2D frequency-domain elastic full-waveform inversion using time-domain modeling and a multistep-length gradient approach

Xu, Kun; McMechan, George A.

doi:10.1190/geo2013-0134.1

Cited by 74 publications

(11 citation statements)

References 41 publications

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“…The absence of perturbation density can cause amplitude errors in predicted reflections and thus expose our RWI to some artifacts. The inverted density in elastic FWI plays the role of absorbing high-wavenumber components mainly on the layer interfaces (Xu and McMechan, 2014). We invert for the perturbations and background models simultaneously, and the inverted model parameters include the perturbations of P-and S-wave velocities and density and the background P-and S-wave velocities.…”

Section: Introductionmentioning

confidence: 99%

Elastic reflection waveform inversion with variable density

Guo

et al. 2019

GEOPHYSICS

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Elastic full-waveform inversion (FWI) provides a better description of the subsurface information than those given by the acoustic assumption. However, it suffers from a more serious cycle-skipping problem compared with the latter. Reflection waveform inversion (RWI) is able to build a good background model, which can serve as an initial model for elastic FWI. Because, in RWI, we use the model perturbation to explicitly fit reflections, such perturbations should include density, which mainly affects the dynamics. We applied Born modeling to generate synthetic reflection data using optimized perturbations of the P- and S-wave velocities and density. The inversion for the perturbations of the P- and S-wave velocities and density is similar to elastic least-squares reverse time migration. An incorrect background model will lead to misfits mainly at the far offsets, which can be used to update the background P- and S-wave velocities along the reflection wavepath. We optimize the perturbations and background models in an alternate way. We use two synthetic examples and a field-data case to demonstrate our proposed elastic RWI algorithm. The results indicate that our elastic RWI with variable density is able to build reasonably good background models for elastic FWI with the absence of low frequencies, and it can deal with the variable density, which is required in real cases.

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Section: Introductionmentioning

confidence: 99%

Elastic reflection waveform inversion with variable density

Guo

et al. 2019

GEOPHYSICS

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“…The combined transmission losses in the receiver wavefield can be properly compensated during back propagation only if two conditions are met; (1) the velocity model is exactly known and (2) all the transmissions and reflections (including those from below the reflectors in the forward propagation) are completely preserved, either by being recorded as traces (in BVR) or as snapshots (in IVR) so that they are available, and the boundary conditions at all reflectors are correct, to enable reconstruction of the originally reflected wavefield at the target during the back propagation. If, for example, the P-velocity model is correct, but the S-velocity and density models are not, it may be possible to use the resulting propagation and amplitude perturbations to refine those additional model components; this, of course, is the basis of elastic inversion (e.g., Xu and McMechan, 2014).…”

Section: Discussionmentioning

confidence: 99%

“…Numbers above or below each bar are the actual storage or runtimes; actual FWS storage cost was 983.89 GB, the workstation runtimes averaged at 266.13 min, and server runtimes averaged at 41.7 min. Abubakar et al (2012), Köhn et al (2012), and Xu and McMechan (2014), in the frequency domain. At present, perhaps the greatest immediate challenge is a 3D implementation of elastic RTM, with sufficient realism (e.g., considerations for anisotropy and viscoelasticity) and computational efficiency, that is commercially viable.…”

Section: Discussionmentioning

confidence: 99%

Five ways to avoid storing source wavefield snapshots in 2D elastic prestack reverse time migration

2015

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Five alternative algorithms were evaluated to circumvent the excessive storage requirement imposed by saving source wavefield snapshots used for the crosscorrelation image condition in 2D prestack elastic reverse time migration. We compared the algorithms on the basis of their ability, either to accurately reconstruct (not save) the source wavefield or to use an alternate image condition so that neither saving nor reconstruction of full wavefields was involved. The comparisons were facilitated by using the same (velocity-stress) extrapolator in all the algorithms, and running them all on the same hardware. We assumed that there was enough memory in a node to do an extrapolation, and that all input data were stored on disk rather than residing in randomaccess memory. This should provide a fair and balanced comparison. Reconstruction of the source wavefield from boundary and/or initial values reduced the required storage to a very small fraction of that needed to store source wavefield snapshots for conventional crosscorrelation, at the cost of adding an additional source extrapolation. Reverse time checkpointing avoided recursive forward recomputation. Two nonreconstructive imaging conditions do not require full snapshot storage or an additional extrapolation. Timebinning the imaging criteria removed the need for image time searching or sorting. Numerical examples using elastic data from the Marmousi2 model showed that the quality of the elastic prestack PP and PS images produced by the cost-optimized alternative algorithms were (virtually) identical to the higher cost images produced by traditional crosscorrelation.

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“…In our GN‐WTI method, the wavefields and Green's functions are numerically calculated by time‐domain finite‐difference modelling and are transformed to the frequency domain by on‐the‐fly discrete Fourier transform (DFT) (Sirgue et al ., 2008; Xu and McMechan, 2014). For completeness, we now describe the on‐the‐fly DFT procedure.…”

Section: Methodsmentioning

confidence: 99%

Memory‐efficient frequency‐domain Gauss–Newton method for wave‐equation first‐arrival traveltime inversion

Wang

Dong

2021

Near Surface Geophysics

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Wave-equation traveltime inversion (WTI) can be used to automatically obtain a background near-surface velocity model (NSM), which overcomes the high-frequency approximation in ray theory. It is generally implemented in the time domain. However, the commonly used gradient-based optimisation methods (such as the steepestdescent method) in WTI have a low convergence rate and may yield less accurate results within limited iterations in geologically complex regions. To increase the convergence rate and improve the inversion accuracy, we propose a frequency-domain truncated Gauss-Newton first-arrival wave-equation traveltime inversion (GN-WTI) method to retrieve the background NSM. As only a few frequencies are used for inversion, the proposed frequency-domain WTI method significantly reduces the computational memory requirements by more than two orders of magnitude in comparison with the conventional time-domain WTI method. Therefore, the proposed method is especially advantageous for the building of large three-dimensional models. In this GN-WTI method, according to the derived explicit traveltime residual kernel, the gradient and Hessian vector products can be computed efficiently using an elegant and improved scattering integral approach as long as the source-side wavefields and nonredundant receiver-side Green's functions are computed and stored in advance. The conjugate gradient approach is used to solve the Gauss-Newton normal equation to obtain the Gauss-Newton direction in inner loops. Here, the Gauss-Newton Hessians of the ray-based traveltime inversion and WTI are compared to demonstrate the advantages of WTI. The trial runs with a simple periodic velocity model example showed that the proposed GN-WTI method outperforms the WTI method when using the steepest-descent and limited-memory Broyden-Fletcher-Goldfarb-Shanno approaches in terms of the convergence rate and inversion accuracy. A complex Marmousi model was further used to illustrate the effectiveness of GN-WTI. The proposed method should be beneficial in near-surface velocity model building.

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2D frequency-domain elastic full-waveform inversion using time-domain modeling and a multistep-length gradient approach

Cited by 74 publications

References 41 publications

Elastic reflection waveform inversion with variable density

Elastic reflection waveform inversion with variable density

Five ways to avoid storing source wavefield snapshots in 2D elastic prestack reverse time migration

Memory‐efficient frequency‐domain Gauss–Newton method for wave‐equation first‐arrival traveltime inversion

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