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Strong ground motion of mine tremors: Some implications for near-source ground motion parameters

U.S. GEOLOGICAL SURVEY, 345 MIDDLEFIELD ROAD, MENLO PARK, CALIFORNIA 94025
BERNARD PRICE INSTITUTE OF GEOPHYSICS UNIVERSITY OF THE WITWATERSRAND, JOHANNESBURG, South Africa
BLYVOORUITZICHT GOLD MINE, P.O. BOX 7001, BLYVOORUITZICHT 2504 TRANSVAAL, South Africa

Abstract

Ground acceleration was recorded at a depth of about 3 km in the East Rand Proprietary Mines, South Africa, for tremors with –1 M_L 2.6 in the hypocentral distance range 50 m < R 1.6 km. The accelerograms typically had predominant frequencies of several hundred Hertz and peak accelerations, a, as high as 12 g. The peak accelerations show a dependence on magnitude, especially when expressed as dynamic shear-stress differences, defined as {small tilde} = Ra, where is density. For the mine tremors, {small tilde} varies from 2 to 500 bars and depends on magnitude according to log {small tilde} = 1.40 + 0.38 · M_L. Accelerograms for 12 events were digitized and then processed to determine velocity and, for seven events with especially good S/N, displacement and seismic source parameters. Peak ground velocities v ranged up to 6 cm/sec and show a well-defined dependence one earthquake size as measured by M_L or by seismic moment, M_o. On the basis of regression fits to the mine data, with –0.76 M_L 1.45, log Rv = 3.95 + 0.57 M_L, where Rv is in cm²/sec, and log Rv = –4.68 + 0.49 log M_o. These regression lines agree excellently with the corresponding data for earthquakes of M_L up to 6.4 or M_o to 1.4 x 10²⁶ dyne-cm. At a given value of M_L or M_o, a, at fixed R, shows considerably greater variation than v and appears to depend on the bandwidth of the recording system. The peak acceleration at small hypocentral distances is broadly consistent with Ra = 1.14 r_of_s/ß, where is stress drop, r_o is the source radius, ß is shear velocity, and f_s is the bandwidth of the recording system. The peak velocity data agree well with Rv = 0.57 ßr_o/µ, where µ is the modulus of rigidity; both expressions follow from Brune's model of the seismic source and were compared with data for events in the size range 5 x 10¹⁶ M_o 1.4 x 10²⁶ dyne-cm. Measurements of the source parameters indicated that, as for earthquakes, the stress drops for the tremors range from 1 to 100 bars and show no consistent dependence on M_o down to M_o = 5 x 10¹⁶ dyne-cm.

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