General Description of the Complex Faulting Process and Some Empirical Relations in Seismology.

Abstract

A theory of the complex faulting process of large earthquakes has been developed. The faulting process is characterized by a deterministic source of coherent rupture on a fault plane as well as by a stochastic source of incoherent ruptures in fault heterogeneous areas. The theory provides an earthquake source spectrum of the complex faulting process in a general manner: Theoretical representations of strong-motion acceleration, total power of acceleration, seismic energy, seismic-wave energy, surface-wave magnitude and body-wave magnitude are derived in terms of deterministic and stochastic source parameters. A low-frequency approximation of the source spectrum provides the description of the deterministic source by parameters of seismic moment, fault length, fault width, fault dislocation, stress drop, dislocation velocity, and rupture propagation velocity. Meanwhile, a high-frequency approximation provides the description of the stochastic source by patch corner frequency, cutoff frequency, variance of stress drop, and variance of dislocation velocity. The present theory of the complex faulting process is constrained empirically against observations. It is shown that empirical relations between seismic moment, fault dimension, seismic energy, and earthquake magnitude are the manifestation of similarity rules among source parameters of the complex faulting process: The geometrical similarity is for the fault shape, the kinematical similarity is for the dislocation and rupture velocities, the dynamical similarity is for the average stress drop, and a new similarity rule, stochastic similarity is derived for the stochastic source parameters. The complex faulting process thus far constrained fully explains the general properties of large earthquakes along subduction zones.