確率過程としてみた地震現象
1979 年 32 巻 3 号 p. 243-265
詳細
1979 年 32 巻 3 号 p. 243-265
The frequency of earthquake occurrence in a given region can be formulated as
dn(t)/dt=rn[1-(n/k)α]/α
where n(t) is the number of earthquakes per unit time, r, k and α are constants. Empirically determined values of α range from 0.67 to 1.0. This is a generalization of the modified Omori formula for aftershocks, the latter being an approximation of the former for n>>k. This formula adequately describes the initial increasing and latter decreasing activities during the Matsushiro and Wakayama swarms as well as aftershocks of large earthquakes.
When random external force is added to this system as a driving mechanism, the equation above becomes
dv(t)/dt=-r[1-exp(αv)]/α+R(t)
where v=ln(n/k) and R(t) is the random Gaussian noise. Repetitive seismic patterns with bursts, which are commonly observed in real earthquake sequences, are predicted from this formulation under stationary conditions. These formulations appear to be quite promising in helping to understand macroscopic features of microearthquake activities.
