Sensitivity of the adjoint method in the inversion of tsunami source parameters

This paper tests a methodology for tsunami waveform inversion, based on the adjoint method. The method is designed to perform the direct optimization of the tsunami fault parameters, from tide-gauge data, imposing strong geophysical constrains to the inverted solutions, leading to a substantial enhancement of the signal-to-noise ratio, when compared with the classical technique based on Green’s functions of the linear long-wave model. A 4-step inversion procedure, which can be fully automated, consists (i) in the source area delimitation by adjoint backward ray-tracing, (ii) adjoint optimization of the initial sea state, from a vanishing first-guess, (iii) non-linear adjustment of the fault model and (iv) final adjoint optimization in the fault parameter space. That methodology is systematically tested with four different idealized bathymetry and coastline setups (flat bathymetry in an open domain, closed conical circular lake, islands in an open domain and submarine mountains in an open domain) and different amounts of synthetic observation data, and of observational and bathymetric errors. Results show that the method works well in the presence of reasonable amounts of error and it provides, as a by-product, a resolution matrix that contains information on the inversion error, identifying the combinations of source parameters that are best and worst resolved by the inversion.