Using a representation theorem from elastodynamics, subsurface slip on a known fault is formulated as the solution to an inverse problem in which recorded surface ground motion is the data. Two methods of solution are presented: the least-squares method, which minimizes the squared differences between theory and data, and the constrained least-squares method which simultaneously maintains a set of linear inequalities. Instabilities in the solution are effectively eliminated in both methods, and the sensitivity of the solution to small changes in the data is quantitatively stated. The inversion methodology is applied to 77 components of near-field ground acceleration recorded during the 15 October 1979 Imperial Valley earthquake. The faulting is constrained to propagate bilaterally away from the epicenter at an average velocity of 90 per cent of the shear wave speed on a vertical fault plane extending from the surface to 10 km depth. Inequality constraints are used to keep the faulting sequence physically reasonable by maintaining right-lateral motion and positive slip velocity. The preferred solution is stable and provides a good fit to the data; it is also realistic and consistent with observed surface offsets and independent estimates of seismic moment

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