Comparison of the smoothing functions in theanalysis of spatially smoothed seismicity

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 instrumental seismic records of these three regions. For the Gaussian smoothing function, a proper value of correlation distance c can be selected by cross-validation method; the smoothed seismicity model can reflect the true characteristics of seismic activity in the investigation regions; 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 activity; it also has the advantage that the smoothing parameters are easily acquired. However, the less smoothed power-law smoothing function is not suitable 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 comparatively 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 activity 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 smoothing parameters are easily acquired.