Reconstruction of the slip distributions in historical earthquakes on the Sunda megathrust, W. Sumatra

Abstract

Spatially heterogeneous inversions for the slip in major earthquakes are typically only available for modern, instrumentally recorded events. Stress reconstructions on active faults, which are potentially vital elements of earthquake hazard assessment, are usually based on one or two instrumental inversions and some semi-quantitative information concerning historical seismic activity. Here we develop a new Bayesian Monte Carlo inversion method for sparse, large uncertainty data, such as is available for many historical earthquakes. We use it to reconstruct the slip in two great historical earthquakes on the Sunda megathrust, from 200 yr of paleogeodetic data recorded in the stratigraphy of coral microatolls on the forearc islands. The technique is based on the stochastic forward modelling of many slip distributions, which are constrained by the observed fractal scaling in the slip field. A set of static elastic Green's functions is used to estimate the vertical displacement at the coral locations resulting from each trial slip distribution. The posterior expected value of the slip and its variance are obtained from the average of the trial slips, weighted by their ability to reproduce the coral displacements. We successfully test the method on a synthetic slip distribution, before applying it to reconstruct the slip in a recent, instrumentally recorded event. We then invert for the great 1797 and 1833 megathrust events under the Mentawai Islands west of Sumatra. When compared with the slip distributions in recent earthquakes, our results unambiguously indicate that the sequence is not consistent with the classic characteristic earthquake model; earthquakes tend to incrementally tessellate the active fault plane rather than repeatedly breaking a segment of it. The results indicate that homogeneous loading of a fault with heterogeneous initial stress is enough to explain the observations on the Mentawai segment of the Sunda megathrust; no time dependence of material properties, for example, is necessary. Furthermore, we speculate that even small amounts of nonlinearity in the rupture process would ensure that any tessellating sequence will not be repeated, even over very long times. This method could be adapted to incorporate other historical information, such as records of tsunami run up and Mercalli Intensity estimates. Finally, we suggest that reconstruction of stress based on long-term slip histories may prove useful in identifying the possible locations of future earthquakes.