Determination of seismic moment and energy from the Earth's free oscillation

Abstract

The energies of free oscillations and long-period surface waves are studied. Two great earthquakes, the Kurile Islands earthquake of October 13, 1963 ( M = 8.25) and the Alaskan earthquake of March 28, 1964 ( M = 8.5), are investigated. Normal mode solutions and excitation functions of free oscillations for a spherical, self-gravitating Gutenberg-Bullen A model are used for the theoretical interpretation. Dipolar point sources on shear faults with arbitrary dip angles are considered. From direct comparisons between the experimental and theoretical free oscillation amplitudes, the seismic moments are determined to be 7.5 × 10 28 dyne · cm for the Kurile Islands earthquake and 7.6 × 10 29 dyne · cm for the Alaskan earthquake. For order numbers from 10 to 15, the energy contained in spheroidal modes excited by the Alaskan earthquake is nearly two orders of magnitude larger than that of the Kurile Islands earthquake. The surface wave energies are also estimated for a period range 20 to 600 s. The effect of the finiteness of the source is considered. The total energies of surface waves are estimated as 3.0 × 10 23 erg for the Kurile Islands earthquake and 4.5 × 10 24 erg for the Alaskan earthquake. The energy spectrum densities of surface waves are also evaluated for each mode