transference of sh-waves in fluid saturated porous medium sandwiched between heterogeneous half-spaces

A mathematical model is considered to investigate the behavior of horizontally polarized shear waves (sh-waves) in fluid saturated porous medium sandwiched between heterogeneous half-spaces. heterogeneity in the upper half-space is due to linear variation of elastic parameters, whereas quadratic variation has been considered for lower half-space. the method of separation of variables and whittaker’s function are used to get an analytical solution for the considered problem. frequency equation of sh waves in considered model has been obtained. also, frequency equations have been derived for several particular cases. it is observed that the heterogeneity and porosity have significant effect on the phase velocity of sh-waves. in particular, heterogeneity and porosity increases the phase velocity of sh-waves. obtained result is matched with classical love wave equation. graphical representation is done efficiently to explain the findings. also the surface plot is added to exhibit the velocity profile of sh-waves in different cases.