We derive and test a set of inversions of surface-slip measurements based on the empirical relation u(t) = uf/(1 + T/t)c proposed by Sharp and Saxton (1989) to estimate the final slip uf, the power-law exponent c, and the power-law duration T. At short times, Sharp's relation behaves like the simple power law, u(t)u1tc, where u1 is the initial slip, that is, the slip at 1 day after the earthquake. At long times, the slip approaches the final slip asymptotically. The inversions are designed in part to exploit the accuracy of measurements of differential slip; that is, measurements of surface slip which are made relative to a set of nails or stakes emplaced after the earthquake. We apply the inversions to slip measurements made at 53 sites along the Superstition Hills fault for the 11 months following the M = 6.2 and 6.6 earthquakes of 24 November 1987. In general, estimates of the initial slip and the power law exponent are well resolved, while estimates of the power-law durations and the final slip are less well resolved because the durations of the surface slip measurements are often less than the derived power-law durations. The slip on the three fault strands is a relatively smooth function of position; the initial slip and final slip are well correlated. The time dependence of surface slip at the 53 sites is roughly similar along the entire fault, where the power-law exponents are distributed as c = 0.14 ± 0.04 and the power-law durations range from 100 < T < 1000 days.

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