Stress-Induced Seismic Anisotropy Revisited

Rasolofosaon, Patrick N.J.

doi:10.2516/ogst:1998061

Cited by 79 publications

(50 citation statements)

References 22 publications

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“…The result concerning the ellipticity of stress-induced anisotropy is consistent with a theoretically proven fact: elastic anisotropy arising from the application of anisotropic stress to an elastic medium that can be described by isotropic third-order elasticity (so that both second-and third-order elasticity tensors are isotropic) is always elliptical (see Rasolofosaon, 1998;Fuck and Tsvankin, 2009). Our model is a particular case of isotropic third-order elasticity.…”

Section: Discussionsupporting

confidence: 88%

“…We will now assume that normal stresses are small compared to P c . This assumption is equivalent to the assumption of third-order elasticity (Rasolofosaon, 1998;Prioul et al, 2004;Fuck and Tsvankin, 2009) and results in linear variation of elastic compliances with stress. With this assumption, the exponential expression in Equation 5 can be approximated by a linear expression…”

Section: Effect Of Stress On Crack Distributionmentioning

confidence: 99%

“…By making this assumption, we restrict ourselves to describing only the first (linear) term in the variation of elastic compliances (and, approximately, of the stiffnesses and elastic wave velocities) with stress. This is equivalent to the assumption of third-order elasticity (Rasolofosaon, 1998;Prioul et al, 2004;Fuck and Tsvankin, 2009). In our laboratory example, the model is approximately consistent with the data up to stresses almost twice the closing pressure.…”

Section: Assumptionsmentioning

confidence: 99%

See 2 more Smart Citations

An analytic model for the stress-induced anisotropy of dry rocks

2011

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One of the main causes of azimuthal anisotropy in sedimentary rocks is anisotropy of tectonic stresses in the earth's crust. We have developed an analytic model for seismic anisotropy caused by the application of a small anisotropic stress. We first considered an isotropic linearly elastic medium (porous or nonporous) permeated by a distribution of discontinuities with random (isotropic) orientation (such as randomly oriented compliant grain contacts or cracks). The geometry of individual discontinuities is not specified. Instead, their behavior is defined by a ratio B of the normal to tangential excess compliances. When this isotropic rock is subjected to a small compressive stress (isotropic or anisotropic), the number of cracks along a particular plane is reduced in proportion to the normal stress traction acting on that plane. This effect is modeled using the Sayers-Kachanov noninteractive approximation. The model predicts that such anisotropic crack closure yields elliptical anisotropy, regardless of the value of the compliance ratio B. It also predicts the ratio of Thomsen's anisotropy parameters e=c as a function of the compliance ratio B and Poisson's ratio of the unstressed rock. A comparison of the model predictions with the results of laboratory measurements indicates a reasonable agreement for moderate magnitudes of uniaxial stress (as high as 30 MPa). These results can be used for differentiating stress-induced anisotropy from that caused by aligned fractures. Conversely, if the cause of anisotropy is known, then the anisotropy pattern allows one to estimate P-wave anisotropy from S-wave anisotropy.

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Section: Discussionsupporting

confidence: 88%

Section: Effect Of Stress On Crack Distributionmentioning

confidence: 99%

Section: Assumptionsmentioning

confidence: 99%

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An analytic model for the stress-induced anisotropy of dry rocks

2011

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“…Rasolofosaon [12] showed that application of anisotropic stress to an isotropic drained rock results in ellipsoidal anisotropy. The stretched HTI porous medium in this case results in elliptical anisotropy, meaning that for drained rock Thomsen's anisotropy parameters ε and δ are equal, which is equivalent to 1 r  or N T Z Z  .…”

Section: The Main Assumption and Its Justificationmentioning

confidence: 99%

SATI algorithm — the calculation of stress aligned HTI stiffness tensor for sandstone reservoir from wireline data

Brajanovski¹

2011

Sci. China Phys. Mech. Astron.

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I present an algorithm that uses cross-dipole wireline data only in order to estimate the HTI stiffness tensor for sandstone formations under in-situ asymmetric lateral (azimuthal) stress conditions. The algorithm is based on the generalization of terms "excess compliance" and "fracture weakness" developed within the linear slip interface theory for fractured rocks and is applied here to describe the effect of grain contacts in loose sandstones. I introduce the term "plane of weakness" being oriented (aligned) orthogonal to the minimal horizontal principal stress direction in order to describe the overall effective weakness of sandstone caused by the different principal stresses. For the quantification of this phenomenon I use the anisotropic Gassmann model. As a result I am able to calculate a HTI stiffness tensor for the interval length of a saturated sandstone formation and the respective Thomsen's parameters. The input data required for these calculations have to be provided by wireline logging and will consist of porosity, density, P-wave velocity, fast and slow shear wave velocities and oil-water saturation ratio. The algorithm in its current form is applicable to sandstone reservoirs only. Its limitation is based on two assumptions, which state that all the measured anisotropy is induced by the present stress in sandstone and that the unstressed sandstone would be nearly isotropic. From a technical viewpoint this algorithm can be implemented fairly easily in data acquisition and interpretation software relying on correct estimation of anisotropy parameters. It is also cheap because it does not require any additional measurements apart from the cross-dipole logging.

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“…e is used to measure the anisotropic intensity of P wave, which reflects the difference between the horizontal phase velocity and vertical phase velocity of P wave, whereas d is a transitional parameter associated with vertical phase velocity and horizontal phase velocity of P wave, reflecting the magnitude of anisotropy of phase velocity near the vertical direction of P wave (Niu et al 2002). Rasolofosaon (1998) suggested that the anisotropy induced by stress may be elliptical anisotropy. Therefore, the elliptically anisotropic media is common in the ground which is the anisotropic media with the least parameters observed so far (Gurvich 1940;Kleyn 1956;Levin 1978;Daley and Hron 1979;Rogister and Slawinski 2005;Grechka 2009).…”

Section: Elliptically Anisotropic Mediamentioning

confidence: 99%

Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

Zhang

Bai

et al. 2017

Earthq Sci

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Seismic ray tracing in anisotropic media with irregular surface is crucial for the exploration of the fine crustal structure. Elliptically anisotropic medium is the type of anisotropic media with only four independent elastic parameters. Usually, this medium can be described by only the vertical phase velocity and the horizontal phase velocity for seismic wave propagation. Model parameterization in this study is described by flexible triangular grids, which is beneficial for the description of irregular surface with high degree of approximation. Both the vertical and horizontal phase velocities are defined in the triangular grids, respectively, which are used for the description of phase velocity distribution everywhere in the model by linear interpolation. We develop a shooting ray tracing method of turning wave in the elliptically anisotropic media with irregular surface. Runge-Kutta method is applied to solve the partial differential equation of seismic ray in elliptically anisotropic media. Linearly modified method is used for adjusting emergent phase angles in the shooting scheme. Numerical tests demonstrate that ray paths coincide well with analytical trajectories in transversely homogeneous elliptically anisotropic media. Seismic ray tracing results in transversely inhomogeneous elliptically anisotropic media demonstrate that our method is effective for further first-arrival tomography in elliptically anisotropic media with an irregular surface.

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Stress-Induced Seismic Anisotropy Revisited

Cited by 79 publications

References 22 publications

An analytic model for the stress-induced anisotropy of dry rocks

An analytic model for the stress-induced anisotropy of dry rocks

SATI algorithm — the calculation of stress aligned HTI stiffness tensor for sandstone reservoir from wireline data

Ray tracing of turning wave in elliptically anisotropic media with an irregular surface

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