TRANSITION PROCESS FROM NUCLEATION TO HIGH-SPEED RUPTURE PROPAGATION - SCALING FROM STICK-SLIP EXPERIMENTS TO NATURAL EARTHQUAKES

The process of earthquake generation is governed by a coupled non-line ar system consisting of the equation of motion in elastodynamics and a fault constitutive relation. On the basis of the results of stick-sli p experiments we constructed a theoretical source model with a slip-de pendent constitutive law. Using the theoretical source model, we simul ated the transition process numerically from quasi-static nucleation t o high-speed rupture propagation and succeeded in quantitatively expla ining the three phases observed in stick-slip experiments, that is ver y slow (1 cm s(-1)) quasi-static nucleation preceding the onset of dyn amic rupture, dynamic but slow (10 m s(-1)) rupture growth without sei smic-wave radiation. and subsequent high-speed (2 km s(-1)) rupture pr opagation, Theoretical computation of far-field waveforms with this mo del shows that a slow initial phase preceding the main P phase expecte d from a classical source model is radiated in the accelerating stage from the slow dynamic rupture growth ts the high-speed rupture propaga tion. On the assumption that the physical law governing rupture proces ses in natural earthquakes is essentially the same as that in stick-sl ip events, we scaled the theoretical source model explaining the stick -slip experiments to the case of natural earthquakes so that the seale d source model explains the observed average stress drop, the critical nucleation-zone size, and the duration of the slow initial phase well . The physical parameters prescribing the source model are the weak-zo ne size L, the critical weakening displacement <(D)over bar (c)>, the breakdown strength drop <(tau)over bar (b)>, and the rigidity mu of th e surrounding elastic medium. In scaling these parameters, we held a n on-dimensional controlling parameter mu' = (<mu(D)over bar (c)>)/(<((t au))over bar L-b>) in numerical simulation constant, From the results of scaling we found the following fundamental relations between the so urce parameters: (1) the critical weakening displacement <(D)over bar (c)> is in proportion to the weak-zone size L, but (2) the breakdown s trength drop <(tau)over bar (b)> is independent of L.