It is shown that Ishimoto-Iida's formula, n(a)da=ka^-mda, for the frequency distribution of earthquakes with respect to the maximum amplitude of earthquake motion at a certain observation station is derived from a deformation-fracture relation.
The number of earthquakes is assumed, as a deformation-fructure relation, to be proportional to the curvature of the plastic deformation of the medium. The frequency distribution of earthquakes with respect to the amplitude of earthquake motion, n(a)da, is assumed to be proportional to the distribution of the earthquakes with respect to the wave number k of the plastic deformation, n(k)dk.
Assuming further that the amplitude of earthquake motion is inversely proportional to the wave number of plastic deformation, which is a kind of the radiation relation, n(k)dk is transformed to n(a)da. Thus, n(a)da is derived from the plastic deformation of the medium.
The power function representation of n(a)da=ka^-mda of Ishimoto-Iida's formula is due to the power function representation for the spectrum of plastic deformation of the medium. The coefficient m indicates the sharpness of the spectrum of the deformation.
It is discussed that Ishimoto-Iida's formula is not a probability distribution of earthquake occurrence, but a causual physical law between the plastic deformation and the number of earthquakes.