A Simple Analogue Experiment to Account for Power-law and Exponential Decays of Earthquake Sequences

An event rate decays either exponentially in earthquake swarms, or according to the power law in aftershock sequences, suggesting different physics for these decays. In order to investigate the physics, I measured decays in the rate of acoustic emissions (AE) that occur to relax thermal stress after turning off a home cooking apparatus. Such AE are analogous to an earthquake induced by fluid intrusion because thermo-elasticity was precisely analogous to poro-elasticity. To consider what controlled the decays, different heating rates and durations were specified in several experimental runs for which the mechanical and thermal properties were identical. Temperature decayed exponentially with the same time constant. However, both a power-law decay with a p value roughly equal to two and an exponential decay were observed. To ascertain what was occurring at the AE source, the stress and frictional strength at the AE source were numerically estimated. The stress at the AE source decayed exponentially for both power-law decay and exponential decay. In power-law decay, strength was initially very low and recovered immediately and significantly. However, in exponential decay, the change in strength during the initial stage was not as large as that in power-law decay. It was demonstrated that the time constant of exponential event-rate decay was identical to that of temperature decay if strength is constant.