Prestack waveform inversion based on analytical solution of the viscoelastic wave equation

Geophysics ◽  
2021 ◽  
Vol 86 (1) ◽  
pp. R45-R61
Author(s):  
Yuanqiang Li ◽  
Jingye Li ◽  
Xiaohong Chen ◽  
Jian Zhang ◽  
Xin Bo
Keyword(s):  
Analytical Solution ◽  
Seismic Reflection ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Low Frequency ◽  
S Wave ◽  
Single Interface ◽  
Wave Velocities ◽  
Avo Inversion ◽  
Viscoelastic Wave

Amplitude-variation-with-offset (AVO) inversion is based on single interface reflectivity equations. It involves some restrictions, such as the small-angle approximation, including only primary reflections, and ignoring attenuation. To address these shortcomings, the analytical solution of the 1D viscoelastic wave equation is used as the forward modeling engine for prestack inversion. This method can conveniently handle the attenuation and generate the full wavefield response of a layered medium. To avoid numerical difficulties in the analytical solution, the compound matrix method is applied to rapidly obtain the analytical solution by loop vectorization. Unlike full-waveform inversion, the proposed prestack waveform inversion (PWI) can be performed in a target-oriented way and can be applied in reservoir study. Assuming that a Q value is known, PWI is applied to synthetic data to estimate elastic parameters including compressional wave (P-wave) and shear wave (S-wave) velocities and density. After validating our method on synthetic data, this method is applied to a reservoir characterization case study. The results indicate that the reflectivity calculated by our approach is more realistic than that computed by using single interface reflectivity equations. Attenuation is an integral effect on seismic reflection; therefore, the sensitivity of seismic reflection to P-and S-wave velocities and density is significantly greater than that to Q, and the seismic records are sensitive to the low-frequency trend of Q. Thus, we can invert for the three elastic parameters by applying the fixed low-frequency trend of Q. In terms of resolution and accuracy of synthetic and real inversion results, our approach performs superiorly compared to AVO inversion.

scholarly journals Elastic envelope inversion using multicomponent seismic data without low frequency

2014 ◽  
Vol 1 (2) ◽  
pp. 1757-1802
Author(s):  
C. Huang ◽  
L. Dong ◽  
Y. Liu ◽  
B. Chi
Keyword(s):  
Seismic Data ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Low Frequency ◽  
Velocity Model ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Full Waveform ◽  
Multicomponent Data

Abstract. Low frequency is a key issue to reduce the nonlinearity of elastic full waveform inversion. Hence, the lack of low frequency in recorded seismic data is one of the most challenging problems in elastic full waveform inversion. Theoretical derivations and numerical analysis are presented in this paper to show that envelope operator can retrieve strong low frequency modulation signal demodulated in multicomponent data, no matter what the frequency bands of the data is. With the benefit of such low frequency information, we use elastic envelope of multicomponent data to construct the objective function and present an elastic envelope inversion method to recover the long-wavelength components of the subsurface model, especially for the S-wave velocity model. Numerical tests using synthetic data for the Marmousi-II model prove the effectiveness of the proposed elastic envelope inversion method, especially when low frequency is missing in multicomponent data and when initial model is far from the true model. The elastic envelope can reduce the nonlinearity of inversion and can provide an excellent starting model.

EXTRACTING SUB-SURFACE INFORMATION FROM LONG OFFSET P-WAVE DATA—A CHEAPER ALTERNATIVE TO MULTICOMPONENT OBC FOR EXPLORATION?

2002 ◽  
Vol 42 (1) ◽  
pp. 627
Author(s):  
R.G. Williams ◽  
G. Roberts ◽  
K. Hawkins
Keyword(s):  
Seismic Energy ◽  
Higher Order ◽  
P Wave ◽  
S Wave ◽  
Additional Information ◽  
Wave Data ◽  
Wave Velocities ◽  
Avo Inversion ◽  
Long Offset ◽  
Multicomponent Data

Seismic energy that has been mode converted from pwave to s-wave in the sub-surface may be recorded by multi-component surveys to obtain information about the elastic properties of the earth. Since the energy converted to s-wave is missing from the p-wave an alternative to recording OBC multi-component data is to examine p-wave data for the missing energy. Since pwave velocities are generally faster than s-wave velocities, then for a given reflection point the converted s-wave signal reaches the surface at a shorter offset than the equivalent p-wave information. Thus, it is necessary to record longer offsets for p-wave data than for multicomponent data in order to measure the same information.A non-linear, wide-angle (including post critical) AVO inversion has been developed that allows relative changes in p-wave velocities, s-wave velocities and density to be extracted from long offset p-wave data. To extract amplitudes at long offsets for this inversion it is necessary to image the data correctly, including correcting for higher order moveout and possibly anisotropy if it is present.The higher order moveout may itself be inverted to yield additional information about the anisotropy of the sub-surface.

scholarly journals Nonlinear FAVO Dispersion Quantification Based on the Analytical Solution of the Viscoelastic Wave Equation

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yuanqiang Li ◽  
Jingye Li ◽  
Xiaohong Chen ◽  
Jian Zhang ◽  
Chen Zhou ◽  
...  
Keyword(s):  
Wave Equation ◽  
Analytical Solution ◽  
Wave Velocity ◽  
Velocity Dispersion ◽  
Estimation Method ◽  
Forward Modeling ◽  
Single Interface ◽  
Viscoelastic Wave Equation ◽  
Reservoir Fluid ◽  
Viscoelastic Wave

Wave-induced fluid flow is the main cause of seismic attenuation and dispersion. So the estimated velocity dispersion information can be used to identify reservoir fluid and effectively reduce the risk of reservoir drilling. Using equivalence of dispersion and attenuation between poroelastic and viscoelastic media, we developed the method of FAVO (frequency-dependent amplitude variation with offset) dispersion quantitative estimation based on the analytical solution of 1D viscoelastic wave equation. Compared with the current single-interface velocity dispersion estimation method, the new nonlinear approach uses the analytical solution of 1D viscoelastic wave equation as the forward modeling engine. This method can conveniently handle the attenuation and generate the full-wave field response of a layered medium. First, the compound matrix method (CMM) was applied to rapidly obtain the analytical solution by vectorization. Further, we analyzed the seismic response characteristics through the model data to clarify the effectiveness of the forward modeling method. Then, the more reliable P-wave velocity, S-wave velocity, and density were recovered based on prestack viscoelastic waveform inversion (PVWI). Combining with the inversion results, the derivative matrix was calculated to perform nonlinear velocity dispersion estimation. Finally, the new estimation method was tested with the model and actual data. The experiments show that the developed method is clearly superior to the single-interface dispersion estimation method in accuracy and resolution. This approach can be used as a new choice reservoir fluid identification.

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.

Elastic model low- to intermediate-wavenumber inversion using reflection traveltime and waveform of multicomponent seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R109-R123 ◽  
Author(s):  
Wencai Xu ◽  
Tengfei Wang ◽  
Jiubing Cheng
Keyword(s):  
Waveform Inversion ◽  
Elastic Model ◽  
S Wave ◽  
Reflected Waves ◽  
Wave Velocities ◽  
Reflection Data ◽  
Model Background ◽  
Mode Decomposition ◽  
Model Components ◽  
Two Stages

Low-, intermediate-, and high-wavenumber components of P- and S-wave velocities jointly influence the elastic wave propagation and scattering in an isotropic medium. By taking advantage of all information in the data, elastic full-waveform inversion (E-FWI) has the potential to recover these model components. However, if the transmitted wave data are insufficient to illuminate the deeper part of the subsurface, we should rely on the solutions using reflection data. To reduce the nonlinearity of waveform inversion, we choose to decouple the effects of the model background and perturbation on the reflected waves within a linearized inversion framework. This resorts to three stages aiming to gradually fit the traveltimes and waveforms of the reflected PP and PS waves based on data or gradient preconditioning through P/S mode decomposition. For the first two stages, once the multicomponent seismograms have been separated into PP and PS reflection recordings, reflection traveltime inversion using an acoustic wave propagator (A-RTI) can successively recover the low-wavenumber components of P- and S-wave velocities. In the last stage, starting from the models having reliable low-wavenumber components, elastic reflection waveform inversion (E-RWI) can easily get out of the local minima and continue to retrieve the increasing wavenumber features sensitive to the waveform and amplitude variations. This is supported by gradient preconditioning through P/S mode decomposition of the extrapolated normal and adjoint wavefields, and alternately updating model background and high-wavenumber components in terms of linearized least-squares inversion. Numerical examples have demonstrated the performance of our E-RWI approach and the validity of the three-stage inversion workflow.

scholarly journals Coda-wave decorrelation sensitivity kernels in 2-D elastic media: a numerical approach

2020 ◽  
Vol 223 (2) ◽  
pp. 934-943
Author(s):  
Alejandro Duran ◽  
Thomas Planès ◽  
Anne Obermann
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Heterogeneous Media ◽  
Synthetic Data ◽  
Numerical Approach ◽  
Coda Waves ◽  
Coda Wave ◽  
Elastic Media ◽  
S Wave ◽  
Velocity Changes

SUMMARY Probabilistic sensitivity kernels based on the analytical solution of the diffusion and radiative transfer equations have been used to locate tiny changes detected in late arriving coda waves. These analytical kernels accurately describe the sensitivity of coda waves towards velocity changes located at a large distance from the sensors in the acoustic diffusive regime. They are also valid to describe the acoustic waveform distortions (decorrelations) induced by isotropically scattering perturbations. However, in elastic media, there is no analytical solution that describes the complex propagation of wave energy, including mode conversions, polarizations, etc. Here, we derive sensitivity kernels using numerical simulations of wave propagation in heterogeneous media in the acoustic and elastic regimes. We decompose the wavefield into P- and S-wave components at the perturbation location in order to construct separate P to P, S to S, P to S and S to P scattering sensitivity kernels. This allows us to describe the influence of P- and S-wave scattering perturbations separately. We test our approach using acoustic and elastic numerical simulations where localized scattering perturbations are introduced. We validate the numerical sensitivity kernels by comparing them with analytical kernel predictions and with measurements of coda decorrelations on the synthetic data.

Seismic envelope inversion and modulation signal model

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA13-WA24 ◽  
Author(s):  
Ru-Shan Wu ◽  
Jingrui Luo ◽  
Bangyu Wu
Keyword(s):  
Velocity Structure ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Low Frequency ◽  
Seismic Signal ◽  
Source Spectrum ◽  
Signal Model ◽  
Waveform Data ◽  
Long Wavelength ◽  
Modulation Signal

We recognized that the envelope fluctuation and decay of seismic records carries ultra low-frequency (ULF, i.e., the frequency below the lowest frequency in the source spectrum) signals that can be used to estimate the long-wavelength velocity structure. We then developed envelope inversion for the recovery of low-wavenumber components of media (smooth background), so that the initial model dependence of waveform inversion can be reduced. We derived the misfit function and the corresponding gradient operator for envelope inversion. To understand the long-wavelength recovery by the envelope inversion, we developed a nonlinear seismic signal model, the modulation signal model, as the basis for retrieving the ULF data and studied the nonlinear scale separation by the envelope operator. To separate the envelope data from the wavefield data (envelope extraction), a demodulation operator (envelope operator) was applied to the waveform data. Numerical tests using synthetic data for the Marmousi model proved the validity and feasibility of the proposed approach. The final results of combined [Formula: see text] (envelope-inversion for smooth background plus waveform-inversion for high-resolution velocity structure) indicated that it can deliver much improved results compared with regular full-waveform inversion (FWI) alone. Furthermore, to test the independence of the envelope to the source frequency band, we used a low-cut source wavelet (cut from 5 Hz below) to generate the synthetic data. The envelope inversion and the combined [Formula: see text] showed no appreciable difference from the full-band source results. The proposed envelope inversion is also an efficient method with very little extra work compared with conventional FWI.

Determination of formation shear attenuation from dipole sonic log data

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. D73-D79 ◽  
Author(s):  
Qiaomu Qi ◽  
Arthur C. H. Cheng ◽  
Yunyue Elita Li
Keyword(s):  
Reservoir Characterization ◽  
Wave Attenuation ◽  
Synthetic Data ◽  
Low Frequency ◽  
P Wave ◽  
Flexural Wave ◽  
S Wave ◽  
Additional Energy ◽  
Log Data ◽  
Sonic Log

ABSTRACT Formation S-wave attenuation, when combined with compressional attenuation, serves as a potential hydrocarbon indicator for seismic reservoir characterization. Sonic flexural wave measurements provide a direct means for obtaining the in situ S-wave attenuation at log scale. The key characteristic of the flexural wave is that it propagates at the formation shear slowness and experiences shear attenuation at low frequency. However, in a fast formation, the dipole log consists of refracted P- and S-waves in addition to the flexural wave. The refracted P-wave arrives early and can be removed from the dipole waveforms through time windowing. However, the refracted S-wave, which is often embedded in the flexural wave packet, is difficult to separate from the dipole waveforms. The additional energy loss associated with the refracted S-wave results in the estimated dipole attenuation being higher than the shear attenuation at low frequency. To address this issue, we have developed a new method for accurately determining the formation shear attenuation from the dipole sonic log data. The method uses a multifrequency inversion of the frequency-dependent flexural wave attenuation based on energy partitioning. We first developed our method using synthetic data. Application to field data results in a shear attenuation log that is consistent with lithologic interpretation of other available logs.

Computation of dry-rock VP/VS ratio, fluid property factor, and density estimation from amplitude-variation-with-offset inversion

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. R669-R679 ◽  
Author(s):  
Gang Chen ◽  
Xiaojun Wang ◽  
Baocheng Wu ◽  
Hongyan Qi ◽  
Muming Xia
Keyword(s):  
Reservoir Characterization ◽  
Synthetic Data ◽  
Pore Fluid ◽  
Inversion Method ◽  
S Wave ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Fluid Identification ◽  
Fluid Property ◽  
Avo Inversion

Estimating the fluid property factor and density from amplitude-variation-with-offset (AVO) inversion is important for fluid identification and reservoir characterization. The fluid property factor can distinguish pore fluid in the reservoir and the density estimate aids in evaluating reservoir characteristics. However, if the scaling factor of the fluid property factor (the dry-rock [Formula: see text] ratio) is chosen inappropriately, the fluid property factor is not only related to the pore fluid, but it also contains a contribution from the rock skeleton. On the other hand, even if the angle gathers include large angles (offsets), a three-parameter AVO inversion struggles to estimate an accurate density term without additional constraints. Thus, we have developed an equation to compute the dry-rock [Formula: see text] ratio using only the P- and S-wave velocities and density of the saturated rock from well-logging data. This decouples the fluid property factor from lithology. We also developed a new inversion method to estimate the fluid property factor and density parameters, which takes full advantage of the high stability of a two-parameter AVO inversion. By testing on a portion of the Marmousi 2 model, we find that the fluid property factor calculated by the dry-rock [Formula: see text] ratio obtained by our method relates to the pore-fluid property. Simultaneously, we test the AVO inversion method for estimating the fluid property factor and density parameters on synthetic data and analyze the feasibility and stability of the inversion. A field-data example indicates that the fluid property factor obtained by our method distinguishes the oil-charged sand channels and the water-wet sand channel from the well logs.

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