Study Of SH-wave Scattering In Heterogeneous Sedimentary Basins By Singular Boundary Method

The damage investigation of many earthquakes in history reveals that the local topography(canyons,sedimentary basins and hills)has a significant amplification effect on ground motion.Thus,buildings locate near the sedimentary basin often suffers severe damage.There are more than 100 sedimentary basins in China.There are several cities with dense population and buildings located near the sedimentary basin,such as Taipei,Chengdu,Xi ’an,Beijing and so on.Earthquake damage in these areas may cause serious casualties and property losses.Researching on the sedimentary basin on ground motion will help us to better understand its influence on motion characteristics,and then serves to the seismic design of structures in earthquake region and finally reduce the losses caused by earthquakes.Because the internal materials of sedimentary basins are often complex,the internal media of sedimentary basins are often heterogeneous,and many geographical factors will lead to multiple sedimentary layers in the actual sedimentary basins.Since the computational domain involved in the scattering of SH waves by sedimentary basins is semi-infinite domain,the boundary-type method is more suitable for solving such problems.Therefore,the singular boundary method is used to study the scattering of SH waves by single-layer continuous heterogeneous and layered heterogeneous sedimentary basins.The singular boundary method is a meshless collocation method that requires only discrete boundaries.This method does not require meshing,and it is easy to program and has high computational efficiency.The method uses the fundamental solution that satisfies the governing equation as the interpolation function and automatically satisfies the Sommerfeld radiation condition,which is very suitable for solving semi-infinite domain problems.The main work of this paper is as follows :(1)Based on the elastic wave equation,the governing equation of SH wave propagation in homogeneous isotropic media is derived.Then some numerical aspects of the SBM is introduced via solving the SH wave scattering in homogeneous basin.The numerical examples verify the feasibility of the SBM.(2)The SBM is extended to solve SH wave propagating in continuous heterogeneous isotropic medium.The fundamental solutions and origin intensity factor(OIF)are derived through the variable transformation method.Then the SBM formulation is established to solve the scattering problem of SH wave in continuous heterogeneous basin and continuous heterogeneous sedimentary basin.The validity of the singular boundary method is verified by several numerical examples.Then,the influence of parameters,including heterogeneity coefficient,shear wave velocity ratio,depth-width ratio of sedimentary basin,incident angle of SH wave and incident wave frequency,are further investigated.(3)The SBM is extended to simulate the scattering problem of SH wave in layered heterogeneous sedimentary basin.The continuous condition between layers are formulated.The numerical effectiveness is illustrated via several numerical examples.The influence of he influence of sedimentary sequence,heterogeneity coefficient,SH wave incident wave frequency and other factors on the site amplification effect in the layered heterogeneous sedimentary basin are further investigated.