空间光滑地震活动性模型中光滑函数的比较研究

Comparison of the smoothing functions in the analysis of spatially smoothed seismicity

使用Frankel提出的基于空间光滑地震活动性模型的地震危险性分析方法,选择华南、华北、川滇3个地区的地震记录,比较分析了高斯、幂律和地震分形分布光滑函数3种光滑函数在不同地区的适用性.结果表明,使用交叉验证法可以为高斯光滑函数选取合适的相关距离c值,光滑得到的地震活动性模型能够真实反映研究区域的地震活动特征,根据活动性模型计算得出的峰值加速度(PGA)分布也符合人们对研究区域地震危险性的认识.幂律光滑函数适用于地震活动性较强的地区,且具有容易求取光滑参数的优点.光滑程度较低的幂律光滑函数不适用于地震活动性弱的地区,在该类地区应选择光滑程度较高的高斯光滑函数.地震分形分布光滑函数不适用于地震活动较强且地震活动强度差异较大的地区,其容易过分高估高震级地震对地震危险性的影响,而忽略了低震级地震对地震危险性的贡献.但对于地震活动较弱且地震活动强度差异较小的地区,可使用地震分形分布光滑函数,且同样具有容易求取光滑参数的优点.

Useing the method of spatially smoothed seismicity introduced by Frankel to compare the respective applicability of three smoothing functions, the Gaussian smoothing function, the power-law smoothing function and the seismic fractal distribution smoothing function, in three different regions, the southern China, northern China and Sichuan-Yunnan region, based on the in- strumental seismic records of these three regions. For the Gaussian smoothing function, a proper value of correlation distance c can be selected by cross-valida- tion method; the smoothed seismicity model can reflect the true characteristicsof seismic activity in the investigation regiona; the distribution of peak ground acceleration （PGA） calculated by using the seismicity model is consistent with the knowledge of seismic hazard analysis for the study regions. The power-law smoothing function is applicable for the region with relatively strong seismic ac- tivity~ it also has the advantage that the smoothing parameters are easily ac- quired. However, the less smoothed power-law smoothing function is not suit- able for the region with weak seismic activity, for such region the significantly smoothed Gaussian smoothing function should be selected. The seismic fractal distribution smoothing function is not applicable for the region with compara- tively strong seismic activity, or for the regions with large difference in level of seismic activity, because it tends to seriously overestimate the influence of high magnitude earthquakes on seismic hazard and ignore the contribution from low magnitude earthquakes. But for the region with comparatively weak seismic ac- tivity and small difference in activity level, the seismic fractal distribution smoothing function can be used effectively;it also has the same advantage as the power-law smoothing function that the quired. smoothing parameters are easily ac