Bulletin of the Seismological Socmty of Amerma, Vol 72, No 2, pp 371-387, April 1982 THE ENERGY RELEASE IN EARTHQUAKES BY M. S. VASSILIOUAND H m o o KANAMORI ABSTRACT Energy calculations are generally made through an empirical application of the famihar 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 rumple trapezoidal far-field displacement source-time function with a ratio x of rise time to total duration To, the seismic energy E is proportional to [1/x(1 - x) 2] Mo2/ To a, where Mo 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 x 10 -s) Mo based on elastostatic considerations. Deep events, despite their possibly differ- ent 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 instru- ments 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. 1. INTRODUCTION The energy released in earthquakes can be estimated in a number of ways (for a comprehensive review see Bath, 1966). We may divide the energy estimates from the variety of methods available into two broad classes: the static estimates and the dynamic estimates. Static estimates can be obtained from static values of moment and stress drop; dynamic estimates, on the other hand, are obtained from seismo- grams. We review static estimates of energy in section 4. We discuss there that with some simple assumptions, a static estimate of energy can be obtained from the formula E = (5 × 10-5)M0 (Knopoff, 1958; Kanamori, 1977). We may subdivide dynamic estimates of energy from body waves into two groups. One procedure involves the direct integration of an observed waveform at a partic- ular station; another involves integration of an inferred displacement source-time function. The familiar energy-magnitude relationships of Gutenberg and Richter (1942, 1956a, b) fall into the first category of dynamic methods. These empirical relation- ships were derived on the basis of a crude approximation to the integral over a group of plane seismic waves passing by a station. The Gutenberg-Richter estimates of energy from Ms agree fairly well with the static estimates mentioned above. This might be expected, as Ms correlates quite well with log Mo (Kanamori and Anderson, 1975). In this paper, we develop dynamic energy estimates of the second kind. We apply the theory of Haskell (1964) to compute the energies of several shallow events (section 2), using moments and source-time histories obtained in the last decade 371