NUMERICAL COMPUTATION OF DISPERSION CURVES AND EIGEN DISPLACEMENTS OF SEISMIC SURFACE WAVES IN A LAYERED INHOMOGENEOUS MEDIA

摘要

The computation of dispersion curves of phase velocities for a stratified earth model plays an important role in the study and synthesizing complete seismogram. A systematic and efficient approach has been developed numerically to compute dispersion curves and the corresponding eigen displacements in a multi-layered inhomogeneous model of earth, even at high frequency. Initially, a layered model of earth with one or more inhomogeneous layer(s) has been considered. The source considered here, is a simple point source and the influence of the source depth on the excitation of different modes has been neglected. The displacement and stress components are continuous at each layer boundaries, except at the source. Numerical computation, like Runge-Kutta method of order 4 to compute a system of first order differential equations with stress free boundary condition on the surface has been used in the study. It has been observed that the dispersion curves are packed together at higher phase velocities and the continuity of phase velocities can be used to get proper layering of earth structure. Numerical overflow and underflow errors have been controlled here by using normalization technique. The study has also been extended to compute energy integrals. The results in a homogeneous medium can be obtained as a particular case. The present study can be extended to evaluate synthetic seismogram by modal summation method.