Amplitude variation with incident angle inversion for Q-factors in viscoelastic media: A case study

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. B419-B435
Author(s):  
Chuanhui Li ◽  
Xuewei Liu
Keyword(s):  
Reservoir Characterization ◽  
Incident Angle ◽  
Dominant Frequency ◽  
Quality Factors ◽  
S Wave ◽  
Amplitude Variation ◽  
Viscoelastic Media ◽  
Wave Velocities ◽  
Phase Velocities ◽  
Reference Phase

At an interface separating two viscoelastic media, the variation of the reflection coefficient with the incident angle is associated with the quality factors ([Formula: see text]-factors) of both media; this sets up a theoretical foundation for [Formula: see text]-factor inversion by amplitude variation with incident angle (AVA). The AVA inversion for [Formula: see text]-factors was applied to a field example of a gas reservoir to detect gas. Considering that the AVA inversion is commonly performed to obtain P- and S-wave velocities in the previous interpretation of the field seismic data, a new AVA inversion process for [Formula: see text]-factors was designed. The existing P- and S-wave velocities were used as the reference phase velocities at the dominant frequency of seismic signals in viscoelastic media, and then the [Formula: see text]-factors for P- and S-waves were inverted from the isofrequency components of the partial angle stack gathers with known reference phase velocities. The application in the field example found that this process obtained stable inverted [Formula: see text]-factor results, providing more powerful evidence for reservoir characterization.

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.

Compensating Q effects in viscoelastic media by adjoint-based least-squares reverse time migration

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. S151-S172 ◽  
Author(s):  
Peng Guo ◽  
George A. McMechan
Keyword(s):  
Least Squares ◽  
Adjoint Operator ◽  
Seismic Attenuation ◽  
Quality Factors ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
S Wave ◽  
Viscoelastic Media ◽  
Time Migration ◽  
Attenuation Loss

Low values of P- and S-wave quality factors [Formula: see text] and [Formula: see text] result in strong intrinsic seismic attenuation in seismic modeling and imaging. We use a linearized waveform inversion approach, by generalizing least-squares reverse time migration (LSRTM) for viscoelastic media ([Formula: see text]-LSRTM), to compensate for the attenuation loss for P- and S-images. We use the first-order particle velocity, stress, and memory variable equations, with explicit [Formula: see text] in the formulations, based on the generalized standard linear solid, as the forward-modeling operator. The linearized two-way viscoelastic modeling operator is obtained with modulus perturbations introduced for the relaxed P- and S-moduli. The viscoelastic adjoint operator and the P- and S-imaging conditions for modulus perturbations are derived using the adjoint-state method and an augmented Lagrangian functional. [Formula: see text]-LSRTM solves the viscoelastic linearized modeling operator for generating synthetic data, and the adjoint operator is used for back propagating the data residual. With the correct background velocity model, and with the inclusion of [Formula: see text] in the modeling and imaging, [Formula: see text]-LSRTM is capable of iteratively updating the P- and S-modulus perturbations, and compensating the attenuation loss caused by [Formula: see text] and [Formula: see text], in the direction of minimizing the data residual between the observed and predicted data. Compared with elastic LSRTM results, the P- and S-modulus perturbation images from [Formula: see text]-LSRTM have stronger (closer to the true modulus perturbation), and more continuous, amplitudes for the structures in and beneath low-[Formula: see text] zones. The residuals in the image space obtained using the correctly parameterized [Formula: see text]-LSRTM are much smaller than those obtained using the incorrectly parameterized elastic LSRTM. However, the data residuals from [Formula: see text]-LSRTM and elastic LSRTM are similar because elastic Born modeling with a weak reflector in the image produces similar reflection amplitudes with viscoelastic Born modeling with a strong reflector.

Thermal effective stress in shales

2019 ◽  
Vol 38 (5) ◽  
pp. 374-378
Author(s):  
Jeremy Gallop
Keyword(s):  
Effective Stress ◽  
Reservoir Characterization ◽  
Time Lapse ◽  
Forward Modeling ◽  
Calibration Data ◽  
S Wave ◽  
Wave Velocities ◽  
Proposed Model ◽  
Stress Coefficient ◽  
The Matrix

Calculating velocities in shales in thermal production settings is important to refine time-lapse reservoir characterization from seismic. The effective stress concept is attractive to potentially reduce the amount of expensive core calibration data required. We propose a formulation for thermal effective stress in shales based on the idea of balancing undrained pore pressure increments from thermal expansion with an increase in the matrix stress to minimize pore deformation. This formulation is motivated by a desire to simplify forward modeling, reduce the number of dimensions that must be experimentally calibrated through core testing, and to leverage existing velocity-stress relations for thermal applications. The concept was tested on data from a well-known set of experiments consisting of two North Sea Kimmeridge shale core samples, which displayed a linear dependence of velocity on pressure and temperature. These data were found to be consistent with the proposed thermal effective stress model with a constant effective stress coefficient when considering elastic changes but do not prove that the concept is universally valid. Thermal effective stress coefficients were calculated for P- and S-wave velocities from the data and were found to lie from 0.66 to 1.22, demonstrating reasonable scaling for the proposed model.

Wavefield simulation of 3D borehole dipole radiation

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. D155-D169 ◽  
Author(s):  
Junxiao Li ◽  
Kristopher A. Innanen ◽  
Guo Tao ◽  
Kuo Zhang ◽  
Laurence Lines
Keyword(s):  
Incident Angle ◽  
Maximum Amplitude ◽  
Anisotropic Media ◽  
Propagation Distance ◽  
Perfectly Matched Layer ◽  
Staggered Grid ◽  
Dipole Source ◽  
S Wave ◽  
Wave Velocities ◽  
Wavefield Simulation

Reflections in acoustic borehole-logging data can be used to image near-borehole geologic structures, using either monopole or dipole measurements, the latter of which resolve azimuthal ambiguities. Dipole methods in particular can characterize small and subtle fractures in reservoir environments. Accurate tools for wavefield simulation are required to account for wave modes in and out of the borehole, and for the receiver responses to these modes. We have evaluated a 3D elastic staggered-grid finite-difference method for isotropic and anisotropic media in the context of the borehole acoustic imaging problem. Based on the convolutional perfectly matched layer and the multiaxial perfectly matched layer schemes, a hybrid perfectly matched layer method was developed and implemented to reduce artificial boundary reflections. The superiority of this hybrid perfectly matched layer beyond the convolutional perfectly matched layer and the multiaxial perfectly matched layer was proven based on numerical benchmarks in isotropic and anisotropic media. Numerical simulation of radiation, reflection, and multipole reception of elastic waves, excited by a dipole source, was carried out. To optimize azimuthal detection, the relationships between S-wave polarization as well as source-receiver offset and source-reflector angle was analyzed. Results indicated that the S-S reflection is most sensitive to the angle between the incident ray and the normal to the reflector. Its maximum amplitude occurs as the incident angle reaches its critical value, a fact that can be used to calculate the total propagation distance of the S-S wave. The critical angle as well as the SH-wave velocities of geologic structures outside the borehole can thus be determined.

scholarly journals Linearized Frequency-Dependent Reflection Coefficient and Attenuated Anisotropic Characteristics of Q-VTI Model

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8506
Author(s):  
Yahua Yang ◽  
Xingyao Yin ◽  
Bo Zhang ◽  
Danping Cao ◽  
Gang Gao
Keyword(s):  
Reflection Coefficient ◽  
Seismic Wave ◽  
Incident Angle ◽  
Transversely Isotropic ◽  
P Wave ◽  
Reference Frequency ◽  
Quality Factors ◽  
S Wave ◽  
Reservoir Properties ◽  
Simultaneous Inversion

Seismic wave exhibits the characteristics of anisotropy and attenuation while propagating through the fluid-bearing fractured or layered reservoirs, such as fractured carbonate and shale bearing oil or gas. We derive a linearized reflection coefficient that simultaneously considers the effects of anisotropy and attenuation caused by fractures and fluids. Focusing on the low attenuated transversely isotropic medium with a vertical symmetry axis (Q-VTI) medium, we first express the complex stiffness tensors based on the perturbation theory and the linear constant Q model at an arbitrary reference frequency, and then we derive the linearized approximate reflection coefficient of P to P wave. It decouples the P- and S-wave inverse quality factors, and Thomsen-style attenuation-anisotropic parameters from complex P- and S-wave velocity and complex Thomsen anisotropic parameters. By evaluating the reflection coefficients around the solution point of the interface of two models, we analyze the characteristics of reflection coefficient vary with the incident angle and frequency and the effects of different Thomsen anisotropic parameters and attenuation factors. Moreover, we realize the simultaneous inversion of all parameters in the equation using an actual well log as a model. We conclude that the derived reflection coefficient may provide a theoretical tool for the seismic wave forward modeling, and again it can be implemented to predict the reservoir properties of fractures and fluids based on diverse inversion methods of seismic data.

Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

2020 ◽  
Vol 22 (4) ◽  
pp. 939-958
Author(s):  
Indrajit Roy ◽  
D. P. Acharya ◽  
Sourav Acharya
Keyword(s):  
Surface Stress ◽  
Incident Angle ◽  
Plane Waves ◽  
Three Dimensional ◽  
Elastic Fibre ◽  
Amplitude Ratios ◽  
Governing Equations ◽  
Rotation Surface ◽  
Wave Velocities ◽  
Magnetic Field Rotation

AbstractThe present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

The relation between seismic P‐ and S‐wave velocity dispersion in saturated rocks

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 87-92 ◽  
Author(s):  
Gary Mavko ◽  
Diane Jizba
Keyword(s):  
Wave Velocity ◽  
Large Scale ◽  
Velocity Dispersion ◽  
Seismic Velocity ◽  
Ultrasonic Velocities ◽  
S Wave ◽  
Local Flow ◽  
Wave Velocities ◽  
Shear Compliance

Seismic velocity dispersionin fluid-saturated rocks appears to be dominated by tow mecahnisms: the large scale mechanism modeled by Biot, and the local flow or squirt mecahnism. The tow mechanisms can be distuinguished by the ratio of P-to S-wave dispersions, or more conbeniently, by the ratio of dynamic bulk to shear compliance dispersions derived from the wave velocities. Our formulation suggests that when local flow denominates, the dispersion of the shear compliance will be approximately 4/15 the dispersion of the compressibility. When the Biot mechanism dominates, the constant of proportionality is much smaller. Our examination of ultrasonic velocities from 40 sandstones and granites shows that most, but not all, of the samples were dominated by local flow dispersion, particularly at effective pressures below 40 MPa.

Finite-Difference Modeling and Characteristics Analysis of Love Waves in Anisotropic-Viscoelastic Media

2021 ◽  
Author(s):  
Shichuan Yuan ◽  
Zhenguo Zhang ◽  
Hengxin Ren ◽  
Wei Zhang ◽  
Xianhai Song ◽  
...  
Keyword(s):  
Finite Difference ◽  
Phase Velocity ◽  
Velocity Dispersion ◽  
Love Waves ◽  
Velocity Anisotropy ◽  
Viscoelastic Media ◽  
Phase Velocities ◽  
Phase Velocity Dispersion ◽  
Anisotropic Elastic ◽  
Attenuation Anisotropy

ABSTRACT In this study, the characteristics of Love waves in viscoelastic vertical transversely isotropic layered media are investigated by finite-difference numerical modeling. The accuracy of the modeling scheme is tested against the theoretical seismograms of isotropic-elastic and isotropic-viscoelastic media. The correctness of the modeling results is verified by the theoretical phase-velocity dispersion curves of Love waves in isotropic or anisotropic elastic or viscoelastic media. In two-layer half-space models, the effects of velocity anisotropy, viscoelasticity, and attenuation anisotropy of media on Love waves are studied in detail by comparing the modeling results obtained for anisotropic-elastic, isotropic-viscoelastic, and anisotropic-viscoelastic media with those obtained for isotropic-elastic media. Then, Love waves in three typical four-layer half-space models are simulated to further analyze the characteristics of Love waves in anisotropic-viscoelastic layered media. The results show that Love waves propagating in anisotropic-viscoelastic media are affected by both the anisotropy and viscoelasticity of media. The velocity anisotropy of media causes substantial changes in the values and distribution range of phase velocities of Love waves. The viscoelasticity of media leads to the amplitude attenuation and phase velocity dispersion of Love waves, and these effects increase with decreasing quality factors. The attenuation anisotropy of media indicates that the viscoelasticity degree of media is direction dependent. Comparisons of phase velocity ratios suggest that the change degree of Love-wave phase velocities due to viscoelasticity is much less than that caused by velocity anisotropy.

Direct shear-wave seismic survey in Sanhu area, Qaidam Basin, west China

2022 ◽  
Vol 41 (1) ◽  
pp. 47-53
Author(s):  
Zhiwen Deng ◽  
Rui Zhang ◽  
Liang Gou ◽  
Shaohua Zhang ◽  
Yuanyuan Yue ◽  
...  
Keyword(s):  
Shear Wave ◽  
Reservoir Characterization ◽  
Qaidam Basin ◽  
P Wave ◽  
Data Sets ◽  
Direct Shear ◽  
Subsurface Structure ◽  
S Wave ◽  
West China ◽  
Wave Data

The formation containing shallow gas clouds poses a major challenge for conventional P-wave seismic surveys in the Sanhu area, Qaidam Basin, west China, as it dramatically attenuates seismic P-waves, resulting in high uncertainty in the subsurface structure and complexity in reservoir characterization. To address this issue, we proposed a workflow of direct shear-wave seismic (S-S) surveys. This is because the shear wave is not significantly affected by the pore fluid. Our workflow includes acquisition, processing, and interpretation in calibration with conventional P-wave seismic data to obtain improved subsurface structure images and reservoir characterization. To procure a good S-wave seismic image, several key techniques were applied: (1) a newly developed S-wave vibrator, one of the most powerful such vibrators in the world, was used to send a strong S-wave into the subsurface; (2) the acquired 9C S-S data sets initially were rotated into SH-SH and SV-SV components and subsequently were rotated into fast and slow S-wave components; and (3) a surface-wave inversion technique was applied to obtain the near-surface shear-wave velocity, used for static correction. As expected, the S-wave data were not affected by the gas clouds. This allowed us to map the subsurface structures with stronger confidence than with the P-wave data. Such S-wave data materialize into similar frequency spectra as P-wave data with a better signal-to-noise ratio. Seismic attributes were also applied to the S-wave data sets. This resulted in clearly visible geologic features that were invisible in the P-wave data.

Nonlinear behavior of soil sediments identified by using borehole records observed at the Ashigra Valley, Japan

1995 ◽  
Vol 85 (6) ◽  
pp. 1821-1834
Author(s):  
Toshimi Satoh ◽  
Toshiaki Sato ◽  
Hiroshi Kawase
Keyword(s):  
Shear Strain ◽  
Main Part ◽  
Nonlinear Behavior ◽  
Strong Motion ◽  
S Wave ◽  
Ground Shaking ◽  
Wave Velocities ◽  
The One ◽  
Soil Sediments ◽  
Strong Ground

Abstract We evaluate the nonlinear behavior of soil sediments during strong ground shaking based on the identification of their S-wave velocities and damping factors for both the weak and strong motions observed on the surface and in a borehole at Kuno in the Ashigara Valley, Japan. First we calculate spectral ratios between the surface station KS2 and the borehole station KD2 at 97.6 m below the surface for the main part of weak and strong motions. The predominant period for the strong motion is apparently longer than those for the weak motions. This fact suggests the nonlinearity of soil during the strong ground shaking. To quantify the nonlinear behavior of soil sediments, we identify their S-wave velocities and damping factors by minimizing the residual between the observed spectral ratio and the theoretical amplification factor calculated from the one-dimensional wave propagation theory. The S-wave velocity and the damping factor h (≈(2Q)−1) of the surface alluvial layer identified from the main part of the strong motion are about 10% smaller and 50% greater, respectively, than those identified from weak motions. The relationships between the effective shear strain (=65% of the maximum shear strain) calculated from the one-dimensional wave propagation theory and the shear modulus reduction ratios or the damping factors estimated by the identification method agree well with the laboratory test results. We also confirm that the soil model identified from a weak motion overestimates the observed strong motion at KS2, while that identified from the strong motion reproduces the observed. Thus, we conclude that the main part of the strong motion, whose maximum acceleration at KS2 is 220 cm/sec2 and whose duration is 3 sec, has the potential of making the surface soil nonlinear at an effective shear strain on the order of 0.1%. The S-wave velocity in the surface alluvial layer identified from the part just after the main part of the strong motion is close to that identified from weak motions. This result suggests that the shear modulus recovers quickly as the shear strain level decreases.

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