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.

Relationships Among Magnitudes and Seismic Moment of Earthquakes in the Taiwan Region

“…Kanamori and Anderson (1975) Equations (2) and (11) both suggest log(M o ) ~ 2 m b . This observed correction is inconsistent with the theoretical correlation: log(M o ) ~ 2.5 m b proposed by Koyama (1994) for three kinds of distributions of peak and trough amplitudes. Hence, his proposition is questionable and needs further study for exploring the theoretical relationship between M o and m b .…”

“…Geller (1976) . Koyama (1994) However, the relationships should be of regional dependence (cf. Chung and Bernreuter 1981).…”

Complex earthquake rupture and local tsunamis

“…While the stochastic source provides a unified model with which to predict seismic ground motions as well as tsunami amplitudes, it is important to note that different components of the source wave number spectrum control generation for each wave type. Seismic waves emanating from discrete fault patches or quanta [e.g., Rundle and Kanamori, 1987;Koyama, 1994;Rydelek and Sacks, 1996] are primarily controlled by the high wave number, k À2 decay part of the spectrum, whereas as shown in this study, the local tsunami waves emanating from coseismic vertical displacement transferred to the water column are primarily controlled by the low wave number part of the spectrum near the corner wave number k c .…”

“…Several authors have demonstrated that the ω −2 falloff in the seismic source spectrum for frequencies higher than the corner frequency and the b value for aftershocks is derived from a self‐similar mode of rupture [ Hanks , 1979; Andrews , 1980; Fukao and Furumoto , 1985; Huang and Turcotte , 1988; Frankel , 1991; Koyama , 1994; Bernard et al , 1996]. The ω −2 model [ Aki , 1967] is best explained by self‐similar irregularities in either the initial stress or the static stress drop distribution [ Andrews , 1981; Huang and Turcotte , 1988; Frankel , 1991; Tsai , 1997], indicating that fault strength is scale invariant or that stress drop scaling is constant.…”

“…For example, Boatwright and Choy [1992] indicate for continental earthquakes the existence of a second corner frequency such that the falloff for intermediate frequencies is approximately γ = 1.5, whereas for the highest frequencies γ = 2.0. Koyama [1994] suggests that the first corner frequency relates to the entire rupture process, whereas the second corner frequency reflects the average rupture characteristics of individual fault patches. The stochastic source model can be adjusted to incorporate different values of γ, according to equation (6).…”