Adjoint Synthesis for Trans-Oceanic Tsunami Waveforms and Simultaneous Inversion of Fault Geometry and Slip Distribution

Tsunamis propagate over long distances and can cause widespread damage even after crossing ocean basins. Prediction of tsunamis in distant areas based on observations near their sources is critical to mitigating damage. In recent years, the accuracy of numerical models of trans-oceanic tsunami propagation has improved significantly due to the incorporation of effects such as the solid earth response to tsunami loading and wave dispersion. However, these models are computationally expensive and have not been fully utilized for real-time prediction. Here, we derive the adjoint operator for the linear set of equations describing deep-ocean tsunami propagation and show how a pre-computed database of adjoint states can achieve rapid synthesis of tsunami waveforms at target sites from nonpoint arbitrary tsunami sources. The adjoint synthesis method allows for an exhaustive parameter search for tsunami source estimation. A method for simultaneous inversion of fault geometry and slip distribution using adjoint synthesis with Sequential Monte Carlo method was proposed and applied to the 2012 Haida Gwaii earthquake tsunami. The influence of model accuracy and the amount of observed data on the estimation of tsunami sources and waveforms was examined. It was found that with a highly accurate propagation model, using only a limited amount of observed data produced source and waveform estimates very similar to the final models obtained with much larger data sets. The final inferred fault model involved megathrust slip distributed between the Haida Gwaii trench and the Queen Charlotte fault. The proposed method can also quantify the uncertainty of the waveform forecasts.