Empirical magnitude and spectral scaling relations for mid-plate and plate-margin earthquakes

Abstract Published values of body-wave magnitude m b , surface-wave magnitude, M s , and seismic moment, M o , for mid-plate and plate-margin earthquakes, are analyzed, to determine their inter-relationship and to develop scaling laws for earthquake spectra. All of the plate-margin earthquakes used in the study occurred near the border of the Pacific Ocean. The mid-plate earthquakes occurred in both continental plate interiors and oceanic plate interiors. For mid-plate earthquakes the m b - M s relation can be represented by two straight lines, of slope one and two. The intersection of the two lines corresponds to the body-wave magnitude for which the corner period of the spectrum is at 1 sec. The M b - M s relation for plate-margin earthquakes is more complicated, because the derived spectra exhibit two corner periods. A principal feature of the m b - M o and M s - M o relations is the fact that the large plate-margin earthquakes have a higher M o value than the mid-plate earthquakes, for the same m b or M s . Because m b is a measure of the spectral amplitude for frequencies at which damaging ground motion occurs, and M 0 is a measure of the spectrum at very long periods, it follows that mb is a good estimator of strong ground motion, whereas a moment-derived magnitude is not. The latter, however, is a good measure of fault rupture area. The derived spectra of the mid-plate earthquakes are flat at the long periods, and have a slope of two at the short periods. Their seismic moment varies as the fourth power of the corner period, implying that the stress drop increases as the moment increases. For the large plate-margin earthquakes the derived spectra are flat at the long periods, have a slope of one at intermediate periods, and a slope of two at short periods. The stress drops are almost independent of moment for the larger plate-margin earthquakes. The moment-magnitude relations for mid-plate earthquakes indicate that an M s = 8.7 event requires a fault rupture length of only 60 km, for a fault width of 20 km. A plate-margin earthquake of M s = 8.7 and fault width of 20 km would require a fault length of 6000 km, obviously impossible. Assuming a fault width of 20 km, an M s = 8.2 earthquake has a rupture length of about 850 km, which is as large as can be expected for strike-slip faults, such as the San Andreas of California. Subduction zone earthquakes, on the other hand, if they have fault widths as great as 200 km, can give rise to M s = 8.7 earthquakes.

[1]  G. A. Bollinger,et al.  On the relation between modified Mercalli intensity and body-wave magnitude , 1979, Bulletin of the Seismological Society of America.

[2]  E. Okal,et al.  EVIDENCE FOR INTERNAL DEFORMATION OF THE INDIAN PLATE , 1978 .

[3]  H. Hasegawa,et al.  The Charlevoix Earthquake of 19 August 1979 and its Seismo-Tectonic Environment , 1980 .

[4]  Robert B. Herrmann,et al.  The denver earthquakes of 1967-1968 , 1981 .

[5]  Thomas C. Hanks,et al.  b values and ω−γ seismic source models: Implications for tectonic stress variations along active crustal fault zones and the estimation of high‐frequency strong ground motion , 1979 .

[6]  C. Richter.  An instrumental earthquake magnitude scale , 1935 .

[7]  D. L. Anderson,et al.  Theoretical Basis of Some Empirical Relations in Seismology by Hiroo Kanamori And , 1975 .

[8]  S. K. Singh,et al.  Seismic gaps and recurrence periods of large earthquakes along the Mexican subduction zone: A reexamination , 1981 .

[9]  H. Kanamori,et al.  Determination of source parameters of mid-plate earthquakes from the waveforms of body waves , 1980 .

[10]  B. Gutenberg.  Amplitudes of P, PP, and S and magnitude of shallow earthquakes , 1945 .

[11]  S. Stein.  Intraplate seismicity on bathymetric features: The 1968 Emperor Trough earthquake , 1979 .

[12]  J. Brune.  Tectonic stress and the spectra of seismic shear waves from earthquakes , 1970 .

[13]  B. Bolt.  The focus of the 1906 California earthquake , 1968 .

[14]  R. Street,et al.  A study of northeastern North American spectral moments, magnitudes, and intensities , 1977, Bulletin of the Seismological Society of America.

[15]  P. C. Jennings,et al.  Determination of local magnitude, ML, from seismoscope records , 1979 .

[16]  S. Stein.  An earthquake swarm on the Chagos-Laccadive Ridge and its tectonic implications , 1978 .

[17]  S. Stein,et al.  An intraplate thrust earthquake in the South China Sea , 1979 .

[18]  H. Kanamori,et al.  A moment magnitude scale , 1979 .

[19]  Robert B. Herrmann,et al.  Surface wave focal mechanisms for eastern North American earthquakes with tectonic implications , 1979 .

[20]  S. Solomon,et al.  Apparent stress and stress drop for intraplate earthquakes and tectonic stress in the plates , 1977 .

[21]  R. Herrmann,et al.  Some Problems With Using Magnitude Scales For Eastern North American Earthquakes , 1976 .

[22]  Robert J. Geller,et al.  Scaling relations for earthquake source parameters and magnitudes , 1976 .

[23]  H. Kanamori.  The energy release in great earthquakes , 1977 .

[24]  Robert B. Herrmann,et al.  Spectral Characteristics of the Lg wave Generated by Central United States Earthquakes , 1975 .

[25]  J. C. Savage.  Relation of corner frequency to fault dimensions , 1972 .

[26]  B. Gutenberg.  Magnitude determination for deep-focus earthquakes , 1945 .

[27]  K. Aki.  Scaling law of seismic spectrum , 1967 .

[28]  O. Nuttli,et al.  Surface-wave magnitudes of Eurasian earthquakes and explosions , 1975, Bulletin of the Seismological Society of America.

[29]  J. Boatwright,et al.  Investigation of two high stress drop earthquakes in the Shumagin Seismic Gap, Alaska , 1980 .