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

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 self-similar 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 space–time organization of the earthquake rupture process is multiscaled and bears significant fractal features; it deviates from the brittle-crack 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.