Tsunami waveform inversion by adjoint methods

An adjoint method for tsunami waveform inversion is proposed, as an alterna tive to the technique based on Green's functions of the linear long wave mo del. The method has the advantage of being able to use the nonlinear shallo w water equations, or other appropriate equation sets, and to optimize an i nitial state given as a linear or nonlinear function of any set of free par ameters. This last facility is used to perform explicit optimization of the focal fault parameters, characterizing the initial sea surface displacemen t of tsunamigenic earthquakes. The proposed methodology is validated with e xperiments using synthetic data, showing the possibility of recovering all relevant details of a tsunami source from tide gauge observations, providin g that the adjoint method is constrained in an appropriate manner. It is fo und, as in other methods, that the inversion skill of tsunami sources incre ases with the azimuthal and temporal coverage of assimilated tide gauge sta tions; furthermore, it is shown that the eigenvalue analysis of the Hessian matrix of the cost function provides a consistent and useful methodology t o choose the subset of independent parameters that can be inverted with a g iven dataset of observations and to evaluate the error of the inversion pro cess. The method is also applied to real tide gauge series, from the tsunam i of the February 28, 1969, Gorringe Bank earthquake, suggesting some reaso nable changes to the assumed focal parameters of that event. It is suggeste d that the method proposed may be able to deal with transient tsunami sourc es such as those generated by submarine landslides.