Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

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.

Download Full-text

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.

Download Full-text

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.

Download Full-text

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

Geophysical Journal International ◽

10.1093/gji/ggz569 ◽

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.

Download Full-text

Unlocking the potential of conventional narrow azimuth data by full-waveform inversion: a deep carbonate imaging case study, offshore Indonesia

10.29118/ipa21-g-163 ◽

2021 ◽

Author(s):

J. Wang

Keyword(s):

Complex Structure ◽

Time Lag ◽

Waveform Inversion ◽

Low Frequency ◽

Time Shift ◽

Full Waveform Inversion ◽

Velocity Models ◽

Full Waveform ◽

Seismic Image ◽

Refraction Tomography

Full-waveform inversion (FWI) has evolved to be the contemporary solution to resolve velocity models in areas of complex structure. Further, wide azimuth, long offset and rich low-frequency seismic data, resulting from broadband seismic acquisition, helps FWI update deeper with better convergence and stability. In this study from the South Mahakam area in offshore Indonesia, multiple layers of carbonate exist from shallow to deep with sharp velocity contrast. The target reservoir is down to 3.5 kilometers. However, for the acquired data with narrow azimuths (NAZ), short offsets (3 kilometers) and low signal to noise in the low frequencies, FWI encounters challenges of cycle skipping and unstable updates in the deeper targets that are beyond the diving-wave penetration depth. Time-lag FWI (TLFWI) (Zhang et al., 2018) uses time-shift differences between observed and modeled data as the cost function, and also makes better use of the low-frequency refraction and reflection energy. TLFWI gave good velocity updates in both the shallow and deep regions and, hence, gave an improved deep carbonate image. The anisotropic model is an important factor for the success of any FWI due to the coupling between velocity and anisotropy. In this paper, joint reflection and refraction tomography (Allemand et al., 2017) were applied in order to obtain stable anisotropy models for TLFWI. Following that, TLFWI with both refraction and reflection energy gives sensible velocity updates down to 3.5 kilometers. These updates to the model improve the seismic image and, importantly, reduce the depth uncertainties in this complex geological setting. The cumulative improvements increase interpretation confidence and can reduce future drilling risks. For the seismic processing community, the reprocessing of narrow azimuth, short-offset data with TLFWI, and associated technologies, offers great potential for generating improved and more reliable images from legacy, conventional, acquisition scenarios.

Download Full-text

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.

Download Full-text

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.

Download Full-text

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.

Download Full-text

Full-waveform inversion via source-receiver extension

Geophysics ◽

10.1190/geo2016-0301.1 ◽

2017 ◽

Vol 82 (3) ◽

pp. R153-R171 ◽

Cited By ~ 25

Author(s):

Guanghui Huang ◽

Rami Nammour ◽

William Symes

Keyword(s):

Model Updating ◽

Quantitative Estimation ◽

Time Lag ◽

Waveform Inversion ◽

Computational Cost ◽

Time Lags ◽

Complex Data ◽

Full Waveform Inversion ◽

Velocity Models ◽

Full Waveform

Full-waveform inversion produces highly resolved images of the subsurface and quantitative estimation of seismic wave velocity, provided that its initial model is kinematically accurate at the longest data wavelengths. If this initialization constraint is not satisfied, iterative model updating tends to stagnate at kinematically incorrect velocity models producing suboptimal images. The source-receiver extension overcomes this “cycle-skip” pathology by modeling each trace with its own proper source wavelet, permitting a good data fit throughout the inversion process. Because source wavelets should be constant (or vary systematically) across a shot gather, a measure of source trace dependence, for example, the mean square of the signature-deconvolved wavelet scaled by time lag, can be minimized to update the velocity model. For kinematically simple data, such measures of wavelet variance are mathematically equivalent to traveltime misfit. Thus, the model obtained by source-receiver extended inversion is close to that produced by traveltime tomography, even though the process uses no picked times. For more complex data, in which energy travels from source to receiver by multiple raypaths, Green’s function spectral notches may lead to slowly decaying trace-dependent wavelets with energy at time lags unrelated to traveltime error. Tikhonov regularization of the data-fitting problem suppresses these large-lag signals. Numerical examples suggest that this regularized formulation of source-receiver extended inversion is capable of recovering reasonably good velocity models from synthetic transmission and reflection data without stagnation at suboptimal models encountered by standard full-waveform inversion, but with essentially the same computational cost.

Download Full-text

A new parameter set for anisotropic multiparameter full-waveform inversion and application to a North Sea data set

Geophysics ◽

10.1190/geo2015-0349.1 ◽

2016 ◽

Vol 81 (4) ◽

pp. U25-U38 ◽

Cited By ~ 32

Author(s):

Nuno V. da Silva ◽

Andrew Ratcliffe ◽

Vetle Vinje ◽

Graham Conroy

Keyword(s):

North Sea ◽

Waveform Inversion ◽

Real Data ◽

Model Parameters ◽

Full Waveform Inversion ◽

Radiation Patterns ◽

Data Set ◽

Full Waveform ◽

Seismic Image ◽

Central North Sea

Parameterization lies at the center of anisotropic full-waveform inversion (FWI) with multiparameter updates. This is because FWI aims to update the long and short wavelengths of the perturbations. Thus, it is important that the parameterization accommodates this. Recently, there has been an intensive effort to determine the optimal parameterization, centering the fundamental discussion mainly on the analysis of radiation patterns for each one of these parameterizations, and aiming to determine which is best suited for multiparameter inversion. We have developed a new parameterization in the scope of FWI, based on the concept of kinematically equivalent media, as originally proposed in other areas of seismic data analysis. Our analysis is also based on radiation patterns, as well as the relation between the perturbation of this set of parameters and perturbation in traveltime. The radiation pattern reveals that this parameterization combines some of the characteristics of parameterizations with one velocity and two Thomsen’s parameters and parameterizations using two velocities and one Thomsen’s parameter. The study of perturbation of traveltime with perturbation of model parameters shows that the new parameterization is less ambiguous when relating these quantities in comparison with other more commonly used parameterizations. We have concluded that our new parameterization is well-suited for inverting diving waves, which are of paramount importance to carry out practical FWI successfully. We have demonstrated that the new parameterization produces good inversion results with synthetic and real data examples. In the latter case of the real data example from the Central North Sea, the inverted models show good agreement with the geologic structures, leading to an improvement of the seismic image and flatness of the common image gathers.

Download Full-text

Velocity model building by 3D frequency-domain, full-waveform inversion of wide-aperture seismic data

Geophysics ◽

10.1190/1.2957948 ◽

2008 ◽

Vol 73 (5) ◽

pp. VE101-VE117 ◽

Cited By ~ 93

Author(s):

Hafedh Ben-Hadj-Ali ◽

Stéphane Operto ◽

Jean Virieux

Keyword(s):

High Resolution ◽

Frequency Domain ◽

Distributed Memory ◽

Waveform Inversion ◽

Steepest Descent Method ◽

Frequency Domain Method ◽

Full Waveform Inversion ◽

Direct Solver ◽

Velocity Models ◽

Full Waveform

We assessed 3D frequency-domain (FD) acoustic full-waveform inversion (FWI) data as a tool to develop high-resolution velocity models from low-frequency global-offset data. The inverse problem was posed as a classic least-squares optimization problem solved with a steepest-descent method. Inversion was applied to a few discrete frequencies, allowing management of a limited subset of the 3D data volume. The forward problem was solved with a finite-difference frequency-domain method based on a massively parallel direct solver, allowing efficient multiple-shot simulations. The inversion code was fully parallelized for distributed-memory platforms, taking advantage of a domain decomposition of the modeled wavefields performed by the direct solver. After validation on simple synthetic tests, FWI was applied to two targets (channel and thrust system) of the 3D SEG/EAGE overthrust model, corresponding to 3D domains of [Formula: see text] and [Formula: see text], respectively. The maximum inverted frequencies are 15 and [Formula: see text] for the two applications. A maximum of 30 dual-core biprocessor nodes with [Formula: see text] of shared memory per node were used for the second target. The main structures were imaged successfully at a resolution scale consistent with the inverted frequencies. Our study confirms the feasibility of 3D frequency-domain FWI of global-offset data on large distributed-memory platforms to develop high-resolution velocity models. These high-velocity models may provide accurate macromodels for wave-equation prestack depth migration.

Download Full-text