}{τ_{W}} \int_{- τ_{W} / 2}^{τ_{W} / 2} d t^{'} W (t - t^{'}) \frac{\partial e_{syn}^{2} (t^{'})}{\partial v}, \end{matrix}

where

\partial e_{W_{syn}} ((), t) / \partial v

is the new envelope Fréchet derivative.…”

Section: Theory and Methodsmentioning

confidence: 99%

Multiscale Direct Envelope Inversion: Algorithm and Methodology for Application to the Salt Structure Inversion

Chen

2019

Earth and Space Science

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For the full‐waveform inversion, obtaining a globally optimal solution is difficult when the seismic data do not contain sufficient low‐frequency information and the inversion object is a salt structure with a large‐scale salt dome. The large salt dome presents difficulty for the inversion of the salt structure; however, it also confers a convenience that can be utilized: A large salt dome makes the events in the seismic record sparse and isolated. We use the envelope to obtain the arrival time of the events in the seismic data and apply multiscale strategies to extract the low‐frequency information of the seismic data that relates to the long‐wavelength components of the subsurface. In calculating the gradient, the envelope Fréchet derivative is used to take advantage of the multiscale envelope for the characteristics of the salt structure. Therefore, the multiscale direct envelope inversion using the window‐averaged envelope and the direct envelope Fréchet derivative is proposed. To further improve the computational efficiency and inversion quality of the multiscale direct envelope inversion, several auxiliary strategies are proposed: A joint misfit function is designed to make the inversion method more adaptable, and an offset weighting factor is introduced to implement the multioffset inversion method to improve the inversion quality of subsalt. We analyze the antinoise performance of the multiscale direct envelope inversion. The SEG/EAGE salt model is used to test the application effect of the multiscale direct envelope inversion. The antinoise ability and insensitivity to low‐frequency data of the method are verified in the numerical experiments.

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\begin{matrix} lefttrue \\ \frac{\partial σ_{W}}{\partial v} = \sum_{italicSRT} r_{W} (t) \frac{\partial r_{W}}{\partial e_{W} (t)} \frac{\partial e_{W_{syn}} (t)}{\partial v}, \\ = \sum_{italicSRT} r_{W} (t) \frac{1}{τ_{W}} \int_{- τ_{W} / 2}^{τ_{W} / 2} d t^{'} W (t - t^{'}) \frac{\partial e_{syn}^{2} (t^{'})}{\partial v}, \end{matrix}

where

\partial e_{W_{syn}} ((), t) / \partial v

is the new envelope Fréchet derivative.…”

Section: Theory and Methodsmentioning

confidence: 99%

Multiscale Direct Envelope Inversion: Algorithm and Methodology for Application to the Salt Structure Inversion

Chen

2019

Earth and Space Science

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“…Bharadwaj introduced the auxiliary bump functional into the FWI to further improve the EI (Bharadwaj, Mulder and Drijkoningen ). In order to invert strong contrast models, multi‐scale EI based on the renormalisation group theory was proposed (Wu, Luo and Chen ; Wu and Chen , b). Multi‐scale EI had been applied to the inversion of the salt model with strong velocity contrast and achieved good results.…”

Section: Introductionmentioning

confidence: 99%

Reflection multi‐scale envelope inversion

Chen

2018

Geophysical Prospecting

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Sufficient low‐frequency information is essential for full‐waveform inversion to get the global optimal solution. Multi‐scale envelope inversion was proposed using a new Fréchet derivative to invert the long‐wavelength component of the model by directly using the low‐frequency components contained in an envelope of seismic data. Although the new method can recover the main structure of the model, the inversion quality of the model bottom still needs to be improved. Reflection waveform inversion reduces the dependence of inversion on low‐frequency and long‐offset data by using travel‐time information in reflected waves. However, when the underground medium contains strong contrast or the initial model is far away from the true model, it is hard to get reliable reference reflectors for the generation of reflected waves. Here, we propose a combination inversion algorithm, i.e., reflection multi‐scale envelope inversion, to overcome the limitations of multi‐scale envelope inversion and reflection waveform inversion. First, wavefield decomposition was introduced into the multi‐scale envelope inversion to improve the inversion quality of the long‐wavelength components of the model. Then, after the initial model had been established to be accurate enough, migration and de‐migration were introduced to achieve multi‐scale reflection waveform inversion. The numerical results of the salt‐layer model and the SEG/EAGE salt model verified the validity of the proposed approach and its potential.

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Seismic Envelope Inversion Based on Hybrid Scale Separation for Data with Strong Noises

Zhang

Han

2018

Pure Appl. Geophys.

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Seismic envelope inversion and renormalization group theory: Nonlinear scale separation and slow dynamics

Cited by 9 publications

References 23 publications

Multiscale Direct Envelope Inversion: Algorithm and Methodology for Application to the Salt Structure Inversion

Multiscale Direct Envelope Inversion: Algorithm and Methodology for Application to the Salt Structure Inversion

Reflection multi‐scale envelope inversion

Seismic Envelope Inversion Based on Hybrid Scale Separation for Data with Strong Noises

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