Inversion for seismic slip rate history and distribution with stabilizing constraints: Application to the 1986 Andreanof Islands Earthquake

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Abstract
We develop and present a method of inverting seismograms, including their absolute amplitudes, to obtain the complete seismic slip time history and distribution, using the method of linear programming. A rectangular fault is discretized into cells and the source duration into time steps. The inversion for the slip rate distribution on the fault as a function of time reduces to the solution of a system of linear equations. The influence on the solution of constraining different source parameters such as the sign of the slip rate and the seismic moment is investigated. It is found that the constraint of positiveness of slip rate and the constraint that the seismic moment determined from, the solution should be close to that obtained from the centroid moment tensor (CMT) solution are very strong constraints and are essential to obtaining a physically reasonable solution. Since the inverse problem is unstable, instead of presenting only one particular solution we examine several solutions equally well fitting the data for all practical purposes. We find that when both constraints are applied the solution becomes quite stable. The method is applied to a data set consisting of the vertical component of available digitally recorded teleseismic P waves at stations within a chosen distance window for the 1986 Andreanof Islands earthquake (Mw = 8.0). The preferred solution is the one in which the slip rate is constrained to be positive and the moment is set to the CMT value. The average rupture speed in the 90‐km segment to the east of the hypocenter was ≈ 3.2 km/s and in the 190‐km section to the west was ≈ 2 km/s. The maximum slip in the area of large moment release to the west was ≈ 5 m and the maximum slip rate, which occurs in the same place as the maximum slip, was ≈ 6.5 m/s. The slip distribution on the fault shows a corrugated pattern with the long axis in the direction of the plate convergence, rather than normal to the arc, which was the slip vector direction for the earthquake, with most of the slip occurring pn a region of the fault to the west of the rupture nucleation zone. This region continued to slip for about 55 s, the total source duration being about 80 s. The results of this analysis suggest that the long‐term motion on this portion of the Aleutian arc is indeed in the direction of plate convergence.