Please use this identifier to cite or link to this item: http://hdl.handle.net/10266/2328
Title: Propagation of sh waves in an elastic layered media
Authors: Vats, Vikas
Supervisor: Singh, Abhishek
Kumar, Satish
Keywords: Elasticity;SH waves;Monoclinic layer
Issue Date: 21-Aug-2013
Abstract: This thesis aims to study the propagation of SH wave in a monoclinic layer lying over an isotropic half-space and propagation of SH wave in double isotropic layer lying over an isotropic half-space. The dispersion relation has been obtained for both the problems. Variation of the phase velocity with the wave number has been depicted by means of graphs. Moreover, for the double layer problem effect of thickness ratio on the dispersion curve has been studied. There are two main types of waves generated during earthquakes, body waves (P-waves, S-waves) and surface waves, which include Love waves and Rayleigh waves. Surface waves are generated by the constructive interference of incident P and S -waves arriving at the free surface and propagating parallel to the surface. The amplitude of surface waves decreases with increasing depth and are affected by lateral variations in structure. Another property that surface waves exhibit is dispersion, i.e., the velocity of a wave on the surface is dependent on its frequency (or period). Love waves are a type of surface wave formed by the constructive interference of multiple reflections of SH waves at the free surface. Love waves are faster than Rayleigh waves and therefore arrive before them on a seismogram. The particle motion for Love waves is parallel to the surface but perpendicular to the direction of propagation and found on the transverse record of a rotated seismogram. Because Love waves need a low-velocity layer over a half-space to exist, they are always dispersive. Dispersion is the apparent surface-wave velocity that depends on the period and reflects the velocity variation with depth. Dispersion appears on a seismogram as different periods arriving at different times. In general, short period surface waves, which sample rocks closer to the surface, travel slower than long period waves. Long periods are sensitive to faster velocities found deeper in the Earth. Love waves exhibit dispersion and are used to estimate shear-velocity variations in the crust and upper mantle. Chapter-1 deals with the study of basic concepts and equation of motion of elastic medium. In this chapter, the importance of problems of elastic wave propagation has been highlighted and the brief outlines of the anisotropic elasticity have been presented. Chapter-2 deals with the study of Love wave propagation in an homogeneous isotropic layer lying over homogeneous isotropic half space. The dispersion relation has been found in closed form. Chapter-3 deals with the propagation of SH wave in a monoclinic layer lying over an isotropic homogeneous half-space. The dispersion relation is found in the closed form and matched with the classical Love wave equation as a particular case. It is observed that phase velocity is depending on the wave number and the thickness of the layer. Graphical illustration is being made for the study. Chapter-4 deals with the propagation of SH wave in the double isotropic homogeneous layer lying over an isotropic homogeneous half-space. The dispersion relation is found in closed form. It is observed that phase velocity is depending on the wave number, thickness of the uppermost layer and thickness ratio of the layers. Some of the important peculiarities have been traced out through graphs.
Description: Master of Science (Mathematics and Computing)
URI: http://hdl.handle.net/10266/2328
Appears in Collections:Masters Theses@SOM

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