Temporal power-laws in mechanical relaxation of rocks and afterslip associated with interplate earthquakes

Temporal variation in afterslip associated with interplate earthquakes is investigated using a constitutive law for mechanical relaxation (viscoelastic behavior) of rocks. This constitutive law is derived from non- equilibrium thermodynamics with internal state variables (i.e. state variables on irreversible processes such as brittle or ductile damage evolution and chemical processes) and represented by the relaxation modulus decaying with a power-law of deformation time. This temporal power-law appears as a collective dynamics of internal states having the respective relaxation times in various time-scales. The constitutive law can explain not only steady-state behavior of rocks but also transient behaviors in response to sudden changes in stress and strain-rate by the difference in exponent of the temporal power-law. Analyzing the time-series in afterslip (cumulative displacement) calculated from the seismic moments of small repeating earthquakes in the northeast Japan subduction zone, the variation in afterslip is described by a temporal power-law. This suggests that afterslip is a summation of lots of transient responses associated with various sizes of seismic events.