Waveform inversion using ABIC for the rupture process of the 1983 Hindu Kush earthquake

Abstract An inversion method was developed to infer earthquake rupture process from far-field velocity waveforms. We devise a source model that has variable slip and variable rupture velocity. The fault plane is divided into many subfaults. Slip amplitude is assumed to be dependent on the subfaults, and slip velocity at a point is assumed to be a triangle function of time. Rupture time is expressed by an interpolation equation using the rupture times at the corners of the subfaults. The slip distribution and the rupture-front motion are estimated by constrained least-squares inversion. We incorporate smoothing constraints on slip distribution and on rupture propagation into the observed data. The degree of the constraints is controlled by hyperparameters. The optimal values of the hyperparameters are determined by minimizing Akaike's Bayesian information criterion (ABIC). Under the assumption of ABIC, we can obtain a unique solution with reasonable resolution. We apply this inversion method to the Hindu Kush earthquake of 30 December 1983 with a depth of 212 km. We found that the rupture process of this earthquake was composed of two subevents. The first subevent occurs near the initiation point of the rupture. The centre of the second subevent region is approximately 20 km to the west of the first subevent. The released moment of the second subevent is about seven times larger than that of the first subevent.

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