3D seismic response of a 2D hill-valley staggered topography modeled by a 2.5D multi-domain IBEM

Abstract

A two and a half dimensional (2.5D) multi-domain indirect boundary element method (IBEM) is developed to study the wave scattering of obliquely incident P-, SV- and SH-waves by a hill-valley staggered topography in a multi-layered half-space. The IBEM algorithm includes using 2.5D full-space and half-space Green’s functions to construct scattered fields in decomposed closed and opened half-space regions, respectively, and using the dynamic stiffness method to solve the free fields. All regions are finally integrated by introducing the compatibility conditions to obtain the total wave fields. The proposed 2.5D IBEM has the flexibility in dealing with complex boundaries by directly applying the fictitious loads on the regions’ boundaries, with a less storage requirement compared to the full 3D models. Besides, by combining the specific advantages of the two kinds of Green’s functions, the method is well suitable for handling coupled topographies with high accuracy. The method is validated by comparison with published results for a single valley as well as a single hill topography. The effects of height-to-width ratio of hill and layering on dynamic responses are further parametrically investigated by numerical implementations in frequency domain. Results show that the interaction between valley and hills can lead to a more significant amplification within the valley region, and dynamic responses are deeply influenced by the height-to-width of hill, simultaneously depending on incident angle and frequency. Besides, the site effects become more complex when the stratification feature is taken into account.