Gutenberg's surface-wave magnitude calibrating function: Theoretical basis from synthetic seismograms

Abstract

The surface-wave magnitude, as originally defined by Gutenberg (1945), appears to be the most stable quantity rating the strengths of seismic sources. It is based on the ground displacement produced by a nearly monochromatic wave train. The calibrating function underlying the magnitude definition was obtained from observations of the amplitudes as a function of epicentral distance for a wealth of earthquakes. No distinction was made as to focal depths. Thus, the calibrating function depends on one parameter—the epicentral distance-only. Subsequent attempts to introduce a focal depth correction were not successful in practice, and one and the same calibrating function continues to be applied to events with focal depths ranging from 0 to about 70 km. Assuming a strike-slip point source located inside a standard Earth model, synthetic seismograms of the fundamental mode SH-(Love-) wave are computed for a range of focal depths and azimuths. Amplitude-distance curves are obtained, and averaged over the azimuths. The curves are the basis for improved calibrating functions. Average depth corrections are obtained and applied to some populations of seismic events. The corrected surface-wave magnitudes are internally more consistent than the uncorrected ones usually published. Applying the depth correction to published surface wave magnitudes and considering the m b - M s relation for a sample of earthquakes and explosions, it has been established that, for a given intensity of short-periodic radiation, the 20-s radiation intensity can vary by orders of magnitude. While it is known that the 20-s radiation intensity is generally lower for explosions than for earthquakes, it turns out to be even lower if the depth correction is applied, yielding a clearer separation between both classes of seismic events.