M.D. Sharma

Seismic wave propagation in a viscoelastic porous solid saturated by viscous liquid

A general solution is deduced of the differential equations describing the propagation of elastic waves in a dissipative liquid-filled viscoelastic porous solid. The velocities of three existing waves have been expressed in convenient form using the moduli of the solid phase and by introducing the frequency-dependent equivalent mass densities. The solution is then used to examine some of the phenomena which arise when each of the three-body waves, in turn, are incident on a traction-free plane boundary. Analytic expressions for the reflection coefficients are obtained. Numerical calculations have been made, for a particular model, in case of incidentPI wave. Effect of viscoelasticity and viscosity on the reflection coefficients has also been exhibited.

Group velocity along general direction in a general anisotropic medium

An attempt has been made to study the three-dimensional wave propagation in a general anisotropic medium. A procedure is presented to solve the inverse problem of finding the group velocity in a given direction of ray travel, without using numerical differentiation. The phase direction, derived from the given ray direction, is used to calculate phase velocity. Then, such a phase velocity and phase direction are used to calculate group velocity. Analytical expressions are derived for the directional derivatives of phase velocity which are used to calculate group velocity. Algebraic expressions are derived in a computation convenient manner. Newtons method (without numerical differentiation) for solving a system of two non-linear simultaneous equations is the only numerical method used. The ray directions along which a wave (or energy) can travel with more than one group velocity may be difficult to treat. Variations of phase velocity and group velocity with ray direction in three dimensions are plotted for a hypothetical model of general anisotropic medium.

Surface wave propagation in a liquid-saturated porous layer overlying a homogeneous transversely isotropic half-space and lying under a uniform layer of liquid

Abstract Dispersion of Rayleigh-type surface waves is studied in a liquid-saturated porous solid layer under a uniform layer of homogeneous liquid, and lying over a transversely isotropic elastic half-space. Special cases have been deduced by reducing the depth of the layer to zero and by changing the transversely isotropic solid to an isotropic elastic solid. A frequency equation in the form of a tenth-order determinant is obtained. For numerical calculations, a particular model consisting of a water-saturated sandstone layer lying over a beryl solid and under a uniform layer of water is considered. To observe the effects of the depths of the layers on the phase velocity, dispersion curves for the phase velocity have been plotted for different values of the ratio of the depths of two layers.

Surface wave propagation in a transversely isotropic elastic layer overlying a liquid saturated porous solid half-space and lying under the uniform layer of liquid

Dispersion of Rayleigh-type surface wave is studied in a homogeneous transversely isotropic elastic layer overlying a nondissipative liquid-saturated porous solid half-space and lying under a uniform layer of homogeneous liquid. The frequency equation in the form of ninth-order determinant is obtained.Special cases have been deduced by reducing the depth of the layers to zero and by changing the transverse isotropic layer to an isotropic layer. Dispersion curves for the phase velocity have been plotted for a particular model.

Dispersion in oceanic crust during earthquake preparation

Abstract Dispersion of Stoneley waves is studied in a sedimentary layer of ocean bottom resting over basaltic solid half space. Sedimentary layer is assumed a transversely isotropic poroelastic medium. Lower-most solid half-space is assumed to be embedded with vertically aligned saturated micro-cracks and behaves transversely isotropic to wave propagation. Frequency equation is obtained in the form of determinantal equation. Role of phase angle is eliminated by expressing slowness of waves in terms of phase velocity and elastic constants. Numerical solutions for phase velocity and group velocity are obtained for a particular model. Calculations are made for different depths of ocean and sediments. Effect of thickness and density of cracks on these velocities are observed. Special cases are discussed which represent the absence of ocean and sediments, in the model considered. Changes in dispersion are discussed during the stress accumulation in an earthquake preparation region.

Reflection and refraction of plane harmonic waves at an interface between elastic solid and porous solid saturated by viscous liquid

A general solution of Biots field equations governing small motions of a porous solid saturated by viscous liquid is employed to study the reflection and refraction at the interface between an elastic solid and a liquid-saturated porous solid. The incident wave is assumed to be plane and homogeneous, propagating through the isotropic elastic solid. The poroelastic solid is considered to be a dissipative one. Amplitude and energy ratios are computed numerically for a particular model. With first-order corrections for the porosity of solid and viscosity of liquid, the limiting cases of low and high frequencies are computed.

Pore alignment between two dissimilar saturated poroelastic media: Reflection and refraction at the interface

Abstract Biots theory is employed to study the reflection and refraction of plane harmonic waves at the welded interface between two dissimilar saturated poroelastic media. A pore alignment parameter is defined to classify the effects of connection between the interstices of the two media. Effects of pore alignment on the amplitude ratios and energy ratios have been calculated numerically, for a particular model. Amplitude and energy ratios do not change significantly as we move from partial alignment to full alignment of pores. However, the effect on amplitudes and energies is quite significant for the values of the pore alignment parameter approaching zero. For extreme values of the pore alignment parameter, the amplitude and energy ratios have been plotted against the angle of incidence.

Reflection and transmission ofSH waves in an initially stressed medium consisting of a sandy layer lying over a fluid-saturated porous solid

Biots theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically.