The energy release in earthquakes

Abstract

Energy calculations are generally made through an empirical application of the familiar Gutenberg-Richter energy-magnitude relationships. The precise physical significance of these relationships is somewhat uncertain. We make use here of the recent improvements in knowledge about the earthquake source to place energy measurements on a sounder physical basis. For a simple trapezoidal far-field displacement source-time function with a ratio x of rise time to total duration T_0, the seismic energy E is proportional to [1/ x(1 - x)^2] M_0^2/T_0^3, where M_0 is seismic moment. As long as x is greater than 0.1 or so, the effect of rise time is not important. The dynamic energies thus calculated for shallow events are in reasonable agreement with the estimate E ≅ (5 × 10^(−5))M_0 based on elastostatic considerations. Deep events, despite their possibly different seismological character, yield dynamic energies which are compatible with a static prediction similar to that for shallow events. Studies of strong-motion velocity traces obtained near the sources of the 1971 San Fernando, 1966 Parkfield, and 1979 Imperial Valley earthquakes suggest that, even in the distance range of 1 to 5 km, most of the radiated energy is below 1 to 2 Hz in frequency. Far-field energy determinations using long-period WWSSN instruments are probably not in gross error despite their band-limited nature. The strong-motion record for the intermediate depth Bucharest earthquake of 1977 also suggests little teleseismic energy outside the pass-band of a long-period WWSSN instrument.

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