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.

Elastic inversion of near- and postcritical reflections using phase variation with angle

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. R149-R159 ◽  
Author(s):  
Xinfa Zhu ◽  
George A. McMechan
Keyword(s):  
Wave Velocity ◽  
Spherical Wave ◽  
Phase Variation ◽  
P Wave ◽  
Wide Angle ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Time Migration ◽  
Elastic Inversion

Near- and postcritical (wide-angle) reflections provide the potential for velocity and density inversion because of their large amplitudes and phase-shifted waveforms. We tested using phase variation with angle (PVA) data in addition to, or instead of, amplitude variation with angle (AVA) data for elastic inversion. Accurate PVA test data were generated using the reflectivity method. Two other forward modeling methods were also investigated, including plane-wave and spherical-wave reflection coefficients. For a two half-space model, linearized least squares was used to invert PVA and AVA data for the P-wave velocity, S-wave velocity, and the density of the lower space and the S-wave velocity of the upper space. Inversion tests showed the feasibility and robustness of PVA inversion. A reverse-time migration test demonstrated better preservation of PVA information than AVA information during wavefield propagation through a layered overburden. Phases of deeper reflections were less affected than amplitudes by the transmission losses, which makes the results of PVA inversion more accurate than AVA inversion in multilayered media. PVA brings useful information to the elastic inversion of wide-angle reflections.

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 Elastic reflection waveform inversion with variable density

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. R553-R567 ◽  
Author(s):  
Yuanyuan Li ◽  
Qiang Guo ◽  
Zhenchun Li ◽  
Tariq Alkhalifah
Keyword(s):  
Waveform Inversion ◽  
Variable Density ◽  
Background Model ◽  
Reverse Time ◽  
S Wave ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Reflection Data ◽  
Time Migration ◽  
Background Models

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

Time-reverse imaging with limited S-wave velocity model information

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. MA33-MA40 ◽  
Author(s):  
Brian Steiner ◽  
Erik H. Saenger ◽  
Stefan M. Schmalholz
Keyword(s):  
Energy Density ◽  
Wave Velocity ◽  
Wave Energy ◽  
Velocity Model ◽  
Body Waves ◽  
P Wave ◽  
S Wave ◽  
Velocity Models ◽  
Wave Energy Density ◽  
Wavefield Extrapolation

Time-reverse imaging is a wave propagation algorithm for locating sources. Signals recorded by synchronized receivers are reversed in time and propagated back to the source location by elastic wavefield extrapolation. Elastic wavefield extrapolation requires a P-wave as well as an S-wave velocity model. The velocity models available from standard reflection seismic methods are usually restricted to only P-waves. In this study, we use synthetically produced time signals to investigate the accuracy of seismic source localization by means of time-reverse imaging with the correct P-wave and a perturbed S-wave velocity model. The studies reveal that perturbed S-wave velocity models strongly influence the intensity and position of the focus. Imaging the results with the individual maximum energy density for both body wave types instead of mixed modes allows individual analysis of the two body waves. P-wave energy density images render stable focuses in case of a correct P-wave and incorrect S-wave velocity model. Thus, P-wave energy density seems to be a more suitable imaging condition in case of a high degree of uncertainty in the S-wave velocity model.

scholarly journals 3D high-resolution seismic imaging of the iron-oxide deposits in Ludvika (Sweden) using full-waveform inversion and reverse-time migration

2021 ◽  
Author(s):  
Brij Singh ◽  
Michał Malinowski ◽  
Andrzej Górszczyk ◽  
Alireza Malehmir ◽  
Stefan Buske ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Velocity Model ◽  
Mine Planning ◽  
Full Waveform Inversion ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Depth Imaging ◽  
Velocity Models ◽  
Full Waveform ◽  
Time Migration

Abstract. A sparse 3D seismic survey was acquired over the Blötberget iron-oxide deposits of the Ludvika Mines in south-central Sweden. The main aim of the survey was to delineate the deeper extension of the mineralisation and to better understand its 3D nature and associated fault systems for mine planning purposes. To obtain a high-quality seismic image in depth, we applied time-domain 3D acoustic full-waveform inversion (FWI) to build a high-resolution P-wave velocity model. This model was subsequently used for pre-stack depth imaging with reverse time migration (RTM) to produce the complementary reflectivity section. We developed a data preprocessing workflow and inversion strategy for the successful implementation of FWI in the hardrock environment. We obtained a high-fidelity velocity model using FWI and assessed its robustness. We extensively tested and optimised the parameters associated with the RTM method for subsequent depth imaging using different velocity models: a constant velocity model, a model built using first-arrival traveltime tomography and a velocity model derived by FWI. We compare our RTM results with a priori data available in the area. We conclude that, from all tested velocity models, the FWI velocity model in combination with the subsequent RTM step, provided the most focussed image of the mineralisation and we successfully mapped its 3D geometrical nature. In particular, a major reflector interpreted as a cross-cutting fault, which is restricting the deeper extension of the mineralisation with depth, and several other fault structures which were earlier not imaged were also delineated. We believe that a thorough analysis of the depth images derived with the combined FWIRTM approach that we presented here can provide more details which will help with better estimation of areas with high mineralization, better mine planning and safety measures.

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.

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.

Computing near-surface velocity models for S-wave static corrections using raypath interferometry

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. U23-U34
Author(s):  
Raul Cova ◽  
David Henley ◽  
Kristopher A. Innanen
Keyword(s):  
Wave Velocity ◽  
Velocity Model ◽  
P Wave ◽  
Surface Velocity ◽  
S Wave ◽  
Converted Wave ◽  
Near Surface ◽  
Velocity Models ◽  
Consistent Solution ◽  
Static Corrections

A near-surface velocity model is one of the typical products generated when computing static corrections, particularly in the processing of PP data. Critically refracted waves are the input usually needed for this process. In addition, for the converted PS mode, S-wave near-surface corrections must be applied at the receiver locations. In this case, however, critically refracted S-waves are difficult to identify when using P-wave energy sources. We use the [Formula: see text]-[Formula: see text] representation of the converted-wave data to capture the intercept-time differences between receiver locations. These [Formula: see text]-differences are then used in the inversion of a near-surface S-wave velocity model. Our processing workflow provides not only a set of raypath-dependent S-wave static corrections, but also a velocity model that is based on those corrections. Our computed near-surface S-wave velocity model can be used for building migration velocity models or to initialize elastic full-waveform inversions. Our tests on synthetic and field data provided superior results to those obtained by using a surface-consistent solution.

scholarly journals 3D wave-equation dispersion inversion of Rayleigh waves

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R673-R691 ◽  
Author(s):  
Zhaolun Liu ◽  
Jing Li ◽  
Sherif M. Hanafy ◽  
Gerard Schuster
Keyword(s):  
Wave Equation ◽  
Wave Velocity ◽  
Rayleigh Waves ◽  
Waveform Inversion ◽  
Shear Velocity ◽  
Velocity Model ◽  
Azimuth Angle ◽  
Inversion Method ◽  
S Wave ◽  
Starting Model

The 2D wave-equation dispersion (WD) inversion method is extended to 3D wave-equation dispersion inversion of surface waves for the shear-velocity distribution. The objective function of 3D WD is the frequency summation of the squared wavenumber [Formula: see text] differences along each azimuth angle of the fundamental or higher modes of Rayleigh waves in each shot gather. The S-wave velocity model is updated by the weighted zero-lag crosscorrelation between the weighted source-side wavefield and the back-projected receiver-side wavefield for each azimuth angle. A multiscale 3D WD strategy is provided, which starts from the pseudo-1D S-velocity model, which is then used to get the 2D WD tomogram, which in turn is used as the starting model for 3D WD. The synthetic and field data examples demonstrate that 3D WD can accurately reconstruct the 3D S-wave velocity model of a laterally heterogeneous medium and has much less of a tendency to getting stuck in a local minimum compared with full-waveform inversion.

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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