A Relation between the Area of After-shock Region and the Energy of Main-shock

The after-shock regions of 39 shallow earthquakes which took place in and near Japan (Table 1) are determined and the relation between thier areas and the magnitudes or energies of main-shocks is investigated. If we assume that the logarithm of the area A (km2) and the magnitude M are in linear relation, i. e., logA=aM+b (Fig. 2-3), the constants a and b become as follows, a=1.02±0.08, b=-4.01±0.57 (for 39 total earthquakes)a=0.93±0.08, b=-3.18±0.61 (for 23 oceanic earthuakes)a=0.85±0.10, b=-3.05±0.72. (for 16 land earthquakes)From the relation between M and E (erg), we get A∝Em, where m≈1/2, then E/A∝A∝√E, this means that the surface density of energy increases as the energy increases.