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

QVOA analysis: P-wave attenuation anisotropy for fracture characterization

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. C37-C48 ◽  
Author(s):  
Tatiana Chichinina ◽  
Vladimir Sabinin ◽  
Gerardo Ronquillo-Jarillo
Keyword(s):  
Wave Reflection ◽  
Wave Attenuation ◽  
Fractured Reservoirs ◽  
Anisotropy Parameter ◽  
P Wave ◽  
Fracture Parameters ◽  
Fractured Medium ◽  
Seismic Quality Factor ◽  
Pp Wave ◽  
Attenuation Anisotropy

This paper investigates [Formula: see text]-anisotropy for characterizing fractured reservoirs — specifically, the variation of the seismic quality factor [Formula: see text] versus offset and azimuth (QVOA). We derive an analytical expression for P-wave attenuation in a transversely isotropic medium with horizontal symmetry axis (HTI) and provide a method (QVOA) for estimating fracture direction from azimuthally varying [Formula: see text] in PP-wave reflection data. The QVOA formula is similar to Rüger’s approximation for PP-wave reflection coefficients, the theoretical basis for amplitude variation with angle offset (AVOA) analysis. The technique for QVOA analysis is similar to azimuthal AVO analysis. We introduce two new seismic attributes: [Formula: see text] versus offset (QVO) gradient and intercept. QVO gradient inversion not only indicates fracture orientation but also characterizes [Formula: see text]-anisotropy. We relate the [Formula: see text]-anisotropy parameter [Formula: see text] to fractured-medium parameters and invert the QVO gradient to estimate [Formula: see text]. The attenuation parameter [Formula: see text] and Thomsen-style anisotropy parameter [Formula: see text] are found to be interdependent. The attenuation anisotropy magnitude strongly depends on the host rock’s [Formula: see text] parameter, whereas the dependence on fracture parameters is weak. This complicates the QVO gradient inversion for the fracture parameters. This result is independent of the attenuation mechanism. To illustrate the QVOA method in synthetic data, we use Hudson’s first-order effective-medium model of a dissipative fractured reservoir with fluid flow between aligned cracks and random pores as a possible mechanism for P-wave attenuation.

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

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.

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.

Frequency-dependent P-wave anisotropy due to scattering in rocks with aligned fractures

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. MR97-MR105 ◽  
Author(s):  
Junxin Guo ◽  
Boris Gurevich ◽  
Da Shuai
Keyword(s):  
Wave Velocity ◽  
Wave Scattering ◽  
Wave Attenuation ◽  
P Wave ◽  
Frequency Dependent ◽  
Velocity Anisotropy ◽  
P Wave Velocity ◽  
Anisotropy Parameters ◽  
Scattering Anisotropy ◽  
Attenuation Anisotropy

Frequency-dependent P-wave anisotropy due to scattering often occurs in fractured formations, whereas the corresponding theoretical study is lacking. Hence, based on a newly developed P-wave scattering model, we have studied the frequency-dependent P-wave scattering anisotropy in rocks with aligned fractures. To describe P-wave scattering anisotropy, we develop the corresponding anisotropy parameters similar to those for elastic anisotropy. Our results indicate that the P-wave velocity anisotropy parameters [Formula: see text] and [Formula: see text] do not change with frequency monotonically, which is different from that caused by wave-induced fluid flow. Fluid saturation in fractures can greatly decrease the P-wave velocity anisotropy, whose effects depend on the ratio of the fluid bulk modulus to the fracture aspect ratio. The P-wave exhibits elliptical anisotropy for the dry fracture case at low frequencies, but anelliptical anisotropy for the case with fluid-filled fractures. The P-wave attenuation anisotropy parameters [Formula: see text] and [Formula: see text] vanish in the low- and high-frequency limits but reach their maxima at the characteristic frequency when the P-wavelength is close to the fracture length. The influence of fluid on the P-wave attenuation anisotropy is similar to that on the velocity anisotropy. To further analyze frequency-dependent P-wave scattering anisotropy, theoretical predictions are compared with experimental results, which indicate reasonable agreement between them.

Plane-wave propagation in attenuative transversely isotropic media

Geophysics ◽  
2006 ◽  
Vol 71 (2) ◽  
pp. T17-T30 ◽  
Author(s):  
Yaping Zhu ◽  
Ilya Tsvankin
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Wave Attenuation ◽  
Transversely Isotropic ◽  
Attenuation Coefficients ◽  
The Real ◽  
Velocity Anisotropy ◽  
Anisotropy Parameters ◽  
Attenuation Anisotropy ◽  
Ti Media

Directionally dependent attenuation in transversely isotropic (TI) media can influence significantly the body-wave amplitudes and distort the results of the AVO (amplitude variation with offset) analysis. Here, we develop a consistent analytic treatment of plane-wave properties for TI media with attenuation anisotropy. We use the concept of homogeneous wave propagation, assuming that in weakly attenuative media the real and imaginary parts of the wave vector are parallel to one another. The anisotropic quality factor can be described by matrix elements [Formula: see text], defined as the ratios of the real and imaginary parts of the corresponding stiffness coefficients. To characterize TI attenuation, we follow the idea of the Thomsen notation for velocity anisotropy and replace the components [Formula: see text] by two reference isotropic quantities and three dimensionless anisotropy parameters [Formula: see text], and [Formula: see text]. The parameters [Formula: see text] and [Formula: see text] quantify the difference between the horizontal- and vertical-attenuation coefficients of P- and SH-waves, respectively, while [Formula: see text] is defined through the second derivative of the P-wave attenuation coefficient in the symmetry direction. Although the definitions of [Formula: see text], and [Formula: see text] are similar to those for the corresponding Thomsen parameters, the expression for [Formula: see text] reflects the coupling between the attenuation and velocity anisotropy. Assuming weak attenuation as well as weak velocity and attenuation anisotropy allows us to obtain simple attenuation coefficients linearized in the Thomsen-style parameters. The normalized attenuation coefficients for P- and SV-waves have the same form as the corresponding approximate phase-velocity functions, but both [Formula: see text] and the effective SV-wave attenuation-anisotropy parameter [Formula: see text] depend on the velocity-anisotropy parameters in addition to the elements [Formula: see text]. The linearized approximations not only provide valuable analytic insight, but they also remain accurate for the practically important range of small and moderate anisotropy parameters — in particular, for near-vertical and near-horizontal propagation directions.

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