Characteristic scale of heterogeneity of seismically active fault and its manifestation in scaling of earthquake source spectra

Abstract

Previously, similarity of source spectra of Kamchatka earthquakes with respect to the common corner frequency fc1 and the expressed deviations from similarity for the second fc2 and the third fc3 corner frequencies were revealed. The value of fc3 reflects the characteristic size Lis of fault surface; correspondingly, Lis ≈ vrTis, where vr is the rupture speed and Tis ≈ 1/fc3 is characteristic time. The estimates of fc3 are used for normalizing fc1 and fc2. In this way one obtains dimensionless rupture temporal parametres τ1 and τ2 and can further study the dependence τ2 (τ1). The growth of a rupture is considered as a process of aggregation of elementary fault spots of the size Lis. The dimensionless width of the random front of aggregation is on the order of τ2. The relationship τ2 (τ1) approximately follows power law with exponent β. The estimates of β derived from earthquake populations of Kamchatka, USA and Central Asia (β = 0.35–0.6) agree with values expected from the known Eden’s theory of random aggregation growth and from its generalizations.