  Sediment deposits are the only leftover records from paleo tsunami events.
Therefore, inverse modeling method based on the information contained in the
deposit is an indispensable way of deciphering the quantitative characteristics
of the tsunamis, e.g., the flow speed and the flow depth. While several models
have been proposed to perform tsunami inversion, i.e., to infer the tsunami
characteristics based on the sediment deposits, the existing methods lack
mathematical rigorousness and are not able to account for uncertainties in the
inferred quantities. In this work, we propose an inversion scheme based on
Ensemble Kalman Filtering (EnKF) to infer tsunami characteristics from sediment
deposits. In contrast to traditional data assimilation methods using EnKF, a
novelty of the current work is that we augment the system state to include both
the physical variables (sediment fluxes) that are observable and the unknown
parameters (flow speed and flow depth) to be inferred. Based on the rigorous
Bayesian inference theory, the inversion scheme provides quantified
uncertainties on the inferred quantities, which clearly distinguishes the
present method with existing schemes for tsunami inversion. Two test cases with
synthetic observation data are used to verify the proposed inversion scheme.
Numerical results show that the tsunami characteristics inferred from the
sediment deposit information have a favorable agreement with the truths, which
demonstrated the merits of the proposed tsunami inversion scheme.
