A direct time-domain numerical approach named the half-plane boundary element method is proposed based on the half-space Green’, s functions for seismic analysis of trapezoidal alluvial hill located on a circular cavity, subjected to propagating vertical incident SH-waves. To analyze the assumed model, a half plane time-domain Boundary Element Method (BEM) was used which can concentrate the meshes only around the boundary of desired features. First, the problem is decomposed into two parts including a pitted half-plane and a trapezoidal filled solid on the surface. Then, the influence coefficients of the matrices are obtained by applying the method to each part. By satisfying the boundary/continuity conditions on the interfaces, a coupled equation is formed to determine unknown boundary values in each time-step. After implementing the method in an advanced developed algorithm, its efficiency is investigated by solving some practical examples and compared with those of the published works. To complete the results, the sensitivity analysis was carried out to obtain the seismic response of hill by considering the key parameters including impedance and shape ratios. In the meantime, the effect of subsurface cavity on the amplification pattern of surface has been studied as well. The results showed that the impedance and shape ratios of the trapezoidal alluvial hill were very effective on the seismic response of surface. The results of the present study can be used by geotechnical engineers to completing and increasing the accuracy of existing codes around the subject of ground surface zonation in presence of different topographic features.

The occurrence of SH wave propagation under the effect of a point source in an orthotropic substratum lying over a heterogeneous orthotropic half space is deliberated in the prospect of a devastating earthquake. The quadratic alteration is acknowledged for density and shear modulus which is hypothesized to be a function of depth. The method of Green's function and transformation technique contributes to obtain the dispersion equation and dispersion curves. An effort has been accomplished to demonstrate the classical equation of Love wave followed from dispersion equation. “ Mathematica” software is applied to depict the graphics. Graphics are designed to show the effect of heterogeneous parameters corresponding to density and shear modulus. Dispersion equation is obtained considering the case that the displacement and stress are continuous at the interface. The present work is an attempt to express the behavior of SH wave in an orthotropic medium under the effect of point source.

In this paper, the strong motion accelerograms of October 17, 2009, Tehran-Ray earthquake (MW = 4.0) of south of Tehran were analyzed. (i) Using derived SH-wave spectral data, at first the parameters Wo (long period spectral level), fc (corner frequency) and Q(f) (frequency dependent, average shear wave quality factor), appropriate for the best-fit Brune w-2 spectrum of this event were estimated. Then a non-linear least square analysis of the SH-wave spectral data was performed to provide objectively approximate near field estimates of the strike, dip and rake of the causative fault. Based on this analysis, the first fault plane solution has been presented for this event, which may be related to Eyvanaki fault closed to Tehran. Near field estimates of the strike, dip and rake of the causative fault of the 2009 Ray-Tehran earthquake are 292o, 36o, and 59o, respectively. Our estimated fault plane solutions suggest a reverse faulting mechanism with minor left lateral strike slip component. The estimated strike is consistent with the direction of isoacceleration map and Eyvanaki fault.

The aim of this paper is to investigates the existence of the dispersion of SH-wave in a heterogeneous orthotropic layer lying over a heterogeneous elastic half-space and underlying an inhomogeneous semi-infinite medium. Hyperbolic variation in upper semi-infinite associated with directional rigidities and density has been considered while linear variation in the intermediate layer associated with initial stress, density, shear moduli and lower half-space associated with rigidity and density has been considered. The dispersion equation of SH-wave has been obtained in a closed form by using variable separation method. The effects of inhomogeneities of the assumed media are illustrated by figures using MATLAB programming. The Earth's composition is heterogeneous that incorporates extremely hard layers. The propagation of SH-wave across crustal layer of the Earth very much depends upon heterogeneity and orthotropic properties. In fact, the observation reveals that the phase velocity of SH-wave is directly proportionate to inhomogeneity parameter, orthotropic parameter and heterogeneity parameter. That means as inhomogeneity parameter and heterogeneity orthotropic parameter increases, the phase velocity of SH-wave increases proportionately. Moreover, the obtained dispersion equation of SH-wave coincides with the classical result of Love wave as initial stress, inhomogeneities, and the upper semiinfinite medium is neglected. This analysis may be helpful to expound the nature of the dispersion of seismic waves in elastic media.

The problem of propagation of plane wave including body and surface waves propagating in a transversely isotropic half-space with a depth-wise axis of material symmetry is investigated in details. Using the advantage of representation of displacement fields in terms of two complete scalar potential functions, the coupled equations of motion are uncoupled and reduced to two independent equations for potential functions. In this paper, the secular equations for determination of body and surface wave velocities are derived in terms of both elasticity coefficients and the direction of propagation. In particular, the longitudinal, transverse and Rayleigh wave velocities are determined in explicit forms. It is also shown that in transversely isotropic materials, a Rayleigh wave may propagate in different manner from that of isotropic materials. Some numerical results for synthetic transversely isotropic materials are also illustrated to show the behavior of wave motion due to anisotropic nature of the problem.