Mathematical Consideration on the Earthquake Source Process (2)

A Fractal Source Model and Seismic Spectra

Abstract

A fractal model of the earthquake source and the spectral structure of seismic waves are considered. This study generalizes conventional spectral models of seismic waves and also takes account of the fractal nature in the focal process. Presented source model consists of numerous unit point sources, whose spatial distributions show the fractal structure like dendritic and Levý flight type. Interestingly, the fractal structure or power law type frequency dependence ω^h is obtained in the amplitude spectra of seismic waves from this source model. Here the exponent value h characterizes physical properties of the earthquake source. More high frequency abundant spectra are expected from this fractal model than conventional source models, which explains observed behavior of high frequency components of seismic waves that cannot be well explained by the conventional models. Analysis also shows the absence of corner frequencies in the amplitude spectra in the case of the fractal source that represent the characteristic space-time scales, although they have been generally expected in the ordinary spectral models.