Title of research project: Clastering of seismicity: multifractal approach. Empirical study and modeling
Period of performance: 1995 to 1996
Principal Investigator: Dr. M. Shnirman
Total funds: US$ 6,000
In this project we planned to study clustering properties of the temporal distribution of aftershocks using a multifractal approach. The temporal distribution of aftershocks for Landers earthquake is investigated comparing with synthetic catalogs of aftershocks emulated by the self-exiting model. The main goal of the project is to find a relation between the global characteristics of the aftershock process, the internal parameters of the self-exiting model and the multifractal properties of the temporal clustering. The single-link clustering is used to obtain the distribution of clusters for different radiuses T. Generalized fractal dimensions D(q) are applied as characteristics of the multifractal properties of distribution of cluster sizes for each T. Self-exiting model described by Y.Ogata is compared with the aftershocks of Landers earthquake. Only temporal and magnitude distributions of events are investigated. The aftershock process is characterized by two global characteristics: b-value of the Gutenberg-Richter law, and a slope of temporal decreasing of number of aftershocks, described by the generalized Omori law.
We obtained that the distribution of sizes of temporal clusters for real and model aftershocks series has a multifractal behavior for radiuses of clustering from 15 minutes to 4 days. Number of events emulated by the self-exiting model has a strong variation for fixed inner parameters of the model. Variations of the number of aftershocks for earthquakes with similar magnitude of the main shock may have the same nature. We obtained a synthetic seria of aftershocks similar to the Landers seria of aftershocks for all visual characteristics of both temporal and magnitude distributions of events. The behavior of the multifractal spectrum D(q,T) calculated for the real and artificial distribution is similar for radiuses of clustering T from 15 minutes to 1 day. The temporal distribution of events in the self-exiting model is sufficiently determined by the inner parameters: p - the power of Omori law for intensity of the aftershocks simulation; A - the slope of magnitude-frequency relation in the simulation. We obtained that the global characteristics of the aftershock process may be the same for synthetic distributions with different p but the multifractal characteristics D(q,T) in this cases are different. Thus the behavior of D(q,T) function reflects better the inner parameters of the aftershocks appearance than the global characteristics of the temporal or magnitude distributions. We obtained that the multifractal spectrum $D(q,T)$ is indifferent to small variations of the inner parameter $A$ of emulation and independent on the choice of a realization if the number of events for a given time interval is approximately the same. The multifractal properties of the aftershocks clustering in time allow to apply the multifractal analysis as the best criteria to obtain synthetic distributions of aftershocks similar to the real aftershock series of strong earthquakes. This kind of simulations is useful for the problem of prediction of a strong aftershock and the total time of the aftershock activity.