Approximate Stochastic Self-Similarity of Envelopes of High-Frequency Teleseismic P-Waves from Large Earthquakes

Abstract

A wavetrain of high-frequency (HF) P waves from a large earthquake, when recorded at a distant station, looks like a segment of modulated noise, with its duration close to the duration of rupture. These wavetrains, with their bursts and fadings, look much more intermittent than a segment of common stationary random noise. We try to describe quantitatively this bursty behavior. To this end, variogram and spectral analyses are applied to time histories of P-wave envelopes (squared-amplitude or instant-power signals) in six HF bands of 1-Hz width. Nine M w = 7.6-9.2 earthquakes were examined, using, in total, 232 records and 992 single-band traces. Variograms of integrated instant power are approximately linear on a log-log scale, indicating that the correlation structure of the instant-power signal is approximately self-similar. Also, estimates of the power spectrum of the instant-power signal look approximately linear on a log-log scale. Log-log slopes of the variograms and spectra deliver estimates of the Hurst exponent H that are mostly in the range 0.6-0.9, markedly above the value H = 0.5 of uncorrelated (white-noise) signals. The preferred estimate over the entire data set is H = 0.83, still, this estimate may include some bias, and must be treated as preliminary. The inter-event scatter of H estimates is about 0.04, reflecting individual event-to-event variations of H. Many of the average log-log spectral plots show slight concavity that perturbs the approximately linear slope; this is a secondary effect that seems to be mostly related to the limited bandwidth of the data. Evidence is given in support of the idea that the observed approximately selfsimilar correlation structure of the P-wave envelope originates in a similar structure of the body wave instant-power signal radiated by the source, so that the propagation-related distortions can be regarded as limited. The facts presented suggest that the spacetime organization of the earthquake rupture process is multiscaled and bears significant fractal features; it deviates from the brittlecrack model with its two well-separated characteristic scales. Phenomenologically, the high-frequency body-wave radiation from an earthquake source can be thought of as a product of stationary noise and the square root of a positive random envelope function with a power-law spectrum. From the viewpoint of applications, the self-similarity of body wave envelopes provides a useful constraint for earthquake source models used to simulate strong ground motions.

The evolving interaction of low-frequency earthquakes during transient slip

“…In contrast, rapid slip during the rupture of the large earthquakes that define the seismic cycle shows a clear clustering in high-frequency radiation. Such clustering has been suggested to represent organized pulses from interacting asperities ( 26 ). This parallel between “fast” and “slow” earthquakes implies a universal clustered rupture process that operates over very different scales in both time and space.…”