Stochastic self-similarity of envelopes of high-frequency teleseismic P-waves from large earthquakes suggests fractal pattern for earthquake rupture

TL;DR

This study reveals that high-frequency seismic signals from large earthquakes exhibit self-similar, fractal-like structures, indicating complex space-time organization of earthquake rupture processes with consistent Hurst exponents around 0.8.

Contribution

It demonstrates the stochastic self-similarity in the envelopes of teleseismic P-waves from large earthquakes using variogram and spectral analyses, revealing fractal characteristics.

Findings

Hurst exponent H ranges from 0.71 to 0.80 from variograms

H ranges from 0.78 to 0.83 from spectral analysis

No dependence on station or frequency band observed

Abstract

High-frequency (HF) seismic radiation of large earthquakes is approximately represented by P wave trains recorded at teleseismic distances. Observed envelopes of such signals look random and intermittent, suggesting non-trivial stochastic structure. Variogram and spectral analyses were applied to instant power calculated from band-filtered observed P-wave signals from eight large (Mw=7.6-9.2) earthquakes, with 8-30 records per event and eight non-overvlapping frequency bands analyzed (total frequency range 0.6-6.2 Hz, bandwidth 0.7 Hz). Estimates for both variograms and power spectra look linear in log-log scale, suggesting in most cases self-similar correlation structure of the signal. The range for the individual-event values of the Hurst exponent H is 0.71-0.80 (averaged over bands and stations) when estimated from variograms, and 0.78-0.83 when estimated from spectra. No systematic dependence on station or frequency band was noticed. The values of H around 0.8 may be characteristic for large earthquakes in general. The result suggests that the space-time organization of earthquake rupture process has significant fractal features. Also, a useful constraint is established for application-oriented earthquake strong motion modeling.