Earthquakes: Recurrence and Interoccurrence Times
Abaimov, S G University of California, Department of Geology, One Shields Ave., Davis, CA 95616 United States
Turcotte, D L - University of California, Department of Geology, One Shields Ave., Davis, CA 95616 United States
Shcherbakov, R - University of California, Department of Geology, One Shields Ave., Davis, CA 95616 United States
Rundle, J B - University of California, Center for Computational Science and Engineering, One Shields Ave., Davis, CA 95616 United States
There is accumulating evidence that the Weibull (stretched exponential) distribution has universal applicability to complex self- organizing phenomena. In this paper we discuss the statistical istributions of recurrence and interoccurrence times of earthquakes. Interoccurrence times are the time intervals between successive earthquakes in a specified region with magnitudes greater than a specified value. We argue that these earthquakes occur randomly although they may have a time dependent driver such as Omori's law. Recurrence times are the time intervals between successive earthquakes at a specified location on a specified fault. We argue that the statistical distribution of recurrence times is Weibull. The reason for this is that the Weibull distribution is the only distribution that has a scale invariant hazard function. The hazard function h(t_0) is the probability that an earthquake will occur at a time t 0 after the last earthquake. For a Weibull distribution h(t)~ t_0β-1 we consider two sets of characteristic earthquakes on the San Andreas fault: 1) the Parkfield earthquakes and 2) the sequence of earthquakes identified by paleoseismic studies at the Wrightwood site. In each case we make comparison with the applicable Weibull distribution. The numbers of earthquakes in each of these sequences are too small to make definitive conclusions. To overcome this difficulty we consider a sequence of earthquakes obtained from a one million year "Virtual California" simulation of San Andreas earthquakes. Very good agreement with a Weibull distribution is found. We also simulate this behavior using a slider-block model. The behavior of this model is sensitive to the stiffness α of the system, α=k_c/k_L, where k_c is the spring constant of the connector springs and k_L is the spring constant of loader springs. For a soft system (small α ) there are no system wide events and the interoccurrence time statistics of large events is Poissonian. For a stiff system (large α ) system wide events dominate the energy dissipation and the statistics of the recurrence times between the system wide events satisfy the Weibull distribution to a good approximation.
