Multifractal Scaling of Thermally-Activated Rupture Processes

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 $p$ linearly increasing with the magnitude $M_L$ 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 $p$ increasing with the mainshock magnitude by approximately $0.1-0.15$ for each magnitude unit increase, from $p(M_L=3) \approx 0.6$ to $p(M_L=7) \approx 1.1$, in good agreement with the prediction of the multifractal model.