Complete phenomenon of reflection at the plane boundary of a dissipative anisotropic elastic medium

2020 ◽  
Vol 224 (2) ◽  
pp. 1015-1027
Author(s):  
M D Sharma ◽  
Suman Nain
Keyword(s):  
Elastic Medium ◽  
Propagation Velocity ◽  
Sagittal Plane ◽  
Amplitude Ratio ◽  
Plane Waves ◽  
Plane Boundary ◽  
Dual Vector ◽  
Inhomogeneous Waves ◽  
Slowness Vector ◽  
Anisotropic Elastic

SUMMARY A complex slowness vector governs the 3-D propagation of harmonic plane waves in a dissipative elastic medium with general anisotropy. In any sagittal plane, this dual vector is specified with phase direction, propagation velocity and coefficients for attenuation. A generalized reflection phenomenon is illustrated for incidence of inhomogeneous waves at the stress free boundary of the medium. Each reflected wave at the boundary is characterized by its propagation direction, propagation velocity, inhomogeneity, amplitude ratio, phase shift and energy flux. These propagation characteristics are exhibited graphically for a numerical example of anisotropic viscoelastic medium.

Boundary attenuation angles for inhomogeneous plane waves in anisotropic dissipative media

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. WA51-WA62 ◽  
Author(s):  
Vlastislav Červený ◽  
Ivan Pšenčík
Keyword(s):  
A Priori ◽  
Plane Waves ◽  
Wave Mode ◽  
Viscoelastic Media ◽  
Inhomogeneous Waves ◽  
Slowness Vector ◽  
Inhomogeneous Plane ◽  
Unbounded Media ◽  
Dissipative Media ◽  
Inhomogeneous Plane Waves

We study behavior of attenuation (inhomogeneity) angles [Formula: see text], i.e., angles between real and imaginary parts of the slowness vectors of inhomogeneous plane waves propagating in isotropic or anisotropic, perfectly elastic or viscoelastic, unbounded media. The angle [Formula: see text] never exceeds the boundary attenuation angle [Formula: see text]. In isotropic viscoelastic media [Formula: see text]; in anisotropic viscoelastic media [Formula: see text] may be greater than, equal to, or less than [Formula: see text]. Plane waves with [Formula: see text] do not exist. Because [Formula: see text] in anisotropic viscoelastic media is usually not known a priori, the commonly used specification of an inhomogeneous plane wave by the attenuation angle [Formula: see text] may lead to serious problems. If [Formula: see text] is chosen close to [Formula: see text] or even larger, indeterminate, unstable or even nonphysical results are obtained. We study properties of [Formula: see text] and show that the approach based on the mixed specification of the slowness vector fully avoids the problems mentioned above. The approach allows exact determination of [Formula: see text] and removes instabilities known from the use of the specification of the slowness vector by [Formula: see text]. For [Formula: see text], the approach yields zero phase velocity, i.e., the corresponding wave is a nonpropagating wave mode. The use of the mixed specification leads to the explanation of the deviation of [Formula: see text] from [Formula: see text] as a consequence of different orientations of energy-flux and propagation vectors in anisotropic media. The approach is universal; it may be used for isotropic or anisotropic, perfectly elastic or viscoelastic media, and for homogeneous and inhomogeneous waves, including strongly inhomogeneous waves, like evanescent waves.

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