Inversion of tsunami waveforms and tsunami warning

Ever since the 2004 Indian Ocean tsunami, the technique of inversion of tsunami data and the importance of tsunami warning have drawn the attention of many researchers. However, since tsunamis are rare and extreme events, developed inverse techniques lack validation, and open questions rise when they are applied to a real event. In this study, several of those open questions are investigated, i.e., the wave dispersion, bathymetry grid size and subfault division. First, tsunami records from three large tsunami events -- 2010 Maule, 2011 Tohoku and 2012 Haida Gwaii -- are analyzed to extract the main characteristics of the leading tsunami waves. Using the tool of wavelet transforming, the instant wave period can be obtained and thus the dispersive parameter mu2 can be calculated. mu2 is found to be smaller than 0.02 for all records, indicating that the wave dispersion is minor for the propagation of tsunami leading waves. Second, inversions of tsunami data are carried out for three tsunami events -- 2011 Tohoku, 2012 Haida Gwaii and 2014 Iquique. By varying the subfault size and the bathymetry grid size in the inversions, general rules are established for choosing those two parameters. It is found that the choice of bathymetry grid size depends on various parameters, such as the subfault size and the depth of subfaults. The global bathymetry data GEBCO with spatial resolution of 30 arcsec is generally good if the subfault size is larger than 40 km x 40 km; otherwise, bathymetry data with finer resolution is desirable. Detailed instructions of choosing the bathymetry size can be found in Chapter 2. By contrast, the choice of subfault size has much more freedom; our study shows that the subfault size can be very large without significant influence on the predicted tsunami waves. For earthquakes with magnitude of 8.0 ∼ 9.0, the subfault size can be 60 km ∼ 100 km. In our study, the maximum subfault size results in 9 ∼ 16 subfault patches on the ruptured fault surface, so we infer that the maximum size of the subfault can be 1/4 to 1/3 of the scale of the faulting area. In Chapter 2, we also developed a method using the inverse residual to evaluate the effectiveness of tsunami buoys of different number and locations in the inversion. Results show that 2 ∼ 4 tsunami buoys are sufficient to constrain the source parameters quite well if they are optimally located. Adding data from more tsunami buoys into the inversion does not significantly improve the results. In addition, near-field stations in the source region do not have advantage against far-field stations in constraining the earthquake source parameters. Conversely, if the near-field data have short but large-amplitude waves and only such data are used in the inversion, it can result in very large but unreal slip near the seabed. The optimal locations for tsunami buoys of different number can also be obtained from this method.;Inversions of tele-seismic data show that the inverse results do not necessarily predict the tsunami waves, unless iterative forward modeling techniques are applied to adjust the inverse parameters. Thus, from the standpoint of tsunami warning, tele-seismic data are not able to precisely predict the tsunami wave height or an accurate inundation map, although the estimation of earthquake magnitude and depth might be enough to issue a crude warning. In addition, numerical experiments are conducted and measurements of the computational time show that the calculation of tsunami Green's functions for an area of ∼ 30° only takes several minutes using 256 computational cores. Thus, it is possible to calculate the Green's functions in real time for a tsunami warning system. Finally, a case study is conducted for the South China Sea using the method of inverse residual, leading to recommendations of number and location of tsunami buoys required for a warning system near the Manila trench.