Travel times and body wave magnitude

Summary

Presently used$\bar Q$-charts for magnitude determinations have been obtained principally on the base of direct observations of ground motion amplitudes, and periods, of several components of seismic waves (such as PZ, PH, SH), as function of epicentral distance. However, observations alone can serve for the definition of a magnitude scale for events with only one particular focal depth. In order to make the magnitude concept applicable to all focal depths, it must be decided when two events with different focal depths should be assigned the same magnitude. Any respective decision, which will assure consistent magnitudes, must be based on the velocity vs. depth, and eventually the anelasticity vs. depth profiles of the Earth.

It is concluded that in magnitude studies the anelasticity is of minor importance. Thus, after the amplitudes are compensated for the radiation pattern at the focus, the observed variation of amplitudes along the surface of the Earth, as function of epicentral distance, is practically due only to the velocity heterogeneity inside the Earth. Assuming a dependence of the velocity on the distance from the center of the Earth (no lateral velocity heterogeneities are permitted), a set of new$\bar Q$-charts is obtained, independent of direct amplitude observations, for PZ-, PH-, and SH-waves. A refinement in the magnitude definition warrants the magnitude figures obtained with the new$\bar Q$-charts to be uniform with regard to focal depths. Examples show the new$\bar Q$-charts to decrease the scatter of magnitude determinations between stations.

Since the efficiency in generating longitudinal and transverse waves is most probably not the same for all events, separate P-wave and S-wave magnitudes are advocated.