Complementary slip distributions of 200 years of megathrust earthquakes

Coral paleo-geodesy on the Mentawai Islands off western Sumatra has produced a multi-seismic-cycle geodetic record which provides physical constraints on the slip distributions of large and great earthquakes. Using a Monte Carlo forward modelling method we have estimated the slip on the great 1797 and 1833 earthquakes and show that their most likely slip distributions are not only complementary but leave unruptured areas on the megathrust which appear to have been filled by the M8.4 and 7.9 Bengkulu earthquakes and the M7.8 Pagai earthquake. These results are consistent with a model in which slip in future earthquakes is controlled not only by secular loading and stress interaction between recent earthquakes, but also by the stress footprints of previous earthquakes potentially over many earthquake cycles. We discuss these results in the context of recent great earthquakes and suggest a mathematical formalism which unites observations of the evolution of slip deficit through heterogeneous tectonic loading, seismic and aseismic slip over many earthquakes. We apply the method to the Mentawai region including 330 years of heterogeneous loading of the Sunda megathrust and slip due to more than 30 historical and instrumentally recorded earthquakes. This complex slip deficit field is heterogeneous not only in the strain energy but also in the resolution and we introduce a new technique to clearly visualise both. We show that these results are consistent with the well published threat of a large tsunamigenic earthquake off western Sumatra and make some comments on constraining the threat.