Abstract
The unified scaling law (also called the BCDS model), merges: (1) Omori’s Law, (2) Gutenberg-Richter’s law, and (3) the geometrical fractal distribution of epicenters, all of which, in combination, investigate the occurrence of earthquakes from a spatial-temporal perspective. This study plans to verify important questions arising from the definition of the BCDS model by doing three experiments. Firstly, we examine the feasibility of applying this model to Taiwan using different cell sizes and cut-off magnitudes. Secondly, we ascertain the difference between aftershocks and main shocks in a unified scaling law by comparing earthquake time sequences with declustered ones. Thirdly, we investigate the differences among scaling relationships obtained from various geological settings in Taiwan. Our results show that no matter how cell size and cut-off magnitude change, they produce a very similar pattern symbolizing the scaling law. Using a Z-map, after declustering, the constant part, which is an apparent indicator of the characteristics of aftershocks, disappears, and the slope of the fast decaying part, which corresponds to the main shock, remains almost the same. In addition, scaling laws obtained from four different sub-regions in Taiwan, although slightly different to each other, all show to be of a similar scaling law.
Highlights
The nature of the spatial-temporal phenomenon of earthquake occurrences is a complicated one
When we look at the relationship between earthquake occurrences from the point of view of time and space, the appearance of a power law can be deduced from the Gutenberg-Richter law (Gutenberg and Richter 1944)
In order to investigate the debate between Lindman et al (2005) and Corral (2006) about whether or not the distinction of correlated earthquakes and uncorrelated earthquakes causes a kink at Tcorr = 1 in the scaling law, we utilized real earthquake data rather than synthetic earthquake data created by simple mathematic modeling, making the exercise both more meaningful and practical
Summary
The nature of the spatial-temporal phenomenon of earthquake occurrences is a complicated one. It is easier as well as more important for seismologists to understand the correlation among earthquakes over a long period of time than to just study an individual isolated earthquake. The relationship between time and earthquakes according to Omori’s Law (Omori 1895) is such that the frequency of aftershocks decreases with time after a main shock, thereby precisely indicating the existence of a power law. When we look at the relationship between earthquake occurrences from the point of view of time and space, the appearance of a power law can be deduced from the Gutenberg-Richter law (Gutenberg and Richter 1944).
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