Earthquake similarity laws

Source parameters of 27 major shallow earthquakes in the magnitude range 7.0–8.6, which occurred during 1906–1969, are used to establish dimensionless invariants involving the fault dimensions, average slip, and the rise time. It is found that these entities are expressible as simple functions of the subsonic shear Mach number (M) and the cube root of the seismic potency, $\text{(}\text{U}\text{S)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$. Moreover, a new principle is suggested according to which all dimensionless numbers which can be constructed from the basic fault elements are simple powers of the contraction factor $\text{(1-M}{}^2\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ with coefficients of the order unity. The laws of dynamical similarity thus found are those appropriate for subsonic rupture in which the Mach number is very close to unity and the radiation efficiency is between $\text{1}\text{6}$ and $\text{1}\text{3}$. The empirical similarity laws are shown to be compatible with a source model in which the fault plane is simulated by a flexible membrane with additional restoring stiffness forces provided by an elastic medium attached to it on one side. Results suggest the possibility that earthquake rupture, together with the radiation of seismic waves, terminates at the moment that Mach 1 is reached.