Vector attenuation: elliptical polarization, raypaths and the Rayleigh‐window effect

Carcione, José M.

doi:10.1111/j.1365-2478.2006.00548.x

Cited by 13 publications

(4 citation statements)

References 19 publications

(35 reference statements)

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“…An attenuated wave is commonly specified by both directions i.e. direction of maximum attenuation and direction of propagation (Carcione, 2006, 2014; Wang et al , 2021). The displacement potentials of the incident wave are written as: where q 0 ( p 0 ) specifies the complex vertical (horizontal) slowness vector.…”

Section: Reflection At the Surfacementioning

confidence: 99%

Inhomogeneous wave reflection from the surface of a partially saturated thermoelastic porous media

Kumar

Liu

Kalkal

et al. 2021

HFF

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Purpose The purpose of this paper is to study the propagation of inhomogeneous waves in a partially saturated poro-thermoelastic media through the examples of the free surface of such media.. Design/methodology/approach The mathematical model evolved by Zhou et al. (2019) is solved through the Helmholtz decomposition theorem. The propagation velocities of bulk waves in partially saturated poro-thermoelastic media are derived by using the potential functions. The phase velocities and attenuation coefficients are expressed in terms of inhomogeneity angle. Reflection characteristics (phase shift, loci of vertical slowness, amplitude, energy) of elastic waves are investigated at the stress-free thermally insulated boundary of a considered medium. The boundary can be permeable or impermeable. The incident wave is portrayed with both attenuation and propagation directions (i.e. inhomogeneous wave). Numerical computations are executed by using MATLAB. Findings In this medium, the permanence of five inhomogeneous waves is found. Incidence of the inhomogeneous wave at the thermally insulated stress-free surface results in five reflected inhomogeneous waves in a partially saturated poro-thermoelastic media. The reflection coefficients and splitting of incident energy are obtained as a function of propagation direction, inhomogeneity angle, wave frequency and numerous thermophysical features of the partially saturated poro-thermoelastic media. The energy of distinct waves (incident wave, reflected waves) accompanying interference energies between distinct pairs of waves have been exhibited in the form of an energy matrix. Originality/value The sensitivity of propagation characteristics (velocity, attenuation, phase shift, loci of vertical slowness, energy) to numerous aspects of the physical model is analyzed graphically through a particular numerical example. The balance of energy is substantiated by virtue of the interaction energies at the thermally insulated stress-free surface (opened/sealed pores) of unsaturated poro-thermoelastic media through the bulk waves energy shares and interaction energy.

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Section: Reflection At the Surfacementioning

confidence: 99%

Inhomogeneous wave reflection from the surface of a partially saturated thermoelastic porous media

Kumar

Liu

Kalkal

et al. 2021

HFF

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“…Its magnitude , is called the complex energy velocity. Note that ‘complex energy velocity’ is different from the ‘energy velocity’ used by Carcione (2006, 2007), where it means a real‐valued time‐averaged quantity.…”

Section: Ray Tracing In Anisotropic Media: Viscoelastic Casementioning

confidence: 99%

Real ray tracing in anisotropic viscoelastic media

Vavryčuk¹

2008

Geophysical Journal International

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S U M M A R YRay tracing equations applicable to smoothly inhomogeneous anisotropic viscoelastic media are derived. The equations produce real rays, in contrast to previous ray-theoretical approaches, which deal with complex rays. The real rays are defined as the solutions of the Hamilton equations, with the Hamiltonian modified for viscoelastic media, and physically correspond to trajectories of high-frequency waves characterized by a real stationary phase. As a consequence, the complex eikonal equation is satisfied only approximately. The ray tracing equations are valid for weakly and moderately attenuating media. The rays are frequency-dependent and must be calculated for each frequency, separately.Solving the ray tracing equations in viscoelastic anisotropy is more time consuming than in elastic anisotropy. The main difficulty is with determining the stationary slowness vector, which is generally complex-valued and inhomogeneous and must be computed at each time step of the ray tracing procedure. In viscoelastic isotropy, the ray tracing equations considerably simplify, because the stationary slowness vector is homogeneous. The computational time for tracing rays in isotropic elastic and viscoelastic media is the same. Using numerical examples, it is shown that ray fields in weakly attenuating media (Q higher than about 30) are almost indistinguishable from those in elastic media. For moderately attenuating anisotropic media (Q between 5-20), the differences in ray fields can be visible and significant.

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“…Applications of the ray theory to wave propagation problems in anisotropic, inhomogeneous and attenuating media have been intensively studied in recent years (Thomson 1997; Hanyga & Seredyňska 2000; Carcione 2006; Vavryčuk 2007a,b; Červený et al 2008; Vavryčuk 2008a,b). The ray theory yields a high‐frequency approximation, which is reasonably accurate in most seismic applications (Červený 2001), and computationally undemanding with respect to other methods solving the equation of motion numerically (Carcione 1990, 1993; Moczo et al 2004, 2007), So far, several ray‐theoretical approaches for solving the eikonal equation and modelling of waves in anisotropic attenuating media have been developed.…”

Section: Introductionmentioning

confidence: 99%

Behaviour of rays at interfaces in anisotropic viscoelastic media

Vavryčuk¹

2010

Geophysical Journal International

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S U M M A R YThe behaviour of rays at interfaces in anisotropic viscoelastic media is studied using three different approaches: the real elastic ray theory, the real viscoelastic ray theory and the complex ray theory. In solving the complex eikonal equation, the highest accuracy is achieved by the complex ray theory. The real elastic and viscoelastic ray theories are less accurate but computationally more effective. In all three approaches, the rays obey Snell's law at the interface, but its form is different for each approach. The complex Snell's law constrains the complex tangential components of the slowness vector. The real viscoelastic and elastic Snell's laws constrain the real tangential components of the slowness vector. In the viscoelastic ray theory, the Snell's law is supplemented by the condition of the stationary slowness vector of scattered waves. The accuracy of all three ray theoretical approaches is numerically tested by solving the complex eikonal equation and by calculating the R/T coefficients. The models of the medium consist of attenuating isotropic and anisotropic homogeneous half-spaces with attenuation ranging from extremely strong (Q = 2.5-3) to moderate (Q = 25-30). Numerical modelling shows that solving the complex eikonal equation by the real viscoelastic ray approach is at least 20 times more accurate than solving it by the real elastic ray approach. Also the R/T coefficients are reproduced with a higher accuracy by the real viscoelastic ray approach than by the elastic ray approach.

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Vector attenuation: elliptical polarization, raypaths and the Rayleigh‐window effect

Cited by 13 publications

References 19 publications

Inhomogeneous wave reflection from the surface of a partially saturated thermoelastic porous media

Inhomogeneous wave reflection from the surface of a partially saturated thermoelastic porous media

Real ray tracing in anisotropic viscoelastic media

Behaviour of rays at interfaces in anisotropic viscoelastic media

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