Love Wave Propagation in the Layered Media

Abstract

This thesis aims to study the propagation of love waves in the layered media. Dispersion equation has been obtained for propagation of Love wave in three different types of problems. Variation of the phase velocity with the wave number has been depicted by graphs. Effect of reinforcement on the dispersion curve is also shown. Comparison is also made to study the effect of reinforced medium over the reinforced free medium. There are two main types of waves generated by 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, where 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. 6 Chapter-2 deals with the study of Love wave propagation in an isotropic layer lying over homogeneous isotropic half space. The dispersion relation has been found in closed form and graphical illustration has been made to get practical insight into the problem. Chapter-3 deals with the study of dispersion relation of Love waves in a sandwiched layer between two homogeneous isotropic half spaces. It is found that phase velocity is depending on the wave number and the thickness of the layer. The dependency relation is found in closed form and graphical illustration is being made. Chapter-4 deals with the dispersion relation of Love waves in a fibre-reinforced layer lying over the homogeneous isotropic half space. The dispersion relation is found in closed form and matched with the classical Love wave dispersion equation as a particular case. The comparative study has been made for reinforced and reinforced free medium through graph. Some of the important peculiarities have been traced out through comparison.