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 Contents & Abstracts Journal of Seismic Exploration



CONTENTS Volume 17, Number 2-3, April 2008

Special issue: SEISMIC ANISOTROPY: State of the Art
Part II: Modelling, Imaging and Parameter Estimation
E. Liu, Z.-J. Zhang and X.-Y. Li
Introduction
B. Zhou and S. Greenhalgh
Kinematic inversion of seismic waves in an arbitrary anisotropic background medium
T. Xu, Z. Zhang, A. Zhao, A. Zhang, X. Zhang and H. Zhang
Sub-triangle shooting ray-tracing in complex 3D VTI media
X.-Y. Li, L. Wang, H. Dai and X. Sun
Estimating anisotropic parameters from PS converted-wave data: a case study
X. Miao and T. Zuk
Anisotropic velocity updating for converted-wave prestack time migration
K. Liang, G. Wu and X. Yin
Migration methods of qP waves in VTI media using Born approximation
Q. Di, M. Wang and M. Zhang
Finite-element prestack depth migration in anisotropic media
A. Zhang and Z. Zhang
Elliptical anisotropy above the crystalline basement from wide-aperture Pg events
I. Obolentseva, B. Bobrov and T. Chichinina
Gyrotropic models of sedimentary rocks: physical modelling studies
Q. Hao, Q.-D. He and S. Shi
A new splitting PML algorithm for the second-order anisotropic wave equation
I. Tsvankin
Properties of evanescent waves in anisotropic media
H. Mansouri
The potential implications of stress-induced anisotropy for 4D seismic
D. Yang, E. Liu and Z. Zhang
Evaluation of the u-W finite element method in anisotropic porous media


ABSTRACTS Vol. 17, No. 2-3, April 2008

Special issue: SEISMIC ANISOTROPY - State of the Art
Part II: Modelling, Imaging and Parameter Estimation
Liu, E., 2007. Introduction.

In October 2006, 120 people from over 20 countries (60 from within China) gathered at the foot of the Great Wall of China in Beijing to attend the 12th International Workshop on Seismic Anisotropy (12IWSA). About 90 papers were presented in the workshop. This special issue is Part I of the workshop proceedings and Part II will be published in early 2008. Part I contains 16 papers on seismic fracture characterization, and Part II contains 8 papers primarily on anisotropic seismic imaging. In this introduction, I will review the recent development in the theory, methodology, and applications of seismic anisotropy with special references to seismic fracture characterizations.
Zhou, B. and Greenhalgh, S., 2008. Kinematic inversion of seismic waves in an arbitrary anisotropic background medium.

Traditional kinematic inversion of seismic body waves in anisotropic media uses the "weak anisotropy" assumption and the eigenvectors of the Christoffel equation. This gives rise to a linearised inversion approach which may encounter a singularity problem with the two quasi-shear waves. This paper presents a new iterative, nonlinear kinematic inversion scheme, which does not make such an assumption, and avoids the singularity problem. It is applicable to arbitrary media, specifically those having dipping symmetry axes, a strong anisotropic background (or reference medium), and heterogeneous structure. For the forward modelling, we describe an anisotropic model with the gridded values of the five independent elastic moduli and the orientation angle of the symmetry axis, and apply a robust ray tracing method to compute the raypaths and traveltimes for all three wave modes (qP, qS1, qS2). For the inversion, we develop a simple analytic method to approximate the Jacobian matrix without the eigenvectors and perform an iterative nonlinear inversion to reconstruct all of the elastic moduli for imaging the subsurface. Using the new scheme, we have conducted several 2D synthetic imaging experiments for VSP, cross-hole and full illumination recording geometries. This involved determination of the distribution of elastic moduli from traveltime data for each of the three wave modes (qP, qSV, qSH). From these experiments, one can see the superiority of the new scheme and the capability of crosshole seismic anisotropic tomographic imaging. The differences in quality of each elastic moduli image are due to the limitations of the raypath coverage and the differing sensitivities of the various wave mode data.
Xu, T., Zhang, Z., Zhao, A., Zhang, A., Zhang, X. and Zhang, H., 2008. Sub-triangle shooting ray-tracing in complex 3D VTI media.

We model a complex 3D anisotropic structure as an aggregate of arbitrarily shaped blocks or volumes separated by triangulated interfaces, and different anisotropic parameters can be defined in different blocks. In anisotropic media, seismic wave travels in the direction of ray vectors with group velocities throughout a ray trajectory, therefore, group velocities expressed by ray angles is required, but difficult to express in terms of phase angles. An approximate expression in terms of ray angles is derived for weak transversely isotropic media with a vertical symmetry axis (VTI). We also propose a simple iterative process to calculate ray angles in terms of the Snell's law still valid for phase velocities and phase angles. Modification of shooting angles is crucial in implementing 3D shooting ray-tracing, and we suggest to use the sub-triangle shooting method to update the shooting angles to enhance the computing efficiency. Numerical tests demonstrate that a blocky model can be a good description of complex 3D VTI media and the sub-triangle shooting ray-tracing is very effective to implement for kinematics two-point ray-tracing.
Li, X.-Y., Wang, L., Dai, H. and Sun, X., 2008. Estimating anisotropic parameters from PS converted-wave data: a case study.

Anisotropic parameters are estimated from PS converted-wave (C-wave) data. The data were acquired by digital MEMS (micro-electro-mechanical system) sensors over a volcanic gas reservoir in Northeast China with a mixed sand and shale sequence in the overburden. This gives rise to both shear-wave splitting and anisotropy moveout effects due to presence of vertical transverse isotropy (VTI). We use a four-parameter theory to evaluate the effects of non-hyperbolic moveout due to an asymmetric raypath and VTI. These four parameters include the PS converted wave stacking velocity (VC2), the vertical velocity ratio (?0), the effective velocity ratio (?eff), and the anisotropy parameter (?eff). This four-parameter theory leads to an improvement in imaging quality and correlation between the P-waves and converted-waves. After compensating for the VTI effects, we analyze the shear-wave splitting in the post stacked data. We find that the amount of splitting determined from the data can be correlated to the known gas reservoirs, and is also consistent with other amplitude and spectral anomalies associated with the gas reservoirs, revealing a potential for using shear-wave splitting to delineate gas reservoirs in volcanic rocks.
Miao, X. and Zuk, T., 2008. Anisotropic velocity updating for converted-wave prestack time migration.

The conventional method to estimate velocities for converted-wave (C-wave) prestack time migration is an awkward procedure, because the P-wave velocity (VP) comes from P-wave processing, the velocity ratio gamma (VP/VS) is estimated from C-wave data, and the S-wave velocity (VS) is then derived from VP and gamma. Instead, by using the C-wave velocity (VC), effective gamma (?eff), and anisotropic parameter ?eff, velocity updating becomes straightforward and more reliable. To update VC for converted-wave time migration, one can carry out hyperbolic moveout analysis on the hyperbolic moveout migrated common mid-point (HMO-MCMP) gathers (Dai and Li (2004). However, the errors in initial ?eff and anisotropic parameter ?eff can only be corrected by a trial-and-error method. In this paper we propose to remove the effects of initial ?eff and ?eff in the HMO-MCMP gathers by inverting the moveout related to the initial ?eff and ?eff. This enables a full non-hyperbolic velocity analysis to be conducted in order to update not only VC but also ?eff and ?eff. To obtain reliable ?eff, we also developed a simultaneous PP/PS anisotropic parameter estimation method so that the ?eff estimated from P-wave is immediately compared with the ?eff derived from ?eff by using C-wave data. This provides a better constraint for estimating anisotropic parameters. The method has been tested and has shown consistent improvement in converted wave prestack time migration velocity estimations.
Liang, K., Wu, G. and Yin, X., 2008. Migration methods of qP waves in VTI media using Born approximation.

Wavefield continuation operator is one of the key factors in depth migration in complex media. Based on qP wave equation in transversely isotropic media with a vertical symmetry axis (VTI media), this paper presents a wavefield continuation method of qP wave in VTI media using Born approximation. According to the theory of equivalent media and principle of medium decomposition, wavefield change caused by anisotropy is considered as the perturbation of isotropic wavefield, and the anisotropic parameters are decomposed into constant isotropic constant slowness and interval generalized perturbation. The generalized perturbation consists of slowness perturbation and anisotropic parameter perturbation. The qP wavefield is decomposed into an isotropic constant slowness background and scattering wavefield. The background wavefield can be calculated by solving acoustic equation in the isotropic constant velocity media using phase-shift method; the scattering wavefield is decomposed into slowness perturbation and anisotropy perturbation. The total wavefield is calculated with one-way dual-domain Born propagator of qP waves in VTI media. The operator has a singularity, which can be avoided with a small angle approximation or an extended local Born approximation. The results of impulse response in an anisotropic model and migration in complex anisotropic media indicate that Born approximation migration method of qP wave in VTI media has a high accuracy and is suitable to complex VTI media. But the operator is conditionally stable, and we can reduce the extrapolation interval or high-frequency component to carry out the computations.
Di, Q., Wang, M. and Zhang, M., 2008. Finite-element prestack depth migration in anisotropic media.

In this paper we present a 3D finite element prestack depth migration algorithm in anisotropic media, and compare 3D migrated results from isotropic and anisotropic algorithms. Our results from four models (a two-layer model, a fault model, a layered model and a crack-model) show that errors can be caused by isotropic migration if anisotropy exists and that accurate position images can be obtained if anisotropy is considered.
Zhang, A. and Zhang, Z., 2008. Elliptical anisotropy above the crystalline basement from wide-aperture Pg events.

Traveltime data of Pg events, which are refractions from the crystalline basement (CB) in the controlled-source wide-aperture seismic sections, provide key constraints on the construction of shallow seismic structures above the crystalline basement. Since sedimentary rock is usually considered to be anisotropic because of the preferred alignment of microcracks and thin layering in the upper crust. So the interpretation of Pg events needs to account for seismic velocity anisotropy. For this reason, it is the prerequisite to establish traveltime-offset relationship for Pg events in anisotropic media. Here, we first derive a traveltime-offset relationship for Pg waves by assuming a model with a linear velocity increase; then we present a scheme to invert Pg traveltime-offset data for velocity anisotropy in shallow crustal structures. We compare the Pg traveltimes calculated by our analytic equation with raytracing to test the accuracy. Finally, real data from the deep-seismic reflection profiles in the southeast China are analyzed to demonstrate the potential of our method.
Obolentseva, I., Bobrov, B. and Chichinina, T., 2008. Gyrotropic models of sedimentary rocks: physical modelling studies.

To find out the nature of gyrotropic properties of sedimentary rocks, physical modelling has been applied to test some hypotheses on possible causes for seismic gyrotropy. The objects of investigation are artificial models of sedimentary rocks, constructed on the principle of "azimuthal turn plus translation", which, from Curie's symmetry principle, creates the preconditions for elastic gyrotropy, namely such a property as the ability to rotate the polarization plane of shear waves. This ability, referred to in optics and acoustics as natural activity, its occurrence or absence, was checked. For laboratory experiments, we used piezoceramic transducers with a frequency of 100 kHz as source and two-component receivers. Polarization of shear waves propagating along a symmetry axis in the models of VTI symmetry was studied with the use of the following three models: the cement block with embedded turning sand strips, the cement block with embedded aluminum-foil turning strips, and a collection of turning fiber-glass plastic plates glued together. All three models appear to be gyrotropic. The polarizational processing of the two-component records has shown a turn of polarization plane of shear waves, and the turn value, at prevailing frequencies of spectra, was proportional to the frequencies of oscillations; besides, the rotation was right-handed at right-hand turning of strips, and it was left-handed at left-hand turning. The determined quantitative characteristics of gyrotropy appeared to be in good agreement with the expected ones.
Hao, Q., He, Q.-D. and Shi, S., 2008. A new splitting PML algorithm for the second-order anisotropic wave equation.

In this paper, we present a new absorbing boundary conditions called splitting perfectly matched layer (SPML) for the second-order anisotropic wave equation. The new SPML can be used in the pseudo-spectral, finite-difference, and finite-element forward modeling to effectively attenuate unwanted reflections from artificial boundaries. It is written in a compact form as the original first-order PML. We have applied the new SPML algorithm to simulate anisotropic wave propagation based on the second-order wave equation. The numerical modelling results show that the new SPML can absorb artificial boundary reflected waves significantly and is numerically stable.
Tsvankin, I., 2008. Properties of evanescent waves in anisotropic media.

Evanescent (inhomogeneous) waves contained in the plane-wave decomposition of point-source radiation produce not only surface waves but also nongeometrical modes that can be recorded far away from the boundary. This paper gives an analytic description of plane evanescent P-, SV-, and SH-waves propagating in the symmetry planes of non-attenuative transversely isotropic and orthorhombic media.

Simple weak-anisotropy approximations for the slowness and polarization vectors of horizontally traveling evanescent waves are obtained by linearizing the Christoffel equation in the anisotropy parameters. The relationship between the horizontal slowness (m1) and the imaginary part of the vertical slowness (m3) (i.e., between the horizontal velocity and the vertical amplitude decay factor) is controlled by the stiffness matrix. For P-waves, this relationship is sensitive even to relatively small values of the Thomsen parameters d and, especially, e. The weak-anisotropy approximation correctly reproduces the trend of the dependence of m1 on m3 for moderately anisotropic media, but deteriorates with increasing difference e-d, as the model deviates from elliptical. The influence of anisotropy on the function m1(m3) is particularly significant for SV-waves because the slowness vector is governed by the parameter s, which often exceeds 0.5. Anisotropy also distorts the particle motion of evanescent P- and SV-waves by changing the eccentricity of the polarization ellipse.

The results of this work can be used to develop asymptotic solutions for nongeometrical waves and design new anisotropic parameter-estimation algorithms for cross-hole and VSP surveys. In particular, measurements of the vertical decay factor of leaking waves traveling between boreholes can help to constrain the anisotropy parameters.
Mansouri, H., 2008. The potential implications of stress-induced anisotropy for 4D seismic monitoring.

Stress-induced anisotropy is important for investigating different seismic attributes, so here I intend to examine its influence on 4D signature. First, I will present a short review of time-lapse seismic monitoring as a tool to assist in reservoir management, although its applications are not restricted to reservoir management. Then, the success and credibility of time-lapse studies are also discussed and linked to the basic assumption of isotropy, which in turn creates an opportunity to link the topic to variations of seismic amplitude with parameters like offset - the distance between seismic source and receivers, and azimuth - the orientation of the source-receiver line relative to north. I will also model the time-lapse response of the Nelson Field in isotropic and anisotropic scenarios. It is predicted that stress-induced anisotropy is likely to have a moderate to large impact on the interpretation of 4D seismic signatures. The effect is most obvious when base and repeat surveys are shot along different azimuths, but it can also be important in surveys shot along similar azimuths. The stress-induced anisotropy effects equate to a very large error in estimating pressure from the top reservoir event in the Palaeocene sands of the Nelson Field and an OWC movement uncertainty of 6 m.
Yang, D.H., Liu, E. and Zhang, Z.J., 2008. Evaluation of the u-W finite element method in anisotropic porous media.

In this paper, we present dynamic equations of elastic wave propagations, the Galerkin variational equations, and the finite element equation in anisotropic porous media. We propose a finite element method based on solid displacements u and "relative fluid displacement" W to solve elastic equation which include both anisotropy of fluid micro-velocity field and Poiseuille macroscopic flow in two-phase anisotropic media. The artificial absorbing boundary conditions for porous VTI media (transversely isotropic medium with a vertical symmetry axis) are also given in this paper. Our numerical modeling results show that both the finite element method and the absorbing boundary conditions are effective and feasible. For the ideal (non-viscous fluid) phase boundary case, the slow quasi P-wave can be seen simultaneously from both solid/fluid wave-field snapshots, and for the viscous phase boundary case whether the slow quasi P-wave can be observed depends on the dissipative property of formations with fluids. The slow quasi P-wave is more easily observed from fluid displacement wave-fields than from the solid displacement wave-fields.





 

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