Analytical Solution of “Go-Game Model” of Earthquake

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  • 地震の“碁石モデル”の解析解
  • ジシン ノ ゴイシ モデル ノ カイセキカイ
  • Analytical Solution of “Go-Game Model” of Earthquake

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Abstract

Otsuka (1971, 1972) proposed a stochastic earthquake model, “Go-Game Model, ” in which an earthquake was simulated by a series of ruptures controled by a simple stochastic law. Using Monte Carlo technique, he demonstrated that the magnitude-frequency relation of earthquakes expected from this model was in good agreement with the observed one. We study this model in terms of probability generating functions and derive an analytical expression for the final size distribution of ruptured area. It is shown that Ishimoto-Iida's relation, or Gutenberg-Richter's relation, is a limiting distribution of this model.

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