Search

Observed high-frequency (HF) radiation from earthquake faults exhibits specific properties that cannot be deduced or extrapolated from low-frequency fault behavior. In particular: (1) HF time functions look like random signals, with smooth mean spectrum and moderately heavy-tailed probability distribution function for amplitudes; (2) well-known directivity of low-frequency radiation related to rupture propagation is strongly reduced at HF, suggesting incoherent (delta-correlated) behavior of the HF radiator, and contradicting the usual picture of a rupture front as a regular, non-fractal moving line; (3) in the spectral domain, HF radiation occupies a certain specific band seen as a plateau on acceleration source spectra $$ K(f) = f^{2} \dot{M}_{0} (f) $$. The lower cutoff frequency f of K(f) spectra is often located significantly higher than the common spectral corner frequency f, or f. In many cases, empirical f( M) trends are significantly slower as compared to the simple f ∝ M, testifying the lack of similarity in spectral shapes; (4) evidence is accumulating in support of the reality of the upper cutoff frequency of K(f): fault-controlled f, or f. However, its identification is often hampered by such problems as: (a) strong interference between f and site-controlled f; (b) possible location of f above the observable spectral range; and (c) substantial deviations of individual source spectra from the ideal spectral shape; (5) intrinsic structure of random-like HF radiation has been shown to bear significant self-similar (fractal) features. A HF signal can be represented as a product of a random HF 'carrier signal' with constant mean square amplitude, and a positive modulation function, again random, that represents a signal envelope. It is this modulation function that shows approximately fractal behavior. This kind of behavior was revealed over a broad range of time scales, from 1 to 300 s from teleseismic data and from 0.04 to 30 s from near-fault accelerogram data. To explain in a qualitative way many of these features, it is proposed that rupture propagation can be visualized as occurring, simultaneously, at two different space-time scales. At a macro-scale (i.e. at a low resolution view), one can safely believe in the reality of a singly connected rupture with a front as a smooth line, like a crack tip, that propagates in a locally unilateral way. At a micro-scale, the rupture front is tortuous and disjoint, and can be visualized as a multiply connected fractal 'line' or polyline. It propagates, locally, in random directions, and is governed by stochastic regularities, including fractal time structure. The two scales and styles are separated by a certain characteristic time, of the order of (0.07-0.15) × rupture duration. The domain of fractal behavior spans a certain HF frequency range; its boundaries, related to the lower and upper fractal limits, are believed to be manifested as f and f. [ABSTRACT FROM AUTHOR]

For any earthquake, the slipping fault and the source of high-frequency seismic waves, by and large, coincide. On a more local scale, however, the areas of high seismic slip rate and of increased high-frequency radiation output (seismic luminosity) need not match. To study in some detail how slip rate and seismic luminosity are interrelated, a systematic study is performed that uses 251 records of teleseismic P waves from 23 intermediate-depth earthquakes of magnitude 6.8 and above. From a broadband trace we extract two time histories: (1) displacement and (2) 0.5–2.5 Hz band-passed and squared velocity, or ``HF power'', and calculate correlation coefficient, ρ between the two. To reduce the bias related to formation of P coda, a special procedure is applied to data. We estimated the average value ρ = 0.52 (range of event averages 0.35 to 0.65) for the correlation coefficient between the radiated time histories for displacement and ``HF power'', which is considerably below the ``ideal'' value of unity. We argue that the same or even lower value characterizes the degree of slip rate - seismic luminosity correlation at the fault. Two factors may contribute to the revealed decorrelation: (1) random fluctuations of observed HF power (inevitable for a signal with a limited bandwidth), and (2) the genuine mismatch of slip rate and mean luminosity. We show that these factors, acting separately, would result in the ρ values equal to, correspondingly, 0.72 and 0.80. We also show that genuine decorrelation is statistically significant. We conclude that the observed values of ρ indicate genuine differences between the distributions of the slip rate and the seismic luminosity over the fault area. These results provide important constraints both for the accurate wide-band simulation of strong ground motion and for theoretical dynamic source models. [ABSTRACT FROM AUTHOR]