Abstract
The current investigation is made to find the analytical solutions of the quasi- SV, SH and P-waves in an inhomogeneous transversely isotropic medium. The paper includes the heterogeneity as an exponential type in density as well as in Young's, and shear modulus with respect to the depth parameter z. Using the Hooke's law, stress-strain and strain-displacement relation in the equation of motion, the phase velocity of the above quasi waves can be evaluated. Again, with the help of analytic solution procedure, the equation of motion will convert to eigen value problem and subsequently the closed-form relation for the quasi velocities will formed. Using the numerical simulations and mathematical calculations, the propagation pattern has been studied. This present finding results the outcome of the heterogeneity constants for different velocities. Two-dimensional graphs have been plotted to show the prominent effect of phase velocity on the surface. The study on quasi wave's may be helpful geophysicists and civil engineers to overcome the problems related to earthquake.