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

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Abstract
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.

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