scholarly journals Elastic reflection-based waveform inversion with a nonlinear approach

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. R309-R321 ◽  
Author(s):  
Qiang Guo ◽  
Tariq Alkhalifah
Keyword(s):  
Wave Velocity ◽  
Equivalent Stress ◽  
Waveform Inversion ◽  
P Wave ◽  
S Wave ◽  
Velocity Models ◽  
Wave Velocities ◽  
Full Waveform ◽  
Highly Nonlinear ◽  
Elastic Reflection

Full-waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low-wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is preferred of the high-wavenumber updates along reflectors. We have developed an elastic RWI that inverts for the low-wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update the perturbation and propagation parts of the velocity models in a nested fashion. Applications on the synthetic isotropic models and field data indicate that our method can efficiently update the low- and high-wavenumber parts of the models.

Elastic reflection traveltime inversion with decoupled wave equation

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. R463-R474 ◽  
Author(s):  
Guanchao Wang ◽  
Shangxu Wang ◽  
Jianyong Song ◽  
Chunhui Dong ◽  
Mingqiang Zhang
Keyword(s):  
Wave Equation ◽  
Wave Velocity ◽  
Waveform Inversion ◽  
P Wave ◽  
Model Parameters ◽  
Local Minima ◽  
S Wave ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Elastic Reflection

Elastic full-waveform inversion (FWI) updates high-resolution model parameters by minimizing the residuals of multicomponent seismic records between the field and model data. FWI suffers from the potential to converge to local minima and more serious nonlinearity than acoustic FWI mainly due to the absence of low frequencies in seismograms and the extended model domain (P- and S-velocities). Reflection waveform inversion can relax the nonlinearity by relying on the tomographic components, which can be used to update the low-wavenumber components of the model. Hence, we have developed an elastic reflection traveltime inversion (ERTI) approach to update the low-wavenumber component of the velocity models for the P- and S-waves. In our ERTI algorithm, we took the P- and S-wave impedance perturbations as elastic reflectivity to generate reflections and a weighted crosscorrelation as the misfit function. Moreover, considering the higher wavenumbers (lower velocity value) of the S-wave velocity compared with the P-wave case, optimizing the low-wavenumber components for the S-wave velocity is even more crucial in preventing the elastic FWI from converging to local minima. We have evaluated an equivalent decoupled velocity-stress wave equation to ERTI to reduce the coupling effects of different wave modes and to improve the inversion result of ERTI, especially for the S-wave velocity. The subsequent application on the Sigsbee2A model demonstrates that our ERTI method with the decoupled wave equation can efficiently update the low-wavenumber parts of the model and improve the precision of the S-wave velocity.

scholarly journals 2-D multiparameter viscoelastic shallow-seismic full-waveform inversion: reconstruction tests and first field-data application

2020 ◽  
Vol 222 (1) ◽  
pp. 560-571
Author(s):  
Lingli Gao ◽  
Yudi Pan ◽  
Thomas Bohlen
Keyword(s):  
Wave Velocity ◽  
Wave Attenuation ◽  
Waveform Inversion ◽  
P Wave ◽  
S Wave ◽  
Velocity Models ◽  
Full Waveform ◽  
Shallow Seismic ◽  
P Wave Velocity ◽  
Data Application

SUMMARY 2-D full-waveform inversion (FWI) of shallow-seismic wavefields has recently become a novel way to reconstruct S-wave velocity models of the shallow subsurface with high vertical and lateral resolution. In most applications, seismic wave attenuation is ignored or considered as a passive modelling parameter only. In this study, we explore the feasibility and performance of multiparameter viscoelastic 2-D FWI in which seismic velocities and attenuation of P and S waves, respectively, and mass density are inverted simultaneously. Synthetic reconstruction experiments reveal that multiple crosstalks between all viscoelastic material parameters may occur. The reconstruction of S-wave velocity is always robust and of high quality. The parameters P-wave velocity and density exhibit weaker sensitivity and can be reconstructed more reliably by multiparameter viscoelastic FWI. Anomalies in S-wave attenuation can be recovered but with limited resolution. In a field-data application, a small-scale refilled trench is nicely delineated as a low P- and S-wave velocity anomaly. The reconstruction of P-wave velocity is improved by the simultaneous inversion of attenuation. The reconstructed S-wave attenuation reveals higher attenuation in the shallow weathering zone and weaker attenuation below. The variations in the reconstructed P- and S-wave velocity models are consistent with the reflectivity observed in a ground penetrating radar (GPR) profile.

A hierarchical elastic full-waveform inversion scheme based on wavefield separation and the multistep-length approach

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. R99-R123 ◽  
Author(s):  
Zhiming Ren ◽  
Yang Liu
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
P Wave ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Wave Velocities ◽  
Full Waveform ◽  
Wavefield Separation ◽  
P Wave Velocity

Elastic full-waveform inversion (FWI) updates model parameters by minimizing the residuals of the P- and S-wavefields, resulting in more local minima and serious nonlinearity. In addition, the coupling of different parameters degrades the inversion results. To address these problems, we have developed a hierarchical elastic FWI scheme based on wavefield separation and a multistep-length gradient approach. First, we have derived the gradients expressed by different wave modes; analyzed the crosstalk between various parameters; and evaluated the sensitivity of separated P-wave, separated S-wave, and P- and S-wave misfit functions. Then, a practical four-stage inversion workflow was developed. In the first stage, conventional FWI is used to achieve rough estimates of the P- and S-wave velocities. In the second stage, we only invert the P-wave velocity applying the separated P-wavefields when strong S-wave energy is involved, or we merely update the S-wave velocity by matching the separated S-wavefields for the weak S-wave case. The PP and PS gradient formulas are used in these two cases, respectively. Therefore, the nonlinearity of inversion and the crosstalk between parameters are greatly reduced. In the third stage, the multistep-length gradient scheme is adopted. The density structure can be improved owing to the use of individual step lengths for different parameters. In the fourth stage, we make minor adjustments to the recovered P- and S-wave velocities and density by implementing conventional FWI again. Synthetic examples have determined that our hierarchical FWI scheme with the aforementioned steps obtains more plausible models than the conventional method. Inversion results of each stage and any three stages reveal that wavefield decomposition and the multistep-length approach are helpful to improve the accuracy of velocities and density, respectively, and all the stages of our hierarchical FWI method are necessary to give a good recovery of P- and S-wave velocities and density.

scholarly journals Time–frequency windowing in multiparameter elastic FWI of shallow seismic wavefield

2020 ◽  
Vol 222 (2) ◽  
pp. 1164-1177
Author(s):  
Nikolaos Athanasopoulos ◽  
Edgar Manukyan ◽  
Thomas Bohlen ◽  
Hansruedi Maurer
Keyword(s):  
Wave Velocity ◽  
Time Window ◽  
Mass Density ◽  
Waveform Inversion ◽  
P Wave ◽  
S Wave ◽  
Time Frequency ◽  
Full Waveform ◽  
Shallow Seismic ◽  
P Wave Velocity

SUMMARY Full-waveform inversion of shallow seismic wavefields is a promising method to infer multiparameter models of elastic material properties (S-wave velocity, P-wave velocity and mass density) of the shallow subsurface with high resolution. Previous studies used either the refracted Pwaves to reconstructed models of P-wave velocity or the high-amplitude Rayleigh waves to infer the S-wave velocity structure. In this work, we propose a combination of both wavefields using continuous time–frequency windowing. We start with the contribution of refracted P waves and gradually increase the time window to account for scattered body waves, higher mode Rayleigh waves and finally the fundamental Rayleigh wave mode. The opening of the time window is combined with opening the frequency bandwidth of input signals to avoid cycle skipping. Synthetic reconstruction tests revealed that the reconstruction of P-wave velocity model and mass density can be improved. The S-wave velocity reconstruction is still accurate and robust and is slightly benefitted by time–frequency windowing. In a field data application, we observed that time–frequency windowing improves the consistency of multiparameter models. The inferred models are in good agreement with independent geophysical information obtained from ground-penetrating radar and full-waveform inversion of SH waves.

Elastic reflection waveform inversion based on the decomposition of sensitivity kernels

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R235-R250 ◽  
Author(s):  
Zhiming Ren ◽  
Zhenchun Li ◽  
Bingluo Gu
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Background Model ◽  
Reverse Time ◽  
S Wave ◽  
Velocity Models ◽  
Time Migration ◽  
Starting Model

Full-waveform inversion (FWI) has the potential to obtain an accurate velocity model. Nevertheless, it depends strongly on the low-frequency data and the initial model. When the starting model is far from the real model, FWI tends to converge to a local minimum. Based on a scale separation of the model (into the background model and reflectivity model), reflection waveform inversion (RWI) can separate out the tomography term in the conventional FWI kernel and invert for the long-wavelength components of the velocity model by smearing the reflected wave residuals along the transmission (or “rabbit-ear”) paths. We have developed a new elastic RWI method to build the P- and S-wave velocity macromodels. Our method exploits a traveltime-based misfit function to highlight the contribution of tomography terms in the sensitivity kernels and a sensitivity kernel decomposition scheme based on the P- and S-wave separation to suppress the high-wavenumber artifacts caused by the crosstalk of different wave modes. Numerical examples reveal that the gradients of the background models become sufficiently smooth owing to the decomposition of sensitivity kernels and the traveltime-based misfit function. We implement our elastic RWI in an alternating way. At each loop, the reflectivity model is generated by elastic least-squares reverse time migration, and then the background model is updated using the separated traveltime kernels. Our RWI method has been successfully applied in synthetic and real reflection seismic data. Inversion results demonstrate that the proposed method can retrieve preferable low-wavenumber components of the P- and S-wave velocity models, which are reliable to serve as a starting model for conventional elastic FWI. Also, our method with a two-stage inversion workflow, first updating the P-wave velocity using the PP kernels and then updating the S-wave velocity using the PS kernels, is feasible and robust even when P- and S-wave velocities have different structures.

Localizing CO2 at Sleipner — Seismic images versus P-wave velocities from waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. B131-B146 ◽  
Author(s):  
Manuel Queißer ◽  
Satish C. Singh
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
P Wave ◽  
Full Waveform Inversion ◽  
Wave Velocities ◽  
Full Waveform ◽  
P Wave Velocity ◽  
Seismic Image ◽  
P Wave Velocities ◽  
Seismic Images

The presence of injected [Formula: see text] in the Utsira Sand at the Sleipner site, Norway, is associated with a high negative P-wave velocity anomaly; that is, a low postinjection velocity and a strong seismic response. Time-lapse seismic imaging of [Formula: see text] injection at Sleipner is thus a viable monitoring tool of the injected [Formula: see text]. The work flow usually involves conventional seismic processing, including stacking, and results in seismic images. Multiple reflections, interference effects such as tuning, and the velocity pushdown effect due to [Formula: see text] injection render these seismic images ambiguous in terms of the localization and the quantification of the [Formula: see text] in the Utsira Sand. Nonetheless, seismic images often form the basis for analyses that aim to quantify the injected [Formula: see text]. We employed elastic 2D full waveform inversion to invert prestack seismic Sleipner data from preinjection (1994) and postinjection (1999) and compared the resulting postinjection P-wave velocity model with the corresponding seismic image. We found that the high-amplitude reflections in the seismic image do not everywhere coincide with low postinjection P-wave velocities. Drawing extensive and integrated conclusions is out of our scope, because this would require full control over the seismic data processing and a more comprehensive forward modeling. For instance, modeling should be done in 3D and an adequate anelasticity formulation should be added. However, the waveform inversion scheme we used accounts for all the aforementioned elastic propagation effects. The results therefore suggested that the exclusive use of seismic images to quantify [Formula: see text] could be revised and full waveform inversion should be added to the analysis toolbox.

scholarly journals Interparameter trade-off quantification for isotropic-elastic full-waveform inversion with various model parameterizations

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R185-R206 ◽  
Author(s):  
Wenyong Pan ◽  
Kristopher A. Innanen ◽  
Yu Geng ◽  
Junxiao Li
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
P Wave ◽  
Physical Parameters ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Trade Off ◽  
Full Waveform ◽  
Trade Offs ◽  
P Wave Velocity

Simultaneous determination of multiple physical parameters using full-waveform inversion (FWI) suffers from interparameter trade-off difficulties. Analyzing the interparameter trade-offs in different model parameterizations of isotropic-elastic FWI, and thus determining the appropriate model parameterization, are critical for efficient inversion and obtaining reliable inverted models. Five different model parameterizations are considered and compared including velocity-density, modulus-density, impedance-density, and two velocity-impedance parameterizations. The scattering radiation patterns are first used for interparameter trade-off analysis. Furthermore, a new framework is developed to evaluate the interparameter trade-off based upon multiparameter Hessian-vector products: Multiparameter point spread functions (MPSFs) and interparameter contamination sensitivity kernels (ICSKs), which provide quantitative, second-order measurements of the interparameter contaminations. In the numerical experiments, the interparameter trade-offs in various model parameterizations are evaluated using the MPSFs and ICSKs. Inversion experiments are carried out with simple Gaussian-anomaly models and a complex Marmousi model. Overall, the parameterization of the P-wave velocity, S-wave velocity, and density, and the parameterization of the P-wave velocity, S-wave velocity, and S-wave impedance perform best for reconstructing all of the physical parameters. Isotropic-elastic FWI of the Hussar low-frequency data set with various model parameterizations verifies our conclusions.

Elastic full waveform inversion of multicomponent ocean-bottom cable seismic data: Application to Alba Field, U. K. North Sea

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. R109-R119 ◽  
Author(s):  
Timothy J. Sears ◽  
Penny J. Barton ◽  
Satish C. Singh
Keyword(s):  
Wave Velocity ◽  
Seismic Data ◽  
Waveform Inversion ◽  
P Wave ◽  
Full Waveform Inversion ◽  
Ocean Bottom ◽  
S Wave ◽  
Wave Data ◽  
Data Inversion ◽  
Full Waveform

Elastic full waveform inversion of multichannel seismic data represents a data-driven form of analysis leading to direct quantification of the subsurface elastic parameters in the depth domain. Previous studies have focused on marine streamer data using acoustic or elastic inversion schemes for the inversion of P-wave data. In this paper, P- and S-wave velocities are inverted for using wide-angle multicomponent ocean-bottom cable (OBC) seismic data. Inversion is undertaken using a two-dimensional elastic algorithm operating in the time domain, which allows accurate modeling and inversion of the full elastic wavefield, including P- and mode-converted PS-waves and their respective amplitude variation with offset (AVO) responses. Results are presented from the application of this technique to an OBC seismic data set from the Alba Field, North Sea. After building an initial velocity model and extracting a seismic wavelet, the data are inverted instages. In the first stage, the intermediate wavelength P-wave velocity structure is recovered from the wide-angle data and then the short-scale detail from near-offset data using P-wave data on the [Formula: see text] (vertical geophone) component. In the second stage, intermediate wavelengths of S-wave velocity are inverted for, which exploits the information captured in the P-wave’s elastic AVO response. In the third stage, the earlier models are built on to invert mode-converted PS-wave events on the [Formula: see text] (horizontal geophone) component for S-wave velocity, targeting first shallow and then deeper structure. Inversion of [Formula: see text] alone has been able to delineate the Alba Field in P- and S-wave velocity, with the main field and outlier sands visible on the 2D results. Inversion of PS-wave data has demonstrated the potential of using converted waves to resolve shorter wavelength detail. Even at the low frequencies [Formula: see text] inverted here, improved spatial resolution was obtained by inverting S-wave data compared with P-wave data inversion results.

Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCC105-WCC118 ◽  
Author(s):  
Romain Brossier ◽  
Stéphane Operto ◽  
Jean Virieux
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Frequency Domain ◽  
Wave Velocity ◽  
Waveform Inversion ◽  
Surface Effects ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Velocity Models ◽  
Full Waveform

Quantitative imaging of the elastic properties of the subsurface at depth is essential for civil engineering applications and oil- and gas-reservoir characterization. A realistic synthetic example provides for an assessment of the potential and limits of 2D elastic full-waveform inversion (FWI) of wide-aperture seismic data for recovering high-resolution P- and S-wave velocity models of complex onshore structures. FWI of land data is challenging because of the increased nonlinearity introduced by free-surface effects such as the propagation of surface waves in the heterogeneous near-surface. Moreover, the short wavelengths of the shear wavefield require an accurate S-wave velocity starting model if low frequencies are unavailable in the data. We evaluated different multiscale strategies with the aim of mitigating the nonlinearities. Massively parallel full-waveform inversion was implemented in the frequency domain. The numerical optimization relies on a limited-memory quasi-Newton algorithm thatoutperforms the more classic preconditioned conjugate-gradient algorithm. The forward problem is based upon a discontinuous Galerkin (DG) method on triangular mesh, which allows accurate modeling of free-surface effects. Sequential inversions of increasing frequencies define the most natural level of hierarchy in multiscale imaging. In the case of land data involving surface waves, the regularization introduced by hierarchical frequency inversions is not enough for adequate convergence of the inversion. A second level of hierarchy implemented with complex-valued frequencies is necessary and provides convergence of the inversion toward acceptable P- and S-wave velocity models. Among the possible strategies for sampling frequencies in the inversion, successive inversions of slightly overlapping frequency groups is the most reliable when compared to the more standard sequential inversion of single frequencies. This suggests that simultaneous inversion of multiple frequencies is critical when considering complex wave phenomena.

scholarly journals Acoustic full-waveform inversion in an elastic world

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. R257-R271 ◽  
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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