Comparison between Utsu's and Vere-Jones' aftershocks model by means of a computer simulation based on the acceptance–rejection sampling of von Neumann

• A new algorithm for generating a stochastic earthquake catalog.
• Comparison between Utsu's and Vere-Jone's aftershock model.
• A new criterion for measuring the randomness of the earthquake series.

In this research, a new algorithm for generating a stochastic earthquake catalog is presented. The algorithm is based on the acceptance–rejection sampling of von Neumann. The result is a computer simulation of earthquakes based on the calculated statistical properties of each zone. Vere-Jones states that an earthquake sequence can be modeled as a series of random events. This is the model used in the proposed simulation. Contrariwise, Utsu indicates that the mainshocks are special geophysical events. The algorithm has been applied to zones of Chile, China, Spain, Japan, and the USA. This allows classifying the zones according to Vere-Jones' or Utsu's model. The results have been quantified relating the mainshock with the largest aftershock within the next 5 days (which has been named as Bath event). The results show that some zones fit Utsu's model and others Vere-Jones'. Finally, the fraction of seismic events that satisfy certain properties of magnitude and occurrence is analyzed.