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SEISMOLOGICAL LABORATORY DIVISION OF GEOLOGICAL AND PLANETARY SCIENCES CALIFORNIA INSTITUTE OF TECHNOLOGY, PASADENA, CALIFORNIA 91125
Abstract
Empirical relations involving seismic moment Mo, magnitude MS, energy ES and fault dimension L (or area S) are discussed on the basis of an extensive set of earthquake data (MS 
6) and simple crack and dynamic dislocation models. The relation between log S and log Mo is remarkably linear (slope 
2/3) indicating a constant stress drop 
; = 30, 100 and 60 bars are obtained for inter-plate, intra-plate and "average" earthquakes, respectively. Except for very large earthquakes, the relation MS (2/3) log Mo 2 log L is established by the data. This is consistent with the dynamic dislocation model for point dislocation rise times and rupture times of most earthquakes. For very large earthquakes MS (1/3) log Mo log L (1/3) log ES. For very small earthquakes MS log Mo 3 log L log ES. Scaling rules are assumed and justified. This model predicts log ES 1.5 MS 3 log L which is consistent with the Gutenberg-Richter relation. Since the static energy is proportional to 
L3, where is the average stress, this relation suggests a constant apparent stress 
where is the efficiency. The earthquake data suggest 
. These relations lead to log S MS consistent with the empirical relation. This relation together with a simple geometrical argument explains the magnitude-frequency relation log N – MS.
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Simultaneous Determination of Site Responses and Source Parameters of Small Earthquakes along the Atotsugawa Fault Zone, Central Japan Bulletin of the Seismological Society of America, December 1, 2000; 90(6): 1430 - 1445.
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Faulting in the 1986 Chalfant, California, Sequence: Local Tectonics and Earthquake Source Parameters Bulletin of the Seismological Society of America, August 1, 2000; 90(4): 813 - 831.
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Source Scaling Properties from Finite-Fault-Rupture Models Bulletin of the Seismological Society of America, June 1, 2000; 90(3): 604 - 615.
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D. S. Dreger, H. Tkal, and M. Johnston Dilational Processes Accompanying Earthquakes in the Long Valley Caldera Science, April 7, 2000; 288(5463): 122 - 125. [Abstract] [Full Text]
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Earthquake Locations in the Inner Continental Borderland, Offshore Southern California Bulletin of the Seismological Society of America, April 1, 2000; 90(2): 425 - 449.
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Apparent Breaks in Scaling in the Earthquake Cumulative Frequency-Magnitude Distribution: Fact or Artifact? Bulletin of the Seismological Society of America, February 1, 2000; 90(1): 86 - 97.
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S. Hartzell, S. Harmsen, A. Frankel, and S. Larsen Calculation of broadband time histories of ground motion: Comparison of methods and validation using strong-ground motion from the 1994 Northridge earthquake Bulletin of the Seismological Society of America, December 1, 1999; 89(6): 1484 - 1504. [Abstract] [PDF]
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D. Sornette and A. Sornette General theory of the modified Gutenberg-Richter law for large seismic moments Bulletin of the Seismological Society of America, August 1, 1999; 89(4): 1121 - 1130. [Abstract] [PDF]
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S. G. Wesnousky Crustal deformation processes and the stability of the Gutenberg-Richter relationship Bulletin of the Seismological Society of America, August 1, 1999; 89(4): 1131 - 1137. [Abstract] [PDF]
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