Accurate and efficient data-assimilated wavefield reconstruction in the time domain

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. A7-A12 ◽  
Author(s):  
Hossein S. Aghamiry ◽  
Ali Gholami ◽  
Stéphane Operto
Keyword(s):  
Wave Equation ◽  
Time Domain ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Search Space ◽  
Velocity Models ◽  
Time Stepping ◽  
Efficient Data ◽  
The Time Domain ◽  
The Right

Wavefield reconstruction inversion (WRI) mitigates cycle skipping in full-waveform inversion by computing wavefields that do not exactly satisfy the wave equation to match data with inaccurate velocity models. We refer to these wavefields as data assimilated wavefields because they are obtained by combining the physics of wave propagation and the observations. Then, the velocity model is updated by minimizing the wave-equation errors, namely, the source residuals. Computing these data-assimilated wavefields in the time domain with explicit time stepping is challenging. This is because the right-hand side of the wave equation to be solved depends on the back-propagated residuals between the data and the unknown wavefields. To bypass this issue, a previously proposed approximation replaces these residuals by those between the data and the exact solution of the wave equation. This approximation is questionable during the early WRI iterations when the wavefields computed with and without data assimilation differ significantly. We have developed a simple backward-forward time-stepping recursion to refine the accuracy of the data-assimilated wavefields. Each iteration requires us to solve one backward and one forward problem, the former being used to update the right side of the latter. An application to the BP salt model indicates that a few iterations are enough to reconstruct data-assimilated wavefields accurately with a crude velocity model. Although this backward-forward recursion leads to increased computational overheads during one WRI iteration, it preserves its capability to extend the search space.

Frequency-domain wave-equation traveltime inversion with a monofrequency component

Geophysics ◽  
2021 ◽  
Vol 86 (6) ◽  
pp. R913-R926
Author(s):  
Jianhua Wang ◽  
Jizhong Yang ◽  
Liangguo Dong ◽  
Yuzhu Liu
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Time Domain ◽  
Computational Cost ◽  
Velocity Model ◽  
Receiver Side ◽  
Data Set ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
The Time Domain

Wave-equation traveltime inversion (WTI) is a useful tool for background velocity model building. It is generally formulated and implemented in the time domain, in which the gradient is calculated by temporally crosscorrelating the source- and receiver-side wavefields. The time-domain source-side snapshots are either stored in memory or are reconstructed through back propagation. The memory requirements and computational cost of WTI are thus prohibitively expensive, especially for 3D applications. To partially alleviate this problem, we provide an implementation of WTI in the frequency domain with a monofrequency component. Because only one frequency is used, it is affordable to directly store the source- and receiver-side wavefields in memory. There is no need for wavefield reconstruction during gradient calculation. In such a way, we have dramatically reduced the memory requirements and computational cost compared with the traditional time-domain WTI realization. For practical implementation, the frequency-domain wavefield is calculated by time-domain finite-difference forward modeling and is transformed to the frequency domain by an on-the-fly discrete Fourier transform. Numerical examples on a simple lateral periodic velocity model and the Marmousi model demonstrate that our method can obtain accurate background velocity models comparable with those from time-domain WTI and frequency-domain WTI with multiple frequencies. A field data set test indicates that our method obtains a background velocity model that well predicts the seismic wave traveltime.

Migration velocity analysis based on focusing diffractions generated using the CRS wavefront attributes: Application to real land data

Geophysics ◽  
2021 ◽  
pp. 1-50
Author(s):  
German Garabito ◽  
José Silas dos Santos Silva ◽  
Williams Lima
Keyword(s):  
Time Domain ◽  
Real Data ◽  
Normal Incidence ◽  
Velocity Model ◽  
Migration Velocity ◽  
Velocity Analysis ◽  
Velocity Models ◽  
Time Migration ◽  
Migration Velocity Analysis ◽  
The Time Domain

In land seismic data processing, the prestack time migration (PSTM) image remains the standard imaging output, but a reliable migrated image of the subsurface depends on the accuracy of the migration velocity model. We have adopted two new algorithms for time-domain migration velocity analysis based on wavefield attributes of the common-reflection-surface (CRS) stack method. These attributes, extracted from multicoverage data, were successfully applied to build the velocity model in the depth domain through tomographic inversion of the normal-incidence-point (NIP) wave. However, there is no practical and reliable method for determining an accurate and geologically consistent time-migration velocity model from these CRS attributes. We introduce an interactive method to determine the migration velocity model in the time domain based on the application of NIP wave attributes and the CRS stacking operator for diffractions, to generate synthetic diffractions on the reflection events of the zero-offset (ZO) CRS stacked section. In the ZO data with diffractions, the poststack time migration (post-STM) is applied with a set of constant velocities, and the migration velocities are then selected through a focusing analysis of the simulated diffractions. We also introduce an algorithm to automatically calculate the migration velocity model from the CRS attributes picked for the main reflection events in the ZO data. We determine the precision of our diffraction focusing velocity analysis and the automatic velocity calculation algorithms using two synthetic models. We also applied them to real 2D land data with low quality and low fold to estimate the time-domain migration velocity model. The velocity models obtained through our methods were validated by applying them in the Kirchhoff PSTM of real data, in which the velocity model from the diffraction focusing analysis provided significant improvements in the quality of the migrated image compared to the legacy image and to the migrated image obtained using the automatically calculated velocity model.

Viscoacoustic waveform inversion of velocity structures in the time domain

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. R103-R119 ◽  
Author(s):  
Jianyong Bai ◽  
David Yingst ◽  
Robert Bloor ◽  
Jacques Leveille
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Field Data ◽  
Wave Equations ◽  
Finite Difference Methods ◽  
Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Difference Methods ◽  
The Time Domain

Because of the conversion of elastic energy into heat, seismic waves are attenuated and dispersed as they propagate. The attenuation effects can reduce the resolution of velocity models obtained from waveform inversion or even cause the inversion to produce incorrect results. Using a viscoacoustic model consisting of a single standard linear solid, we discovered a theoretical framework of viscoacoustic waveform inversion in the time domain for velocity estimation. We derived and found the viscoacoustic wave equations for forward modeling and their adjoint to compensate for the attenuation effects in viscoacoustic waveform inversion. The wave equations were numerically solved by high-order finite-difference methods on centered grids to extrapolate seismic wavefields. The finite-difference methods were implemented satisfying stability conditions, which are also presented. Numerical examples proved that the forward viscoacoustic wave equation can simulate attenuative behaviors very well in amplitude attenuation and phase dispersion. We tested acoustic and viscoacoustic waveform inversions with a modified Marmousi model and a 3D field data set from the deep-water Gulf of Mexico for comparison. The tests with the modified Marmousi model illustrated that the seismic attenuation can have large effects on waveform inversion and that choosing the most suitable inversion method was important to obtain the best inversion results for a specific seismic data volume. The tests with the field data set indicated that the inverted velocity models determined from the acoustic and viscoacoustic inversions were helpful to improve images and offset gathers obtained from migration. Compared to the acoustic inversion, viscoacoustic inversion is a realistic approach for real earth materials because the attenuation effects are compensated.

scholarly journals Extended-space full waveform inversion in the time domain with the augmented Lagrangian method

Geophysics ◽  
2021 ◽  
pp. 1-57
Author(s):  
Ali Gholami ◽  
Hossein S. Aghamiry ◽  
Stéphane Operto
Keyword(s):  
Wave Equation ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Waveform Inversion ◽  
Normal Equation ◽  
Full Waveform Inversion ◽  
Penalty Parameter ◽  
Time Stepping ◽  
Full Waveform ◽  
The Time Domain

The search space of Full Waveform Inversion (FWI) can be extended via a relaxation of the wave equation to increase the linear regime of the inversion. This wave equation relaxation is implemented by solving jointly (in a least-squares sense) the wave equation weighted by a penalty parameter and the observation equation such that the reconstructed wavefields closely match the data, hence preventing cycle skipping at receivers. Then, the subsurface parameters are updated by minimizing the temporal and spatial source extension generated by the wave-equation relaxation to push back the data-assimilated wavefields toward the physics.This extended formulation of FWI has been efficiently implemented in the frequency domain with the augmented Lagrangian method where the overdetermined systems of the data-assimilated wavefields can be solved separately for each frequency with linear algebra methods and the sensitivity of the optimization to the penalty parameter is mitigated through the action of the Lagrange multipliers.Applying this method in the time domain is however hampered by two main issues: the computation of data-assimilated wavefields with explicit time-stepping schemes and the storage of the Lagrange multipliers capturing the history of the source residuals in the state space.These two issues are solved by recognizing that the source residuals on the right-hand side of the extended wave equation, when formulated in a form suitable for explicit time stepping, are related to the extended data residuals through an adjoint equation.This relationship first allows us to relate the extended data residuals to the reduced data residuals through a normal equation in the data space. Once the extended data residuals have been estimated by solving (exactly or approximately) this normal equation, the data-assimilated wavefields are computed with explicit time stepping schemes by cascading an adjoint and a forward simulation.

scholarly journals Mitigating elastic effects in marine 3-D full-waveform inversion

2019 ◽  
Vol 220 (3) ◽  
pp. 2089-2104
Author(s):  
Òscar Calderón Agudo ◽  
Nuno Vieira da Silva ◽  
George Stronge ◽  
Michael Warner
Keyword(s):  
Wave Equation ◽  
Field Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Data Sets ◽  
Acoustic Wave Equation ◽  
Data Set ◽  
Velocity Models ◽  
Full Waveform

SUMMARY The potential of full-waveform inversion (FWI) to recover high-resolution velocity models of the subsurface has been demonstrated in the last decades with its application to field data. But in certain geological scenarios, conventional FWI using the acoustic wave equation fails in recovering accurate models due to the presence of strong elastic effects, as the acoustic wave equation only accounts for compressional waves. This becomes more critical when dealing with land data sets, in which elastic effects are generated at the source and recorded directly by the receivers. In marine settings, in which sources and receivers are typically within the water layer, elastic effects are weaker but can be observed most easily as double mode conversions and through their effect on P-wave amplitudes. Ignoring these elastic effects can have a detrimental impact on the accuracy of the recovered velocity models, even in marine data sets. Ideally, the elastic wave equation should be used to model wave propagation, and FWI should aim to recover anisotropic models of velocity for P waves (vp) and S waves (vs). However, routine three-dimensional elastic FWI is still commercially impractical due to the elevated computational cost of modelling elastic wave propagation in regions with low S-wave velocity near the seabed. Moreover, elastic FWI using local optimization methods suffers from cross-talk between different inverted parameters. This generally leads to incorrect estimation of subsurface models, requiring an estimate of vp/vs that is rarely known beforehand. Here we illustrate how neglecting elasticity during FWI for a marine field data set that contains especially strong elastic heterogeneities can lead to an incorrect estimation of the P-wave velocity model. We then demonstrate a practical approach to mitigate elastic effects in 3-D yielding improved estimates, consisting of using a global inversion algorithm to estimate a model of vp/vs, employing matching filters to remove elastic effects from the field data, and performing acoustic FWI of the resulting data set. The quality of the recovered models is assessed by exploring the continuity of the events in the migrated sections and the fit of the latter with the recovered velocity model.

A unified approach to 3-D seismic reflection imaging, Part I: Basic concepts

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 742-758 ◽  
Author(s):  
Peter Hubral ◽  
Jörg Schleicher ◽  
Martin Tygel
Keyword(s):  
Time Domain ◽  
Seismic Reflection ◽  
Velocity Model ◽  
Unified Approach ◽  
Seismic Record ◽  
Kirchhoff Type ◽  
Velocity Models ◽  
Reflection Imaging ◽  
The Time Domain ◽  
Image Transformations

Given a 3-D seismic record for an arbitrary measurement configuration and assuming a laterally and vertically inhomogeneous, isotropic macro‐velocity model, a unified approach to amplitude‐preserving seismic reflection imaging is provided. This approach is composed of (1) a weighted Kirchhoff‐type diffraction‐stack integral to transform (migrate) seismic reflection data from the measurement time domain into the model depth domain, and of (2) a weighted Kirchhoff‐type isochrone‐stack integral to transform (demigrate) the migrated seismic image from the depth domain back into the time domain. Both the diffraction‐stack and isochrone‐stack integrals can be applied in sequence (i.e., they can be chained) for different measurement configurations or different velocity models to permit two principally different amplitude‐preserving image transformations. These are (1) the amplitude‐preserving transformation (directly in the time domain) of one 3-D seismic record section into another one pertaining to a different measurement configuration and (2) the transformation (directly in the depth domain) of a 3-D depth‐migrated image into another one for a different (improved) macro‐velocity model. The first transformation is referred to here as a “configuration transform” and the second as a “remigration.” Additional image transformations arise when other parameters, e.g., the ray code of the elementary wave to be imaged, are different in migration and demigration. The diffraction‐ and isochrone‐stack integrals incorporate a fundamental duality that involves the relationship between reflectors and the corresponding reflection‐time surfaces. By analytically chaining these integrals, each of the resulting image transformations can be achieved with only one single weighted stack. In this way, generalized‐Radon‐transform‐type stacking operators can be designed in a straightforward way for many useful image transformations. In this Part I, the common geometrical concepts of the proposed unified approach to seismic imaging are presented in simple pictorial, nonmathematical form. The more thorough, quantitative description is left to Part II.

Wave-equation reflection traveltime inversion with dynamic warping and full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. R223-R233 ◽  
Author(s):  
Yong Ma ◽  
Dave Hale
Keyword(s):  
Wave Equation ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Local Minima ◽  
Low Frequencies ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Dynamic Warping

In reflection seismology, full-waveform inversion (FWI) can generate high-wavenumber subsurface velocity models but often suffers from an objective function with local minima caused mainly by the absence of low frequencies in seismograms. These local minima cause cycle skipping when the low-wavenumber component in the initial velocity model for FWI is far from the true model. To avoid cycle skipping, we discovered a new wave-equation reflection traveltime inversion (WERTI) to update the low-wavenumber component of the velocity model, while using FWI to only update high-wavenumber details of the model. We implemented the low- and high-wavenumber inversions in an alternating way. In WERTI, we used dynamic image warping (DIW) to estimate the time shifts between recorded data and synthetic data. When compared with correlation-based techniques often used in traveltime estimation, DIW can avoid cycle skipping and estimate the time shifts accurately, even when shifts vary rapidly. Hence, by minimizing traveltime shifts estimated by dynamic warping, WERTI reduces errors in reflection traveltime inversion. Then, conventional FWI uses the low-wavenumber component estimated by WERTI as a new initial model and thereby refines the model with high-wavenumber details. The alternating combination of WERTI and FWI mitigates the velocity-depth ambiguity and can recover subsurface velocities using only high-frequency reflection data.

scholarly journals Receiver-extension strategy for time-domain full waveform inversion using a relocalization approach

Geophysics ◽  
2021 ◽  
pp. 1-85
Author(s):  
Ludovic Métivier ◽  
Romain Brossier
Keyword(s):  
Time Domain ◽  
Field Data ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Geological Environment ◽  
Extension Method ◽  
Velocity Models ◽  
Full Waveform

A receiver-extension strategy is presented as an alternative to recently promoted source-extension strategies, in the framework of high resolution seismic imaging by full waveform inversion. This receiver-extension strategy is directly applicable in time-domain full waveform inversion, and unlike source-extension methods it incurs negligible extra computational cost. After connections between difference source-extension strategies are reviewed, the receiver-extension method is introduced and analyzed for single-arrival data. The method results in a misfit function convex with respect to the velocity model in this context. The method is then applied to three exploration scale synthetic case studies representative of different geological environment, based on: the Marmousi model, the BP 2004 salt model, and the Valhall model. In all three cases the receiver-extension strategy makes it possible to start full waveform inversion with crude initial models, and reconstruct meaningful subsurface velocity models. The good performance of the method even considering inaccurate amplitude prediction due to noise, imperfect modeling, and source wavelet estimation, bodes well for field data applications.

3D Laplace-domain waveform inversion using a low-frequency time-domain modeling algorithm

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R1-R13 ◽  
Author(s):  
Wansoo Ha ◽  
Seung-Goo Kang ◽  
Changsoo Shin
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Domain Modeling ◽  
Laplace Domain ◽  
Long Wavelength ◽  
Velocity Models ◽  
Time Domain Modeling ◽  
The Time Domain ◽  
Domain Inversion

We have developed a Laplace-domain full-waveform inversion technique based on a time-domain finite-difference modeling algorithm for efficient 3D inversions. Theoretically, the Laplace-domain Green’s function multiplied by a constant can be obtained regardless of the frequency content in the time-domain source wavelet. Therefore, we can use low-frequency sources and large grids for efficient modeling in the time domain. We Laplace-transform time-domain seismograms to the Laplace domain and calculate the residuals in the Laplace domain. Then, we back-propagate the Laplace-domain residuals in the time domain using a predefined time-domain source wavelet with the amplitude of the residuals. The back-propagated wavefields are transformed to the Laplace domain again to update the velocity model. The inversion results are long-wavelength velocity models on large grids similar to those obtained by the original approach based on Laplace-domain modeling. Inversion examples with 2D Gulf of Mexico field data revealed that the method yielded long-wavelength velocity models comparable with the results of the original Laplace-domain inversion methods. A 3D SEG/EAGE salt model example revealed that the 3D Laplace-domain inversion based on time-domain modeling method can be more efficient than the inversion based on Laplace-domain modeling using an iterative linear system solver.

scholarly journals Zero-offset sections with a deblurring filter in the time domain

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. S239-S249
Author(s):  
Shihang Feng ◽  
Oz Yilmaz ◽  
Yuqing Chen ◽  
Gerard T. Schuster
Keyword(s):  
Time Domain ◽  
Constant Velocity ◽  
Field Data ◽  
Velocity Model ◽  
Velocity Models ◽  
Time Migration ◽  
Prestack Time Migration ◽  
Zero Offset ◽  
Image Volume ◽  
The Time Domain

The conventional common-midpoint stack is not equivalent to the zero-offset section due to the existence of velocity uncertainty. To obtain a zero-offset reflection section that preserves most reflections and diffractions, we have developed a velocity-independent workflow for reconstructing a high-quality zero-offset reflection section from prestack data with a deblurring filter. This workflow constructs a migration image volume by prestack time migration using a series of constant-velocity models. A deblurring filter for each constant-velocity model is applied to each time-migration image to get a deblurred image volume. To preserve all events in the image volume, each deblurred image panel is demigrated and then summed over the velocity axis. Compared with the workflow without a deblurring filter, the composite zero-offset reflection section has higher resolution and fewer migration artifacts. We evaluate applications of our method to synthetic and field data to validate its effectiveness.

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