Earthquake magnitude, intensity, energy, and acceleration

Abstract This supersedes Paper 1 (Gutenberg and Richter, 1942). Additional data are presented. Revisions involving intensity and acceleration are minor. The equation log a = I/3 − 1/2 is retained. The magnitude-energy relation is revised as follows: (20) log ⁡ E = 9.4 + 2.14 M − 0.054 M 2 A numerical equivalent, for M from 1 to 8.6, is (21) log ⁡ E = 9.1 + 1.75 M + log ⁡ ( 9 − M ) Equation (20) is based on (7) log ⁡ ( A 0 / T 0 ) = − 0.76 + 0.91 M − 0.027 M 2 applying at an assumed point epicenter. Eq. (7) is derived empirically from readings of torsion seismometers and USCGS accelerographs. Amplitudes at the USCGS locations have been divided by an average factor of 2 1/2 to compensate for difference in ground; previously this correction was neglected, and log E was overestimated by 0.8. The terms M2 are due partly to the response of the torsion seismometers as affected by increase of ground period with M, partly to the use of surface waves to determine M. If MS results from surface waves, MB from body waves, approximately (27) M S − M B = 0.4 ( M S − 7 ) It appears that MB corresponds more closely to the magnitude scale determined for local earthquakes. A complete revision of the magnitude scale, with appropriate tables and charts, is in preparation. This will probably be based on A/T rather than amplitudes.