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Two-parameter scaling of source spectra: Love waves from deep-focus Bonin Islands earthquakes

NTNF/NORSAR, POST BOX 51 N-2007 KJELLER, Norway

Abstract

Starting with the one-parameter scaling law of Aki, a two-parameter expression is developed to model the source factor of the far-field spectrum from a dislocation fault source for both ^–2 and ^–3 high-frequency asymptotic types. Aki's assumption of similarity is relaxed in two respects: it is neither here assumed that wD₀ L² (L = fault length, w = fault width, D₀ = average dislocation) nor that k_T = v k_L (k_T^–1 = correlation time, k_L^–1 = correlation length, v = velocity of rupture propagation), the latter being equivalent to allowing for Brune's fractional stress drop. From this two-parameter model a four-parameter model of spectral ratio is obtained and fitted to observed spectral ratios by computer optimization of the four parameters. Observed spectral ratios have been determined from the Love waves recorded at NORSAR from six deep-focus Bonin Islands earthquakes using a common-path method. From the optimal values of the four parameters, values are determined for corner frequency (f 0.2 Hz for m 6.0; f 0.3 Hz for m = 5.3; m = PDE body-wave magnitude), relative fault length, relative seismic moment (and magnitudes), and p, the slope of the corner-frequency locus. Values found for p are all greater than 3 and such p, in combination with an ^–3 scaling law, can yield a reasonable m:M relation, i.e., with no ceiling imposed on m. A slightly better fit is obtained by starting with an ^–3 model than with ^–2.

Footnotes

^* Present address: Department of Applied Geophysics, University of Luleå, S-951 87 Luleå, Sweden.