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

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.

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Acoustic full-waveform inversion in an elastic world

Geophysics ◽

10.1190/geo2017-0063.1 ◽

2018 ◽

Vol 83 (3) ◽

pp. R257-R271 ◽

Cited By ~ 12

Author(s):

Òscar Calderón Agudo ◽

Nuno Vieira da Silva ◽

Michael Warner ◽

Joanna Morgan

Keyword(s):

Wave Velocity ◽

Waveform Inversion ◽

Velocity Model ◽

P Wave ◽

Data Sets ◽

Full Waveform Inversion ◽

Data Set ◽

Velocity Models ◽

Full Waveform ◽

Elastic Data

Full-waveform inversion (FWI) is a technique used to obtain high-quality velocity models of the subsurface. Despite the elastic nature of the earth, the anisotropic acoustic wave equation is typically used to model wave propagation in FWI. In part, this simplification is essential for being efficient when inverting large 3D data sets, but it has the adverse effect of reducing the accuracy and resolution of the recovered P-wave velocity models, as well as a loss in potential to constrain other physical properties, such as the S-wave velocity given that amplitude information in the observed data set is not fully used. Here, we first apply conventional acoustic FWI to acoustic and elastic data generated using the same velocity model to investigate the effect of neglecting the elastic component in field data and we find that it leads to a loss in resolution and accuracy in the recovered velocity model. Then, we develop a method to mitigate elastic effects in acoustic FWI using matching filters that transform elastic data into acoustic data and find that it is applicable to marine and land data sets. Tests show that our approach is successful: The imprint of elastic effects on the recovered P-wave models is mitigated, leading to better-resolved models than those obtained after conventional acoustic FWI. Our method requires a guess of [Formula: see text] and is marginally more computationally demanding than acoustic FWI, but much less so than elastic FWI.

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Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Geophysics ◽

10.1190/geo2018-0082.1 ◽

2019 ◽

Vol 84 (1) ◽

pp. R1-R10 ◽

Cited By ~ 11

Author(s):

Zhendong Zhang ◽

Tariq Alkhalifah ◽

Zedong Wu ◽

Yike Liu ◽

Bin He ◽

...

Keyword(s):

Field Data ◽

Extreme Values ◽

Time Lag ◽

Waveform Inversion ◽

Optimal Time ◽

Full Waveform Inversion ◽

Data Set ◽

Velocity Models ◽

Full Waveform ◽

The Earth

Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

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Full-waveform inversion for full-wavefield imaging: Decades in the making

The Leading Edge ◽

10.1190/tle40050324.1 ◽

2021 ◽

Vol 40 (5) ◽

pp. 324-334

Author(s):

Rongxin Huang ◽

Zhigang Zhang ◽

Zedong Wu ◽

Zhiyuan Wei ◽

Jiawei Mei ◽

...

Keyword(s):

Model Building ◽

Seismic Imaging ◽

Structural Information ◽

Waveform Inversion ◽

Velocity Model ◽

Data Sets ◽

Full Waveform Inversion ◽

Data Types ◽

Velocity Models ◽

Full Waveform

Seismic imaging using full-wavefield data that includes primary reflections, transmitted waves, and their multiples has been the holy grail for generations of geophysicists. To be able to use the full-wavefield data effectively requires a forward-modeling process to generate full-wavefield data, an inversion scheme to minimize the difference between modeled and recorded data, and, more importantly, an accurate velocity model to correctly propagate and collapse energy of different wave modes. All of these elements have been embedded in the framework of full-waveform inversion (FWI) since it was proposed three decades ago. However, for a long time, the application of FWI did not find its way into the domain of full-wavefield imaging, mostly owing to the lack of data sets with good constraints to ensure the convergence of inversion, the required compute power to handle large data sets and extend the inversion frequency to the bandwidth needed for imaging, and, most significantly, stable FWI algorithms that could work with different data types in different geologic settings. Recently, with the advancement of high-performance computing and progress in FWI algorithms at tackling issues such as cycle skipping and amplitude mismatch, FWI has found success using different data types in a variety of geologic settings, providing some of the most accurate velocity models for generating significantly improved migration images. Here, we take a step further to modify the FWI workflow to output the subsurface image or reflectivity directly, potentially eliminating the need to go through the time-consuming conventional seismic imaging process that involves preprocessing, velocity model building, and migration. Compared with a conventional migration image, the reflectivity image directly output from FWI often provides additional structural information with better illumination and higher signal-to-noise ratio naturally as a result of many iterations of least-squares fitting of the full-wavefield data.

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Anisotropic 3D full-waveform inversion

Geophysics ◽

10.1190/geo2012-0338.1 ◽

2013 ◽

Vol 78 (2) ◽

pp. R59-R80 ◽

Cited By ~ 233

Author(s):

Michael Warner ◽

Andrew Ratcliffe ◽

Tenice Nangoo ◽

Joanna Morgan ◽

Adrian Umpleby ◽

...

Keyword(s):

High Velocity ◽

Field Data ◽

Waveform Inversion ◽

Velocity Model ◽

Full Waveform Inversion ◽

Low Velocity ◽

Data Set ◽

Reflection Data ◽

Full Waveform ◽

Gas Cloud

We have developed and implemented a robust and practical scheme for anisotropic 3D acoustic full-waveform inversion (FWI). We demonstrate this scheme on a field data set, applying it to a 4C ocean-bottom survey over the Tommeliten Alpha field in the North Sea. This shallow-water data set provides good azimuthal coverage to offsets of 7 km, with reduced coverage to a maximum offset of about 11 km. The reservoir lies at the crest of a high-velocity antiformal chalk section, overlain by about 3000 m of clastics within which a low-velocity gas cloud produces a seismic obscured area. We inverted only the hydrophone data, and we retained free-surface multiples and ghosts within the field data. We invert in six narrow frequency bands, in the range 3 to 6.5 Hz. At each iteration, we selected only a subset of sources, using a different subset at each iteration; this strategy is more efficient than inverting all the data every iteration. Our starting velocity model was obtained using standard PSDM model building including anisotropic reflection tomography, and contained epsilon values as high as 20%. The final FWI velocity model shows a network of shallow high-velocity channels that match similar features in the reflection data. Deeper in the section, the FWI velocity model reveals a sharper and more-intense low-velocity region associated with the gas cloud in which low-velocity fingers match the location of gas-filled faults visible in the reflection data. The resulting velocity model provides a better match to well logs, and better flattens common-image gathers, than does the starting model. Reverse-time migration, using the FWI velocity model, provides significant uplift to the migrated image, simplifying the planform of the reservoir section at depth. The workflows, inversion strategy, and algorithms that we have used have broad application to invert a wide-range of analogous data sets.

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Challenges in shallow targets reconstruction by 3D elastic full-waveform inversion — Which initial model?

Geophysics ◽

10.1190/geo2019-0523.1 ◽

2021 ◽

pp. 1-91

Author(s):

Daniela Teodor ◽

Cesare Cesare ◽

Farbod Khosro Anjom ◽

Romain Brossier ◽

Valentina Socco Laura ◽

...

Keyword(s):

Field Data ◽

Weighting Function ◽

Waveform Inversion ◽

P Wave ◽

Full Waveform Inversion ◽

Initial Model ◽

Near Surface ◽

Velocity Models ◽

Full Waveform ◽

3D Acquisition

Elastic full-waveform inversion (FWI) is a powerful tool for high-resolution subsurface multi-parameter characterization. However, 3D FWI applied to land data for near-surface applications is particularly challenging, since the seismograms are dominated by highly energetic, dispersive, and complex-scattered surface waves (SWs). In these conditions, a successful deterministic FWI scheme requires an accurate initial model. This study, primarily focused on field data analysis for 3D applications, aims at enhancing the resolution in the imaging of complex shallow targets, by integrating devoted SW analysis techniques with a 3D spectral-element-based elastic FWI. From dispersion curves (DCs), extracted from seismic data recorded over a sharp-interface shallow target, we built different initial S-wave (VS) and P-wave (VP) velocity models (laterally homogeneous and laterally variable), using a specific data-transform. Starting from these models, we carry out 3D FWI tests on synthetic and field data, using a relatively straightforward inversion scheme. The field data processing before FWI consists of bandpass filtering and muting of noisy traces. During FWI, a weighting function is applied to the far-offset traces. We test both 2D and 3D acquisition layouts, with different positions of the sources and variable offsets. The 3D FWI workflow enriched the overall content of the initial models, allowing a reliable reconstruction of the shallow target, especially when using laterally variable initial models. Moreover, a 3D acquisition layout guaranteed a better reconstruction of the target’s shape and lateral extension. In addition, the integration of model-oriented (preliminary monoparametric FWI) and data-oriented (time-windowing) strategies into the main optimization scheme has granted further improvement of the FWI results.

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Tomographic modeling of a cross‐borehole data set

Geophysics ◽

10.1190/1.1442584 ◽

1989 ◽

Vol 54 (10) ◽

pp. 1249-1257 ◽

Cited By ~ 16

Author(s):

Larry R. Lines ◽

Edward D. LaFehr

Keyword(s):

Wave Equation ◽

Ray Tracing ◽

Velocity Model ◽

Velocity Estimation ◽

P Wave ◽

Seismic Survey ◽

Equation Modeling ◽

Data Set ◽

True Solution ◽

Velocity Models

In this paper we describe a methodology for estimating P‐wave velocities from a cross‐borehole seismic survey that uses straight‐ray tomography, ray tracing, and finite‐difference wave‐equation modeling to produce velocity models that fit the first‐break traveltimes. After a starting model is established by straight‐ray tomography, the velocity model is checked by ray tracing and wave‐equation modeling. Since the models for each procedure show consistent results and the modeled traveltimes closely match those traveltimes from the actual data, we felt our interpretation was confirmed. However, the fitting of cross‐well first break traveltimes is only a necessary validity check and is not sufficient to guarantee that the true solution has been found. Two wells were drilled through the areas that were anomalous on the derived tomogram and check‐shot velocity surveys were run. Due primarily to a lateral ambiguity in velocity estimation caused by too few near‐vertical raypaths, the check‐shot surveys did not agree with the tomogram velocities. However, subsequently the check‐shot traveltimes were used to place bounds on velocity in a constrained least‐squares procedure; the combined modeling of uphole and cross‐well rays produced an optimum velocity model which satisfies all available data.

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Estimation of acoustic macro models using a genetic full-waveform inversion: Applications to the Marmousi model

Geophysics ◽

10.1190/geo2015-0198.1 ◽

2016 ◽

Vol 81 (4) ◽

pp. R173-R184 ◽

Cited By ~ 32

Author(s):

Angelo Sajeva ◽

Mattia Aleardi ◽

Eusebio Stucchi ◽

Nicola Bienati ◽

Alfredo Mazzotti

Keyword(s):

Prior Information ◽

Waveform Inversion ◽

Velocity Model ◽

Forward Modeling ◽

Coarse Grid ◽

P Wave ◽

Stochastic Methods ◽

Full Waveform Inversion ◽

Velocity Models ◽

Full Waveform

We have developed a stochastic full-waveform inversion that uses genetic algorithms (GA FWI) to estimate acoustic macro models of the P-wave velocity field. Stochastic methods such as GA severely suffer the curse of dimensionality, meaning that they require unaffordable computer resources for inverse problems with many unknowns and expensive forward modeling. To mitigate this issue, we have proposed a two-grid technique with a coarse grid to represent the subsurface for the GA inversion and a finer grid for the forward modeling. We have applied this procedure to invert synthetic acoustic data of the Marmousi model, and we have developed three different tests. The first two tests use a velocity model derived from standard stacking velocity analysis as prior information and differ only for the parameterization of the coarse grid. Their comparison indicates that a smart parameterization of the coarse grid may significantly improve the final result. The third test uses a linearly increasing 1D velocity model as prior information, a layer-stripping procedure, and a large number of model evaluations. All three tests return velocity models that fairly reproduce the long-wavelength structures of the Marmousi. First-break cycle skipping related to the seismograms of the final GA-FWI models is significantly reduced compared with that computed on the models used as prior information. Descent-based FWIs starting from final GA-FWI models yield velocity models with low and comparable model misfits and with an improved reconstruction of the structural details. The quality of the models obtained by GA FWI plus descent-based FWI is benchmarked against the models obtained by descent-based FWI started from a smoothed version of the Marmousi and started directly from the prior information models. Our results are promising and demonstrate the ability of the two-grid GA FWI to yield velocity models suitable as input to descent-based FWI.

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

Geophysics ◽

10.1190/geo2013-0004.1 ◽

2013 ◽

Vol 78 (6) ◽

pp. R223-R233 ◽

Cited By ~ 148

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.

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

Geophysics ◽

10.1190/geo2020-0922.1 ◽

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.

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Bayesian trans-dimensional full waveform inversion: synthetic and field data application

Geophysical Journal International ◽

10.1093/gji/ggaa201 ◽

2020 ◽

Vol 222 (1) ◽

pp. 610-627 ◽

Cited By ~ 1

Author(s):

Peng Guo ◽

Gerhard Visser ◽

Erdinc Saygin

Keyword(s):

Bayesian Inference ◽

Field Data ◽

Waveform Inversion ◽

Velocity Model ◽

Full Waveform Inversion ◽

Layer Model ◽

Model Assumption ◽

Velocity Models ◽

Full Waveform ◽

Starting Model

SUMMARY Seismic full waveform inversion (FWI) is a state-of-the-art technique for estimating subsurface physical models from recorded seismic waveform, but its application requires care because of high non-linearity and non-uniqueness. The final outcome of global convergence from conventional FWI using local gradient information relies on an informative starting model. Bayesian inference using Markov chain Monte Carlo (MCMC) sampling is able to remove such dependence, by a direct extensive search of the model space. We use a Bayesian trans-dimensional MCMC seismic FWI method with a parsimonious dipping layer parametrization, to invert for subsurface velocity models from pre-stack seismic shot gathers that contain mainly reflections. For the synthetic study, we use a simple four-layer model and a modified Marmousi model. A recently collected multichannel off-shore seismic reflection data set, from the Lord Howe Rise (LHR) in the east of Australia, is used for the field data test. The trans-dimensional FWI method is able to provide model ensembles for describing posterior distribution, when the dipping-layer model assumption satisfies the observed data. The model assumption requires narrow models, thus only near-offset data to be used. We use model stitching with lateral and depth constraints to create larger 2-D models from many adjacent overlapping submodel inversions. The inverted 2-D velocity model from the Bayesian inference can then be used as a starting model for the gradient-based FWI, from which we are able to obtain high-resolution subsurface velocity models, as demonstrated using the synthetic data. However, lacking far-offset data limits the constraints for the low-wavenumber part of the velocity model, making the inversion highly non-unique. We found it challenging to apply the dipping-layer based Bayesian FWI to the field data. The approximations in the source wavelet and forward modelling physics increase the multimodality of the posterior distribution; the sampled velocity models clearly show the trade-off between interface depth and velocity. Numerical examples using the synthetic and field data indicate that trans-dimensional FWI has the potential for inverting earth models from reflection waveform. However, a sparse model parametrization and far offset constraints are required, especially for field application.

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