On relations between earthquake population and asperity population on a fault

Abstract

Gusev, A.A., 1992. On relations between earthquake population and asperity population on a fault. In: T. Mikumo, K. Aki, M. Ohnaka, L.J. Ruff and P.K.P. Spudich (Editors), Earthquake Source Physics and Earthquake Precursors. Tectonophysics, 211: 85–98. Data were compiled on the trend of telescismic short-period ( T ≈ 1.4 s) peak amplitude and spectral level vs M 0. For log M 0 > 26, slopes (in log-log scale) of these trends were estimated as b = 0.35 and β = 0.39, respectively. For a similar trend of Scismogram peak factor (peak to rms amplitude ratio) the slope estimate is p = 0.13. β = 0.39 disagrees with the ω −2 spectral model but can be explained by the multiasperity fault model of Gusev (1989) if the typical asperity size 2 R a is assumed to grow slowly with M 0. If R a ∝ M δ 0, then β = 1 3 + δ , and the empirical estimate of δ is 0.06. This value generally agrees with the | max vs M 0 trend revealed recently. The last is supposed to reflect the R a vs M 0 trend as well. p = 0.13 is fully incompatible with a Gaussian process record model (predicting p ≈ 0.03) and indicates a peak distribution of a heavy-tailed type. Assuming a power-law distribution for amplitudes of individual pulses (each one produced by failure of a single asperity) that add up to the observed record, we estimated the exponent a of the power law to be about 2.3. This may indicate that α ≈ 2.3 for the distribution of stress drop values of individual asperities. This α value agrees reasonably with α ≈ 2 found in Gusev (1989) from near-field data. Theoretical α values are estimated for two hypothetical regular hierarchical asperity structures on a fault: a grid-like structure, giving α = 2, and a clustered structure giving α ⩾ 1. To obtain these estimates, we assumed a near-critical mode of overcoming barriers of successive scales during rupture propagation. Comparison with empirical data shows no contradiction, and suggests that some hierarchical asperity structure, probably a grid-like one, actually exists on natural faults.