Multifractal Scaling of Thermally-Activated Rupture Processes

Didier Sornette

Published 2005, SCEC Contribution #796

We propose a “multifractal stress activation'' model combining thermally activated rupture and long memory stress relaxation, which predicts that seismic decay rates after mainshocks follow the Omori law $\sim 1/t^p$ with exponents $ linearly increasing with the magnitude $ of the mainshock and the inverse temperature. We carefully test this prediction on earthquake sequences in the Southern California Earthquake catalog: we find power law relaxations of seismic sequences triggered by mainshocks with exponents $ increasing with the mainshock magnitude by approximately $0.1-0.15$ for each magnitude unit increase, from (M_L=3) \approx 0.6$ to (M_L=7) \approx 1.1$, in good agreement with the prediction of the<br>multifractal model.

Sornette, D. (2005). Multifractal Scaling of Thermally-Activated Rupture Processes. Physical Review Letters, 94(3), 038501.1-038501.4. doi: 10.1103/PhysRevLett.94.038501.