[S-SS29_28PM1] Earthquake Source Processes and Physics of Earthquakes

[SSS29-07] Similar Characteristics between the earthquake source process and Vere-Jones' Branching model

Jiancang ZHUANG¹, *Dun WANG² (1.Institute of Statistical Mathematics, 2.Earthquake Research Institute, University of Tokyo)

Keywords:Branching process, Gutenberg-Richter Magnitude-Frequency Relation, Tapered Pareto distribution, Earthquake source

Vere-Jones' branching crack model was develop in 1970s. In this model, the earthquake source is regarded as the results of the total population of crack elements in a critical or near-critical branching process, where the crack does not propagate in a single continuous movement, but through a series of steps. At each step, each crack element simply terminates or generates several other crack elements nearby. Regarding the total number of steps (generation) as the duration time and the total number of crack elements as the total energy released, the following similarities are found between earthquake sources and this model:1. The distribution of energies is asymptotically a Pareto distribution (power law) for the critical case, or a tapered Pareto distribution (tapered power law, Kagan distribution) for the subcritical case. 2. The duration time of ruptures has a tapered inverse power distribution. 3. The number of crack elements at each generation (time step) show similar patterns of earthquake source time functions.Figure 1 (a) and (b): Plots of the numbers of crack elements at each time step in two simulation examples. (c): Distribution of half duration times in real earthquake catalog. (d): Distribution of duration times in synthetic catalogs.