Wave velocities in a pre-stressed anisotropic elastic medium

Sharma, M. D.; Garg, Neetu

doi:10.1007/bf02702040

Cited by 29 publications

(16 citation statements)

References 26 publications

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“…In a recent study, Prikazchikov and Rogerson (2003) analyzed the dynamic properties of anisotropic pre-stressed elastic solids. More recently, the effects of initial stress are studied on the velocities of three waves in general anisotropic elastic medium (Sharma and Garg 2006) and anisotropic poroelastic medium (Sharma 2005). The applications of the studies to the earth-system were also discussed.…”

Section: Introductionmentioning

confidence: 98%

Effect of initial stress on reflection at the free surface of anisotropic elastic medium

Sharma

2007

J Earth Syst Sci

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The propagation of plane waves is considered in a general anisotropic elastic medium in the presence of initial stress. The Christoffel equations are solved into a polynomial of degree six. The roots of this polynomial represent the vertical slowness values for the six quasi-waves resulting from the presence of a discontinuity in the medium. Three of these six values are identified with the three quasi-waves traveling in the medium but away from its boundary. Reflection at the free plane surface is studied for partition of energy among the three reflected waves. For post-critical incidence, the reflected waves are inhomogeneous (evanescent) waves. Numerical examples are considered to exhibit the effects of initial stress on the phase direction, attenuation and reflection coefficients of the reflected waves. The phase velocities and energy shares of the reflected waves change significantly with initial stress as well as anisotropic symmetry. The presence of initial stress, however, has a negligible effect on the phase directions of reflected waves.

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Section: Introductionmentioning

confidence: 98%

Effect of initial stress on reflection at the free surface of anisotropic elastic medium

Sharma

2007

J Earth Syst Sci

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“…These stresses modify the elastic properties of the layers and, hence affect the propagation of waves there (Biot 1965). In the past, a number of researchers (Cauchy 1827;Biot 1939Biot , 1940Biot , 1965Birch 1947Birch , 1952Truesdell 1952;Hayes 1963;Tolstoy 1982;Man and Lu 1987;Degtyar and Rokhlin 1998;Prikazchikov and Rogerson 2003;Sharma and Garg 2006) have considered various problems on wave propagation in pre-stressed elastic materials.…”

Section: Introductionmentioning

confidence: 99%

Existence of longitudinal waves in pre-stressed anisotropic elastic medium

Garg

2009

J Earth Syst Sci

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In a pre-stressed anisotropic elastic medium, three types of quasi-waves propagate along an arbitrary direction. In general, none of the waves is truly longitudinal. The present study finds the specific directions in a pre-stressed anisotropic elastic medium along which longitudinal waves may propagate. This paper demonstrates how the propagation of longitudinal waves is affected by various pre-stresses present in the medium. The study establishes the explicit expressions defining the existence and propagation of longitudinal waves in pre-stressed anisotropic elastic medium. These expressions involve not only the direction and elastic stiffness of the medium, but also the prestresses present in the medium. Changes in conditions for the existence of longitudinal waves in orthotropic, monoclinic and triclinic anisotropies are discussed in detail. The most important part of the paper is a practical aspect suggested to calculate the specific directions for the existence of longitudinal waves in pre-stressed anisotropic elastic medium. In this approach, only those parameters are used that can be observed by the receiver in a geophysical experiment of wave propagation. The existence of longitudinal waves has been shown graphically using a numerical example for three types of anisotropic symmetries in elastic medium.

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“…A large number of studies in the later years improved the understanding of wave propagation characteristics of materials under initial stress. [1][2][3][4][5][6][7][8] However, some theoretical models only describe the stress sensitivity of plane-wave velocities. 1,2 An alternative approach that has been successfully applied to the estimation of stress is based on the acoustoelastic theory.…”

Section: Introductionmentioning

confidence: 99%

“…[1][2][3][4][5][6][7][8] However, some theoretical models only describe the stress sensitivity of plane-wave velocities. 1,2 An alternative approach that has been successfully applied to the estimation of stress is based on the acoustoelastic theory. 6,[9][10][11][12][13][14] The acoustoelastic effect, i.e., the velocity change of the acoustic waves in the presence of stresses, has been investigated for more than about sixty years.…”

Section: Introductionmentioning

confidence: 99%

Acoustoelastic effects of Stoneley waves in a borehole surrounded by a transversely isotropic elastic solid

et al. 2014

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Stoneley wave in a fluid-filled pressurized borehole surrounded by a transversely isotropic elastic solid with nine independent third-order elastic constants in presence of biaxial stresses are studied. A simplified acoustoelastic formulation of Stoneley wave is presented for the parallelism of the borehole axis and the formation axis of symmetry. Sensitivity coefficients and velocity dispersions for Stoneley wave due to the presence of stresses are numerically investigated, respectively. The acoustoelastic formulation explicitly shows that the velocity dispersions of Stoneley wave depend on seven independent third-order elastic constants in presence of biaxial stresses and on six independent third-order elastic constants in the presence of borehole pressurization alone. Numerical results of both sensitivity coefficients and velocity dispersions of Stoneley wave show that at low frequency the velocity change of Stoneley wave is sensitive to c111 and c112. Stoneley wave velocity at low frequencies can be simplified by 3 independent third order elastic constants (c111, c112 and c123) instead of nine constants. In presence of biaxial stresses, at low frequencies the speed of the Stoneley wave is similar to White’s formula.

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Wave velocities in a pre-stressed anisotropic elastic medium

Cited by 29 publications

References 26 publications

Effect of initial stress on reflection at the free surface of anisotropic elastic medium

Effect of initial stress on reflection at the free surface of anisotropic elastic medium

Existence of longitudinal waves in pre-stressed anisotropic elastic medium

Acoustoelastic effects of Stoneley waves in a borehole surrounded by a transversely isotropic elastic solid

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