Magnitude determination for deep-focus earthquakes*

Abstract

Summary The magnitude of deep-focus earthquakes is so defined as to make the energy released in two shocks of the same magnitude equal, regardless of focal depth.—Charts are given which, in connection with the equations for the magnitude of shallow shocks, permit the calculation of the magnitude of a shock at any given depth if the maximum ground amplitude and the corresponding wave period of P, PP, or S at a given epicentral distance are known.—It is found that the energies released in the longitudinal and transverse waves of an earthquake are about equal, regardless of focal depth.—The “shadow zone” for P and S waves at epicentral distances near 10°, indicating a slight minimum in wave velocity at a depth near 100 km., has been confirmed, and quantitative results for amplitudes of P as a function of focal depth are given.—Earthquake magnitudes of 7 ¾ to 8 have been found throughout the range of focal depths, but, during the past forty years, seem to have been relatively less frequent in deep-focus than in shallow shocks. In contrast with shallow shocks, no deep-focus earthquakes of magnitudes 8 ¼ to 8 ½ have been established thus far. This indicates (but does not yet prove) that at depths of about 100 to 700 km. roughly one-tenth as much energy can be stored as at depths of 15 to 40 km. At a depth of about 700 km. earthquake activity seems to stop abruptly.—The amplitudes of surface waves in deep-focus shocks decrease with increasing focal depth approximately as given by the theory.