山脊线与坡度和峰值速度放大系数的相关性研究

A study on the correlation of ridge line and slope with Peak Ground Velocity amplification factor

地形效应是地震工程和地震学的重要研究内容.数值方法是研究地形效应的重要工具.然而以往关于地形特征对地形效应的影响的研究大多是基于二维简单模型.对三维真实地形特征和地震动放大的关系缺乏详细的研究.为了更好地描述三维地形特征,本文将地形用不同的地形特征因子来描述,并用算法将它们从地形数据中提取出来.从而使地形和放大系数的相关性的研究转换为不同地形特征因子和放大系数的相关性的研究上.本文中,我们选择芦山地区作为研究对象,用算法提取出特征因子山脊线和坡度.它们分别表征了山脊形态和山体的陡峭程度.我们又用谱元法分别模拟三种不同主频Ricker子波的地震波在起伏地表和水平地表模型中的传播,并得到了它们各自的峰值速度(PGV)放大系数.通过分析三个主频的PGV放大系数在山脊线上分布,我们发现放大系数幅值在山脊线上分布不均匀.放大系数较高的地方位于山脊线弯曲或宽度发生变化的附近.我们又统计了三个放大系数在滑动平均坡度上分布,并得到了放大系数均值和坡度的正相关曲线.结果表明坡度和放大系数两者在幅值分布上具有正相关性.

This article uses Spectral-Element Method（SEM）to calculate Peak Ground Velocity amplification factor,and uses ridge line and slope to quantify topographic characters.We use SEM to simulate the 3-D wave propagation in Lushan region.The size of the region is 120×110km horizontally and 50 km in depth.The hypocenter is determined by the 20 th April 2014 Lushan earthquake.To reduce complexity,we choose horizontal layered medium and an explosive source with Ricker wavelet time function.For time function,three dominant frequencies of 0.8,1.2,1.5Hz are chosen in the simulation.In order to separate topographic effects,two models are considered：one model incorporates topography of Lushan area and the other uses flat surface.The surface elevation of the first model is defined based on Gtopo30.Simulated ground motion of each model is obtained and their Peak Ground Velocity（PGV）are computed.The PGV amplification factor is calculated by dividing PGV in flat model by PGV in topographic model.This amplificationfactor is used to quantify the difference of PGV.Next,we extract ridge line and slope,two topographic variables,from the Digital Elevation Model and study their correlation to PGV amplification factor.The first topographic character is ridge line,which represents mountain structure.It is extracted by using CATCH,aprogram for measuring catchment area.A surface point with flow accumulate value larger than a threshold is classified as ridge line point.The second character is slope,which quantifies the steepness of a mountain.It is obtained by a thirdorder finite difference method in a moving 3×3window.We first study the correlation between ridge lines and PGV amplification factor.Then the relationship between amplification factor and slope is analyzed in four selected zones.Additionally,the moving average slope is obtained by averaging slope values of surface points within a moving window.We then count the average value of amplification factor in each average slope interval.This average factor allows us to quantify its correlation with average slope.Firstly,we compare PGV distributions generated by point source with 1.5 Hz dominant frequency in two models：PGV in the flat model shows that large values are found in areas close to the epicenter.In the model with Lushan topography,complex PGV patterns occur in mountainous areas and their values are amplified compared with surrounding areas.Secondly the PGV amplification factor illustrates that amplification factor on mountain tops or ridges has large value.This means PGV is increased at mountain tops.Especially,at some mountain tops,amplification factor could be larger than 1.6.The valley reduces PGV value and the corresponding amplification factor is less than 1.0.In some parts,amplification factor is less than 0.4.Thirdly,we analyze PGV amplification factors of the three frequencies on ridge lines.All of them show uneven distribution,and large values often occur in the following cases：the first case is in the places where ridge lines fork.Often in this case,wide ridge lines develop into narrow branches.The second case is the converge of ridge lines.The ridge lines in this case develop into wider lines.The third case is more complicated.The width of the ridge lines changes with the occurrence of new branches or curved trend in extension. Fourthly, we analyze PGV amplification factor distribution on slope.Observation in four selected zones indicates that PGV amplification factor has positive correlation to the value of slope.To quantify this correlation,we calculate the average amplification factor of three frequencies based on the moving average slope.All three curves show positive correlation.The curve corresponding to 1.5Hz dominant frequency shows the strongest correlation,while results from 0.8Hz show weakest correlation.This phenomena indicates that topographic effect resulted from different dominant frequencies have different degrees of correlation.Especially,in the 1.5Hz case,the average amplification factor increases from 1.03 to 1.38 along the positive direction of moving average slope.Our numerical simulation of three dominant frequencies 0.8,1.2,1.5Hz show that surface irregularity strongly changes PGV values.It is very important to take the effect of real topography on ground motion into account when assessing hazard analysis.To further validation,numerical simulations in different area with more realistic models are needed and other topographic characters should also be taken into account.