基于快速多极边界元法的局部场地对地震波高频散射二维模拟

Two-dimensional simulation of high-frequency scattering of seismic waves by local sites based on fast multi-pole boundary element method

结合快速多极子展开技术与间接边界元法,发展一种新的高频地震波散射(二维平面内)快速模拟方法。精度和效率检验表明该方法具有很高的计算精度、求解效率及良好的数值稳定性,同时可大幅度降低计算存储量。进而以半空间峡谷与凸起地形对平面SV波的高频散射为例,讨论了峡谷及凸起周围地震波宽频散射基本特征,给出了千米尺度局部场地、0~25 Hz频带宽度的散射模拟结果。分析表明:高频SV波垂直入射下,峡谷角部水平和竖向位移均表现出明显的放大效应,而峡谷底部的散射效应较弱;半圆凸起顶部附近水平位移谱峰值高达5.0,山脚处位移反应则受到明显的抑制作用;斜入射情况,峡谷地形迎波面一侧位移幅值较大,而凸起地形则是背波面一侧放大显著。数值结果可为复杂局部场地中大型工程抗震设计提供部分理论依据。

A new high-precise fast indirect boundary element method is developed to solve the two-dimensional scattering problems of high-frequency seismic waves（2 D in-plane） based on the fast multi-pole expansion technique.It is verified that this method has high accuracy,efficiency and excellent numerical stability,and can greatly reduce the computational storage.Taking the seismic response of a canyon and a hill in a half space under high-frequency incident plane SV waves as an example,the basic characteristics of high-frequency scattering around the canyon and hill are discussed,and the scattering results of 0~25 Hz broadband waves by large-scale local sites of thousands-meters are illustrated.The numerical results show that under the high-frequency incident SV waves,the amplification effect of the canyon on the horizontal and vertical displacement under high-frequency incident SV waves can be seen clearly at the corner of the canyon,but seems not so pronounced at the bottom of the canyon.The spectral peak of displacement amplitudes reaches up to 5.0 near the top of the hill,while the displacement response at the foot of the hill is constrained.As for the obliquely incident SV waves,the displacement at the canyon surface is more pronounced,but the amplification effect is more significant at the back of hill surface.The numerical results may provide a theoretical basis for the seismic design of large-scale projects constructed in complex local sites.