Source Spectra of Near Kamchatka Earthquakes: Recovering them from S-Wave Spectra, and Determination of Scaling for Three Corner Frequencies

Abstract

We describe a procedure for mass determination of the “source-controlled f _max”—an important though not conventional parameter of earthquake source spectrum, relabeled here as “the third corner frequency,” f _c3, and discuss the results of its application. f _max is the upper cutoff frequency of Fourier acceleration spectrum of a record of a local earthquake; both source and path attenuation contribute to f _max. Most researchers believe the role of attenuation (“κ” parameter) to be dominating or exclusive. Still, source effect on f _max is sometimes revealed. If real, it may be important for source physics. To understand better the f _max phenomena, the constituents of f _max must be accurately separated. With this goal, we process seismograms of moderate earthquakes from Kamchatka subduction zone. First, we need reliable estimates of attenuation to recover source spectra. To this goal, an iterative processing procedure is constructed, that adjusts the attenuation model until the recovered source acceleration spectra become, on the average, flat up either to f _c3, or up to the high-frequency limit of the frequency range analyzed. The latter case occurs when f _c3 is non-existent or unobservable. Below f _c3, the double-corner source spectral model is thought to be valid, and the lower bound of acceleration spectral plateau is considered as the second corner frequency of earthquake source spectrum, fc2. The common corner frequency, f _c1, is also estimated. Following this approach, more than 500 S-wave spectra of M = 4–6.5 Kamchatka earthquakes with hypocentral distances 80–220 km were analyzed. In about 80 % of the cases, f _c3 is clearly manifested; the remaining cases show, at high frequency, flat source acceleration spectra. In addition, in about 2/3 of cases, f _c2 is clearly above f _c1, showing that double-corner spectra may dominate even at moderate magnitudes. Scaling behavior was examined for each of the corners. The f _c1 vs. M ₀ trend is common and close to similarity (f _c1 ∝ M ^−1/3₀ ), whereas the trends for two other corners (f _c2 ∝ M ^−0.17₀ ; f _c3 ∝ M ^−0.11₀ ) dramatically contradict the concept of similarity. Physical interpretation of such a behavior is discussed. The origin of f _c3 is ascribed to existence of the lowermost wavelength/size of fault heterogeneity. Its dependence on M ₀ may reflect evolution of maturity of a fault in geological time. The approximate scaling f _c2 ∝ $f_{c1}^{0.5}$ suggests that during propagation of slip pulse over a fault, its width, assumedly related to 1/f _c2, grows in a stochastic manner; this reminds the random evolution of propagating boundary in the framework of the known Eden model of random growth.