In this study, we present a linear inverse approach for the computation of the initial water displacement of a tsunami. The method uses empirical Green functions and linear shallow water wave theory. We apply this methodology to study the source of the 24 September 2013 tsunami off the Makran coast. We re-analyze the 2013 tsunami data, particularly the tide records in the coast of Oman and the DART buoy record in the Arabian Sea, to infer its source. We use wavelet and Fourier analyses to characterize the frequency content of the tide records and the possible influence of local harbor effects. We compute empirical Green functions for the possible source area, and then use a linear shallow water inversion technique to assess the water disturbance in the early stage of tsunami propagation. The comparison between forward modeling and observations shows a fair agreement with available data, particularly in what concerns the DART record. It also suggests the existence of local amplifications in a number of Omani harbors. The free surface elevation obtained by inversion of the waveforms is coherent with a landslide located close to 61.5° E, 24° N, sliding to the S or SSE direction. Our results show that the inversion technique used here leads to a better characterization of the tsunami source than the simple backward ray tracing which assumes a simple point source. In addition, these results strengthen the hypothesis that landslides might have played an important role in previous tsunami events in the area, and must be taken into account for tsunami hazard assessment on the Omani coast.
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