Earthquake source scaling relationships from −1 to 5 ML using seismograms recorded at 2.5‐km depth

The scaling relationships of earthquake sources less than about magnitude 3 have been the subject of considerable controversy over the last two decades. Studies of such events have shown a tendency for the constant stress drop, self similarity of larger earthquakes to breakdown at small magnitudes, and an apparent minimum source dimension of about 100 m has been observed. Other studies showed that this apparent breakdown in scaling could be an artifact of severe near-surface attenuation, limiting the spatial resolution of surface data. In this study, source parameters are determined for over 100 nearby, tectonic earthquakes, from recordings at a depth of 2.5 km (in granite) in the Cajon Pass scientific drill hole, southern California. Comparison of the seismograms recorded at this depth with those at the wellhead clearly demonstrates the effect of the severe attenuation in the upper kilometers of the Earth's crust. Source parameters are calculated by spectral modeling of three-component P and S waves, assuming four source models based on the Brune ω−2 (n = 2) model. In model l, n = 2 is fixed, and Q of P and S waves is determined to be 912 (581–1433) and 1078 (879–1323), respectively (the numbers in parentheses are ±1 standard deviation). In model 2, QP = QS = 1000 is assumed and n is allowed to vary. The ω−2 model is a good average for the data set, but there is some real scatter supported by the data. In model 3, QP = QS = 1000 is also assumed and ω−2 is constrained, and in model 4, attenuation is ignored and n is allowed to vary. Source dimensions of less than 10m are observed for all four models, 10 times smaller than the proposed “minimum”. No breakdown in constant stress drop scaling is seen in the downhole data (approximately ML-1 to 5.5, M0 = 109 - 1016 Nm). The ratio between radiated seismic energy (estimated by integrating the velocity squared spectra with adequate signal bandwidth) and seismic moment appears to decrease gradually with decreasing moment in the magnitude range −1 to 7. This is not incompatible with a constant stress drop but could result from errors in calculating energy. The ratio of the S wave energy to that radiated by the P waves is about 14, after correction for attenuation. This low value is consistent with the corner frequency shift of about 1.3. This corner frequency shift is observed for all four source models and therefore is interpreted as being source controlled.

[1]  William L. Ellsworth,et al.  The October 17, 1989, Loma Prieta, California, Earthquake and its aftershocks: Geometry of the sequence from high-resolution locations , 1990 .

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

[3]  P. Leary,et al.  Source parameters of small earthquakes recorded at 2.5 km depth, Cajon Pass, southern California: Implications for earthquake scaling , 1993 .

[4]  Keiiti Aki,et al.  Magnitude‐frequency relation for small earthquakes: A clue to the origin of ƒmax of large earthquakes , 1987 .

[5]  P. Malin,et al.  High-frequency site effects at two Parkfield downhole and surface stations , 1991 .

[6]  T. Hanks The corner frequency shift, earthquake source models, and Q , 1981 .

[7]  Jim Mori,et al.  Source parameters for small events associated with the 1986 North Palm Springs, California, earthquake determined using empirical Green functions , 1990 .

[8]  Masayuki Kikuchi,et al.  Seismic wave energy inferred from long-period body wave inversion , 1988 .

[9]  J. Humphrey,et al.  Seismic source parameters from the Guerrero subduction zone , 1994 .

[10]  G. Natale,et al.  Source parameters of microearthquakes at Phlegraean Fields (Southern Italy) volcanic area , 1987 .

[11]  J. Boatwright,et al.  A spectral theory for circular seismic sources; simple estimates of source dimension, dynamic stress drop, and radiated seismic energy , 1980 .

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

[13]  Jon B. Fletcher,et al.  A general inversion scheme for source, site, and propagation characteristics using multiply recorded sets of moderate-sized earthquakes , 1991 .

[14]  Thomas H. Heaton,et al.  Initial investigation of the Landers, California, Earthquake of 28 June 1992 using TERRAscope , 1992 .

[15]  D. Turcotte Fractals in geology and geophysics , 2009, Encyclopedia of Complexity and Systems Science.

[16]  Frank L. Vernon,et al.  Multitaper spectral analysis of high-frequency seismograms , 1987 .

[17]  J. Brune,et al.  Corner frequencies of P and S waves and models of earthquake sources , 1973, Bulletin of the Seismological Society of America.

[18]  J. Boatwright Regional propagation characteristics and source parameters of earthquakes in northeastern North America , 1994, Bulletin of The Seismological Society of America (BSSA).

[19]  J. D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  Thomas C. Hanks,et al.  Earthquake stress drops, ambient tectonic stresses and stresses that drive plate motions , 1977 .

[21]  Peter M. Shearer,et al.  High-frequency borehole seismograms recorded in the San Jcinto Fault zone, Southern California Part 2. Attenuation and site effects , 1991, Bulletin of the Seismological Society of America.

[22]  Susan E. Hough,et al.  High-frequency spectra observed at Anza, California: Implications for Q structure , 1988 .

[23]  H. Kanamori,et al.  Determination of earthquake energy release and ML using TERRAscope , 1993 .

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

[25]  D. Hatzfeld,et al.  EXPERIMENTAL STUDY OF THE SPECTRAL CONTENT FOR SHALLOW EARTHQUAKES , 1982 .

[26]  Charles S. Mueller,et al.  Source parameters of the 1980 Mammoth Lakes, California, earthquake sequence , 1982 .

[27]  John G. Anderson,et al.  A MODEL FOR THE SHAPE OF THE FOURIER AMPLITUDE SPECTRUM OF ACCELERATION AT HIGH FREQUENCIES , 1984 .

[28]  J. C. Savage Relation between P- and S-wave corner frequencies in the seismic spectrum , 1974, Bulletin of the Seismological Society of America.

[29]  Douglas S. Dreger,et al.  Source parameters of the Sierra Madre Earthquake from regional and local body waves , 1991 .

[30]  R. Abercrombie Earthquake locations using single‐station deep borehole recordings: Implications for microseismicity on the San Andreas fault in southern California , 1995 .

[31]  R. Abercrombie The magnitude-frequency distribution of earthquakes recorded with deep seismometers at Cajon Pass , 1996 .

[32]  Jon B. Fletcher,et al.  The partition of radiated energy between P and S waves , 1984 .

[33]  H. Houston Broadband source spectrum, seismic energy, and stress drop of the 1989 MacQuarie Ridge Earthquake , 1990 .

[34]  David M. Boore,et al.  Moment‐magnitude relations in theory and practice , 1984 .

[35]  Max Wyss,et al.  Stress estimates for South American shallow and deep earthquakes , 1970 .

[36]  T. Heaton Evidence for and implications of self-healing pulses of slip in earthquake rupture , 1990 .

[37]  E. W. James,et al.  Geologic setting and lithologic column of the Cajon Pass Deep Drillhole , 1988 .

[38]  A. Frankel,et al.  Reply to K. Aki's “Comment on ‘microearthquake spectra from the Anza, California seismic network: Site response and source scaling’” , 1989, Bulletin of the Seismological Society of America.

[39]  J. A. Snoke,et al.  Apparent stress: An estimate of the stress drop , 1983 .

[40]  R. Madariaga Dynamics of an expanding circular fault , 1976, Bulletin of the Seismological Society of America.

[41]  Microearthquakes and the nature of the creeping-to-locked transition of the San Andreas fault zone near San Juan Bautista, California , 1984 .

[42]  Thomas C. Hanks,et al.  Source parameters of southern California earthquakes , 1973 .

[43]  John E. Vidale,et al.  Influence of focal mechanism on peak accelerations of strong motions of the Whittier Narrows, California, earthquake and an aftershock , 1989 .