A large number of earthquake site investigation and theoretical studies have shown that local site conditions have a significant effect on seismic damage and ground motion characteristics, which is usually manifested as amplification or reduction of ground motion. The mountain topographic effect of strong ground motion plays a great role in the antiseismic defense of major projects in mountainous areas. Currently, there are three main ways to study the topographic effect: topographic effect observation array, analytical analysis and numerical simulation calculation. The strong motion observation data from the array can directly reflect the characteristics caused by the complex terrain, and analysis results are more intuitive, real and reliable.
Based on the nine aftershock records after the 2008 Wenchuan M_{S}8.0 earthquake, the baseline-correction and filtration were carried out, and the Fourier spectral ratios and particle motion displacement trajectory diagrams were achieved.
The average spectral ratio curve of the two horizontal records of 9 aftershocks has good consistency with the spectral ratio curve of a single aftershock. The natural frequency of the mountain is not unique, and the maximum spectral ratio will appear in different frequency bands, indicating a clear multi-order nature of the mountain vibration. 1.0−4.0 Hz is the lower-order vibration mode of the mountain, and 9.0−15.0 Hz is the higher-order vibration mode. There are significant differences in the source, magnitude, epicenter distance, and propagation path of each aftershock, but the spectral ratio curves of each aftershock have good consistency, indicating that the natural frequency of the mountain is related to factors such as the geometric shape of the mountain itself.
The particle motion displacement trajectory diagrams show that under different earthquake input, the maximum displacement amplitude of the mountain vibration can appear in the transverse or longitudinal direction of the mountain.
There exists the obvious polarization effect in the mountain vibration. The EW and NS acceleration records of the nine aftershocks were decomposed in 10° increments to obtain 324 new time histories. The amplification coefficients of the peak ground acceleration and the Fourier spectral ratio were analyzed for each decomposition angle. The orientation of the maximum peak acceleration amplification coefficient is basically the same as that of the maximum displacement amplitude of the mountain vibration, and the peak acceleration amplification coefficients of each decomposition angle have obvious polarization effects. The frequency bands of the nine aftershocks with the largest Fourier spectral ratios at different decomposition angles are relatively close to each other, and all of them are distributed in the frequency bands of 0.8−2.8 Hz, 7.8−10.2 Hz, and 11.5−16.0 Hz.
However, the angular range in which the extreme values of the Fourier spectral ratios are located varies from one aftershock to another, with aftershocks 1, 3, 4, and 9. For the Fourier spectral ratio in the low frequency band of 0.8−2.8 Hz, the maximum amplitude appears in the range of 110°−160° i.e. transverse direction of the mountain; in the middle and high frequency bands of 7.8−10.2 Hz, the maximum amplitude appears in the range of 30°−60° i.e. longitudinal direction of the mountain.
The seismic energy of the aftershocks 2, 5, 6, 7, and 8 is mainly concentrated in the mid- and high-frequency bands, and the maximum value of the spectral ratio is concentrated in the range of 30°−60° i.e. longitudinal direction of the mountain, which is more easily to stimulate of higher-order vibration modes of the mountain in this angular range, and the phenomenon is also roughly similar to that of the particle motion displacement trajectory diagrams and the orientation of polarization of the peak ground acceleration.
Considering the Fourier spectrum analysis of the nine aftershock records at the foot of the slope, we can obtain that the frequency content is different. The low frequency band is easy to stimulate the lower-order vibration mode of the mountain that leads to polarization in the transverse direction; the high-order vibration mode is easily stimulated by the high-frequency band that leads to polarization in the longitudinal direction of the mountain; the mountain can produce both low-order and high-order polarization effects when the low and high frequency exist at the same time. The maximum displacement amplitude of the mountain under the action of different earthquakes will appear in the transverse and longitudinal direction of the mountain, which is closely related to the spectral characteristics of the input earthquake. In the seismic design of large-scale structures such as bridges, tunnels and hydropower stations across mountain areas, the polarization effect of the mountain topography should be given priority consideration.