Multifractal Scaling of Thermally Activated Rupture Processes

Abstract

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 approximately 1/t(p) with exponents p linearly increasing with the magnitude M(L) of the mainshock. 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) approximately 0.6 to p(M(L) = 7) approximately 1.1, in good agreement with the prediction of the multifractal model.