Physical modeling and analysis of P-wave attenuation anisotropy in transversely isotropic media

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. D1-D7 ◽  
Author(s):  
Yaping Zhu ◽  
Ilya Tsvankin ◽  
Pawan Dewangan ◽  
Kasper van Wijk
Keyword(s):  
Attenuation Coefficient ◽  
Symmetry Axis ◽  
Wave Attenuation ◽  
Transversely Isotropic ◽  
P Wave ◽  
Velocity Variation ◽  
Ratio Method ◽  
Fracture Detection ◽  
Wide Range ◽  
Attenuation Anisotropy

Anisotropic attenuation can provide sensitive attributes for fracture detection and lithology discrimination. This paper analyzes measurements of the P-wave attenuation coefficient in a transversely isotropic sample made of phenolic material. Using the spectral-ratio method, we estimate the group (effective) attenuation coefficient of P-waves transmitted through the sample for a wide range of propagation angles (from [Formula: see text] to [Formula: see text]) with the symmetry axis. Correction for the difference between the group and phase angles and for the angular velocity variation help us to obtain the normalized phase attenuation coefficient [Formula: see text] governed by the Thomsen-style attenuation-anisotropy parameters [Formula: see text] and [Formula: see text]. Whereas the symmetry axis of the angle-dependent coefficient [Formula: see text] practically coincides with that of the velocity function, the magnitude of the attenuation anisotropy far exceeds that of the velocity anisotropy. The quality factor [Formula: see text] increases more than tenfold from the symmetry axis (slow direction) to the isotropy plane (fast direction). Inversion of the coefficient [Formula: see text] using the Christoffel equation yields large negative values of the parameters [Formula: see text] and [Formula: see text]. The robustness of our results critically depends on several factors, such as the availability of an accurate anisotropic velocity model and adequacy of the homogeneous concept of wave propagation, as well as the choice of the frequency band. The methodology discussed here can be extended to field measurements of anisotropic attenuation needed for AVO (amplitude-variation-with-offset) analysis, amplitude-preserving migration, and seismic fracture detection.

Plane-wave attenuation anisotropy in orthorhombic media

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. D9-D19 ◽  
Author(s):  
Yaping Zhu ◽  
Ilya Tsvankin
Keyword(s):  
Attenuation Coefficient ◽  
Wave Attenuation ◽  
Fractured Reservoirs ◽  
The Body ◽  
P Wave ◽  
Attenuation Coefficients ◽  
Velocity Anisotropy ◽  
Homogeneous Wave ◽  
Anisotropy Parameters ◽  
Attenuation Anisotropy

Orthorhombic models are often used in the interpretation of azimuthally varying seismic signatures recorded over fractured reservoirs. Here, we develop an analytic framework for describing the attenuation coefficients in orthorhombic media with orthorhombic attenuation (i.e., the symmetry of both the real and imaginary parts of the stiffness tensor is identical) under the assumption of homogeneous wave propagation. The analogous form of the Christoffel equation in the symmetry planes of orthorhombic and VTI (transversely isotropic with a vertical symmetry axis) media helps to obtain the symmetry-plane attenuation coefficients by adapting the existing VTI equations. To take full advantage of this equivalence with transverse isotropy, we introduce a parameter set similar to the VTI attenuation-anisotropy parameters [Formula: see text], [Formula: see text], and [Formula: see text]. This notation, based on the same principle as Tsvankin’s velocity-anisotropy parameters for orthorhombic media, leads to concise linearized equations for thesymmetry-plane attenuation coefficients of all three modes (P, [Formula: see text], and [Formula: see text]).The attenuation-anisotropy parameters also allow us to simplify the P-wave attenuation coefficient [Formula: see text] outside the symmetry planes under the assumptions of small attenuation and weak velocity and attenuation anisotropy. The approximate coefficient [Formula: see text] has the same form as the linearized P-wave phase-velocity function, with the velocity parameters [Formula: see text] and [Formula: see text] replaced by the attenuation parameters [Formula: see text] and [Formula: see text]. The exact attenuation coefficient, however, also depends on the velocity-anisotropy parameters, while the body-wave velocities are almost unperturbed by the presence of attenuation. The reduction in the number of parameters responsible for the P-wave attenuation and the simple approximation for the coefficient [Formula: see text] provide a basis for inverting P-wave attenuation measurements from orthorhombic media. The attenuation processing must be preceded by anisotropic velocity analysis that can be performed (in the absence of pronounced velocity dispersion) using existing algorithms for nonattenuative media.

Role of the inhomogeneity angle in anisotropic attenuation analysis

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. WB177-WB191 ◽  
Author(s):  
Jyoti Behura ◽  
Ilya Tsvankin
Keyword(s):  
Attenuation Coefficient ◽  
Seismic Data ◽  
Spectral Ratio ◽  
Ratio Method ◽  
Attenuation Coefficients ◽  
Anisotropic Models ◽  
High Attenuation ◽  
Wide Range ◽  
Anisotropy Parameters ◽  
Attenuation Anisotropy

The inhomogeneity angle (the angle between the real and imaginary parts of the wave vector) is seldom taken into account in estimating attenuation coefficients from seismic data. Wave propagation through the subsurface, however, can result in relatively large inhomogeneity angles [Formula: see text], especially for models with significant attenuation contrasts across layer boundaries. Here we study the influence of the angle [Formula: see text] on phase and group attenuation in arbitrarily anisotropic media using the first-order perturbation theory verified by exact numerical modeling. Application of the spectral-ratio method to transmitted or reflected waves yields the normalized group attenuation coefficient [Formula: see text], which is responsible for amplitude decay along seismic rays. Our analytic solutions show that for a wide range of inhomogeneity angles, the coefficient [Formula: see text] is close to the normalized phase attenuation coefficient [Formula: see text] computed for [Formula: see text] [Formula: see text]. The coefficient[Formula: see text] can be inverted directly for the attenuation-anisotropy parameters, so no knowledge of the inhomogeneity angle is required for attenuation analysis of seismic data. This conclusion remains valid even for uncommonly high attenuation with the quality factor [Formula: see text] less than 10 and strong velocity and attenuation anisotropy. However, the relationship between group and phase attenuation coefficients becomes more complicated for relatively large inhomogeneity angles approaching so-called ‘‘forbidden directions.’’ We also demonstrate that the velocity function remains practically independent of attenuation for a wide range of small and moderate angles [Formula: see text]. In principle, estimation of the attenuation-anisotropy parameters from the coefficient [Formula: see text] requires computation of the phase angle, which depends on the anisotropic velocity field. For moderately anisotropic models, however, the difference between the phase and group directions should not significantly distort the results of attenuation analysis.

Estimation of interval anisotropic attenuation from reflection data

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. A69-A74 ◽  
Author(s):  
Jyoti Behura ◽  
Ilya Tsvankin
Keyword(s):  
Attenuation Coefficient ◽  
Reservoir Characterization ◽  
Symmetry Plane ◽  
Transversely Isotropic ◽  
Spectral Ratio ◽  
P Wave ◽  
Ratio Method ◽  
Reflection Seismic ◽  
Reflection Data ◽  
Target Layer

Knowledge of interval attenuation can be highly beneficial in reservoir characterization and lithology discrimination. We combine the spectral-ratio method with velocity-independent layer stripping to develop a technique for the estimation of the interval attenuation coefficient from reflection seismic data. The layer-stripping procedure is based on identifying the reflections from the top and bottom of the target layer that share the same ray segments in the overburden. The algorithm is designed for heterogeneous, arbitrarily anisotropic target layers, but the overburden is assumed to be laterally homogeneous with a horizontal symmetry plane. Although no velocity information about the overburden is needed, interpretation of the computed anisotropic attenuation coefficient involves the phase angle in the target layer. Tests on synthetic P-wave data from layered transversely isotropic and orthorhombic media confirm the high accuracy of 2D and 3D versions of the algorithm. We also demonstrate that the interval attenuation estimates are independent of the inhomogeneity angle of the incident and reflected waves.

Fracture detection using P-wave and S-wave vertical seismic profiling at The Geysers

Geophysics ◽  
1988 ◽  
Vol 53 (1) ◽  
pp. 76-84 ◽  
Author(s):  
E. L. Majer ◽  
T. V. McEvilly ◽  
F. S. Eastwood ◽  
L. R. Myer
Keyword(s):  
Fractured Rock ◽  
Geothermal Field ◽  
P Wave ◽  
Velocity Variation ◽  
Fracture Detection ◽  
S Wave ◽  
Fracture Geometry ◽  
Seismic Profiling ◽  
Vertical Seismic Profiling ◽  
The Geysers

In a pilot vertical seismic profiling study, P-wave and cross‐polarized S-wave vibrators were used to investigate the potential utility of shear‐wave anisotropy measurements in characterizing a fractured rock mass. The caprock at The Geysers geothermal field was found to exhibit about an 11 percent velocity variation between SH-waves and SV-waves generated by rotating the S-wave vibrator orientation to two orthogonal polarizations for each survey level in the well. The effect is generally consistent with the equivalent anisotropy expected from the known fracture geometry.

P-wave attenuation anisotropy in TI media and its application in fracture parameters inversion

2016 ◽  
Vol 13 (4) ◽  
pp. 649-657 ◽  
Author(s):  
Yi-Yuan He ◽  
Tian-Yue Hu ◽  
Chuan He ◽  
Yu-Yang Tan
Keyword(s):  
Wave Attenuation ◽  
P Wave ◽  
Fracture Parameters ◽  
Parameters Inversion ◽  
Attenuation Anisotropy ◽  
Ti Media

scholarly journals The offset-midpoint traveltime pyramid in 3D transversely isotropic media with a horizontal symmetry axis

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. T51-T62 ◽  
Author(s):  
Qi Hao ◽  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
P Wave ◽  
Analytic Representation ◽  
Velocity Inversion ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Time Domains ◽  
Isotropic Media ◽  
Hti Media

Analytic representation of the offset-midpoint traveltime equation for anisotropy is very important for prestack Kirchhoff migration and velocity inversion in anisotropic media. For transversely isotropic media with a vertical symmetry axis, the offset-midpoint traveltime resembles the shape of a Cheops’ pyramid. This is also valid for homogeneous 3D transversely isotropic media with a horizontal symmetry axis (HTI). We extended the offset-midpoint traveltime pyramid to the case of homogeneous 3D HTI. Under the assumption of weak anellipticity of HTI media, we derived an analytic representation of the P-wave traveltime equation and used Shanks transformation to improve the accuracy of horizontal and vertical slownesses. The traveltime pyramid was derived in the depth and time domains. Numerical examples confirmed the accuracy of the proposed approximation for the traveltime function in 3D HTI media.

P-wave attenuation anisotropy in fractured media: A seismic physical modelling study

2012 ◽  
Vol 61 ◽  
pp. 420-433 ◽  
Author(s):  
A.M. Ekanem ◽  
J. Wei ◽  
X.-Y. Li ◽  
M. Chapman ◽  
I.G. Main
Keyword(s):  
Wave Attenuation ◽  
Physical Modelling ◽  
Fractured Media ◽  
P Wave ◽  
Attenuation Anisotropy ◽  
Modelling Study

Normal moveout from dipping reflectors in anisotropic media

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 268-284 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Transversely Isotropic ◽  
Anisotropic Media ◽  
Weak Anisotropy ◽  
Anisotropic Models ◽  
Transversely Isotropic Media ◽  
Wide Range ◽  
Isotropic Media ◽  
The Difference

Description of reflection moveout from dipping interfaces is important in developing seismic processing methods for anisotropic media, as well as in the inversion of reflection data. Here, I present a concise analytic expression for normal‐moveout (NMO) velocities valid for a wide range of homogeneous anisotropic models including transverse isotropy with a tilted in‐plane symmetry axis and symmetry planes in orthorhombic media. In transversely isotropic media, NMO velocity for quasi‐P‐waves may deviate substantially from the isotropic cosine‐of‐dip dependence used in conventional constant‐velocity dip‐moveout (DMO) algorithms. However, numerical studies of NMO velocities have revealed no apparent correlation between the conventional measures of anisotropy and errors in the cosine‐of‐dip DMO correction (“DMO errors”). The analytic treatment developed here shows that for transverse isotropy with a vertical symmetry axis, the magnitude of DMO errors is dependent primarily on the difference between Thomsen parameters ε and δ. For the most common case, ε − δ > 0, the cosine‐of‐dip–corrected moveout velocity remains significantly larger than the moveout velocity for a horizontal reflector. DMO errors at a dip of 45 degrees may exceed 20–25 percent, even for weak anisotropy. By comparing analytically derived NMO velocities with moveout velocities calculated on finite spreads, I analyze anisotropy‐induced deviations from hyperbolic moveout for dipping reflectors. For transversely isotropic media with a vertical velocity gradient and typical (positive) values of the difference ε − δ, inhomogeneity tends to reduce (sometimes significantly) the influence of anisotropy on the dip dependence of moveout velocity.

Quartic moveout coefficient: 3D description and application to tilted TI media

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1600-1610 ◽  
Author(s):  
Andres Pech ◽  
Ilya Tsvankin ◽  
Vladimir Grechka
Keyword(s):  
Heterogeneous Media ◽  
Symmetry Axis ◽  
High Sensitivity ◽  
Transversely Isotropic ◽  
Seismic Inversion ◽  
P Wave ◽  
Individual Values ◽  
Weak Anisotropy ◽  
Essential Information ◽  
Ti Media

Nonhyperbolic (long‐spread) moveout provides essential information for a number of seismic inversion/processing applications, particularly for parameter estimation in anisotropic media. Here, we present an analytic expression for the quartic moveout coefficient A4 that controls the magnitude of nonhyperbolic moveout of pure (nonconverted) modes. Our result takes into account reflection‐point dispersal on irregular interfaces and is valid for arbitrarily anisotropic, heterogeneous media. All quantities needed to compute A4 can be evaluated during the tracing of the zero‐offset ray, so long‐spread moveout can be modeled without time‐consuming multioffset, multiazimuth ray tracing. The general equation for the quartic coefficient is then used to study azimuthally varying nonhyperbolic moveout of P‐waves in a dipping transversely isotropic (TI) layer with an arbitrary tilt ν of the symmetry axis. Assuming that the symmetry axis is confined to the dip plane, we employed the weak‐anisotropy approximation to analyze the dependence of A4 on the anisotropic parameters. The linearized expression for A4 is proportional to the anellipticity coefficient η ≈ ε − δ and does not depend on the individual values of the Thomsen parameters. Typically, the magnitude of nonhyperbolic moveout in tilted TI media above a dipping reflector is highest near the reflector strike, whereas deviations from hyperbolic moveout on the dip line are substantial only for mild dips. The azimuthal variation of the quartic coefficient is governed by the tilt ν and reflector dip φ and has a much more complicated character than the NMO–velocity ellipse. For example, if the symmetry axis is vertical (VTI media, ν = 0) and the dip φ < 30°, A4 goes to zero on two lines with different azimuths where it changes sign. If the symmetry axis is orthogonal to the reflector (this model is typical for thrust‐and‐fold belts), the strike‐line quartic coefficient is defined by the well‐known expression for a horizontal VTI layer (i.e., it is independent of dip), while the dip‐line A4 is proportional to cos4 φ and rapidly decreases with dip. The high sensitivity of the quartic moveout coefficient to the parameter η and the tilt of the symmetry axis can be exploited in the inversion of wide‐azimuth, long‐spread P‐wave data for the parameters of TI media.

Seismic anisotropy in exploration and reservoir characterization: An overview

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A15-75A29 ◽  
Author(s):  
Ilya Tsvankin ◽  
James Gaiser ◽  
Vladimir Grechka ◽  
Mirko van der Baan ◽  
Leon Thomsen
Keyword(s):  
Reservoir Characterization ◽  
Seismic Anisotropy ◽  
Body Wave ◽  
Transverse Isotropy ◽  
Time Lapse ◽  
P Wave ◽  
Fracture Detection ◽  
Fracture Characterization ◽  
Anisotropic Models ◽  
Wide Range

Recent advances in parameter estimation and seismic processing have allowed incorporation of anisotropic models into a wide range of seismic methods. In particular, vertical and tilted transverse isotropy are currently treated as an integral part of velocity fields employed in prestack depth migration algorithms, especially those based on the wave equation. We briefly review the state of the art in modeling, processing, and inversion of seismic data for anisotropic media. Topics include optimal parameterization, body-wave modeling methods, P-wave velocity analysis and imaging, processing in the [Formula: see text] domain, anisotropy estimation from vertical-seismic-profiling (VSP) surveys, moveout inversion of wide-azimuth data, amplitude-variation-with-offset (AVO) analysis, processing and applications of shear and mode-converted waves, and fracture characterization. When outlining future trends in anisotropy studies, we emphasize that continued progress in data-acquisition technology is likely to spur transition from transverse isotropy to lower anisotropic symmetries (e.g., orthorhombic). Further development of inversion and processing methods for such realistic anisotropic models should facilitate effective application of anisotropy parameters in lithology discrimination, fracture detection, and time-lapse seismology.

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