SEISMIC MOMENT (M0), RADIATED ENERGY, AND
MOMENT MAGNITUDE (M)
[c6, p178]

Magnitude scales based on finite-bandwidth seismographs approach a maximum near which events of clearly different size or energy are indistinguishable. Saturation of ML is apparent for both the 1906 and 1952 earthquakes listed in Table 6.1. Recent work by Hutton and Boore (1987) suggests that the local-magnitude scale may begin to saturate at about ML=6. Such saturation, which is understood to arise from the scaling law of the seismic spectrum (Aki, 1967), occurs when the peak of the energy spectrum lies below the frequency range of the Wood-Anderson seismograph.

By using the well-known properties of the seismic spectrum, magnitude scales can be constructed with uniform validity. One such scale, Mw, proposed by Kanamori (1977) is based on the seismic energy radiated in the form of elastic waves by the source. Another nearly equivalent magnitude scale, M, the moment magnitude, is based on the seismic moment, M0 = mu A u (Aki, 1966), where A is the area of the earthquake rupture surface, u is the average fault displacement, and mu is the shear modulus of the crustal volume containing the fault. Hanks and Kanamori (1979) took advantage of the nearly identical relations between M0 and both ML and Ms to define M=2/3log10 M0-10.7, where M0 is measured in dyne-centimeters.

These two magnitude scales, though closely related, are not identical. Singh and Havskov (1980) showed that Mw=2/3(log10 M0+log10 delta sigma / mu - 12-1), where delta sigma is the stress drop. Earthquake stress drops generally fall in a narrow range over the entire magnitude spectrum, and so with delta sigma / mu ~~ 10-4 (Kanamori, 1977), Mw=M. One advantage to M for the purpose at hand is its dependence on only the static fault offset and rupture area, which can be determined for the 1857 and 1872 earthquakes.