A physical basis for earthquakes based on the elastic rebound model

Abstract

abstract The elastic rebound model explaining seismological data quantitatively is derived by developing the original elastic rebound theory proposed by H. F. Reid. Assuming that the dislocation front propagates in one direction along the long axis of the fault plane, the shear strain drop Δɛ, the earthquake volume V, the stiffness of the fault, the mass of inertia, and the seismic energy radiated Es are evaluated in terms of the fault-plane dimensions, the dislocation D, the propagating velocity of dislocation v, and the Shear-wave velocity. The elastic strain energy released is evaluated in terms of V, Δɛ, and the initial shear strain. It is shown that the order of magnitude of Es is virtually given by μWD2, where μ is the rigidity and W is the fault width. The order of magnitude of the initial slip acceleration is estimated by making use of the formula derived in a previous paper. The moment of the elastic rebound force is calculated. The maximum amplitude of the far-field wave motion is in proportion to vM0/L, where M0 is the seismic moment and L is the fault length: this predicts that log (M0/L) is linearly related to the magnitude M, if v is assumed to be almost constant for actual earthquakes. The good linear relation, log (M0/L) = 1.2M + 11.7 (M0/L in dynes), is found empirically over a wide range of M (2 ≦ M ≦ 8.5). The directly proportional relationship between the logarithm of seismic moment per unit area and the magnitude seems to hold empirically.