Gleb Yakovlev

Model for the Distribution of Aftershock Interoccurrence Times

In this work the distribution of interoccurrence times between earthquakes in aftershock sequences is analyzed and a model based on a nonhomogeneous Poisson (NHP) process is proposed to quantify the observed scaling. In this model the generalized Omoris law for the decay of aftershocks is used as a time-dependent rate in the NHP process. The analytically derived distribution of interoccurrence times is applied to several major aftershock sequences in California to confirm the validity of the proposed hypothesis.

Simulation-Based Distributions of Earthquake Recurrence Times on the San Andreas Fault System

Earthquakes on a specified fault (or fault segment) with magnitudes greater than a specified value have a statistical distribution of recurrence times. The mean recurrence time can be related to the rate of strain accumulation and the strength of the fault. Very few faults have a recorded history of earthquakes that define a distribution well. For hazard assessment, in general, a statistical distribution of recurrence times is assumed along with parameter values. Assumed distributions include the Weibull (stretched exponential) distribution, the lognormal distribution, and the Brownian passage-time (inverse Gaussian) distribution. The distribution of earthquake waiting times is the conditional probability that an earthquake will occur at a time in the future if it has not occurred for a specified time in the past. The distribution of waiting times is very sensitive to the distribution of recurrence times. An exponential distribution of recurrence times is Poissonian, so there is no memory of the last event. The distribution of recurrence times must be thinner than the exponential if the mean waiting time is to decrease as the time since the last earthquake increases. Neither the lognormal or the Brownian passage time distribution satisfies this requirement. We use the “Virtual California” model for earthquake occurrence on the San Andreas fault system to produce a synthetic distribution of earthquake recurrence times on various faults in the San Andreas system. We find that the synthetic data are well represented by Weibull distributions. We also show that the Weibull distribution follows from both damage mechanics and statistical physics.

A damage-mechanics model for fracture nucleation and propagation

In this paper a composite model for earthquake rupture initiation and propagation is proposed. The model includes aspects of damage mechanics, fiber-bundle models, and slider-block models. An array of elements is introduced in analogy to the fibers of a fiber bundle. Time to failure for each element is specified from a Poisson distribution. The hazard rate is assumed to have a power-law dependence on stress. When an element fails it is removed, the stress on a failed element is redistributed uniformly to a specified number of neighboring elements in a given range of interaction. Damage is defined to be the fraction of elements that have failed. Time to failure and modes of rupture propagation are determined as a function of the hazard-rate exponent and the range of interaction.