小震空间分在奇异性谱f（α）研究

The f(α) Singularity Spectrum of Spatial Distribution of Small Earthquakes

本文用数盒子法计算了１９７９年３月２日固镇５．０级、１９７４年４月２２日溧阳５．５级和１９７９年７月９日溧阳６．０级地震前后小震空间分布分形集合的奇异性谱ｆ（α），详细讨论了ｆ（α）谱所揭示的主震前后各阶段小震空间分布从稀疏到密集的各种密度分布不均匀性的定量特征。经分析可以看出，奇异性谱ｆ（α）较多重分形谱Ｄｑ的概念更直观、清晰，它包含了空间分布的全部信息，且计算量明显减少。

The f(α) singularity spectra of spatial distribution of small earthquakes around the Guzhen earthquake (Mar. 2, 1979, Ms=5. 0) and two Liyang earthquakes (Apr, 22, 1974,Ms= 5. 5 and Jul. 9, 1979, Ms=6. 0) have been calculated by the box-counting method.The results show that the f(α) spectrum can reveal quantitatively the global pattern of spatial distribution of seismic activities for various density profiles from dense to rare.Hence, the concept of singularity spectrum is more directly and straightforward perceived through the senses than the Dq multifractal dimension spectrum. It contains clearly all information about the variation of the spatial distribution of small shocks around the main earthquakes. However the algorithm calculating the f(α) spectrum given in this paper'consumes less computational resources and time than the usual determination via Dq calculation.