Robust uncertainty quantification of the volume of tsunami ionospheric holes for the 2011 Tohoku-Oki earthquake: towards low-cost satellite-based tsunami warning systems

We develop a new method to analyze the total electron content (TEC) depression in the ionosphere after a tsunami occurrence. We employ Gaussian process regression to accurately estimate the TEC disturbance every 30 s using satellite observations from the global navigation satellite system (GNSS) network, even over regions without measurements. We face multiple challenges. First, the impact of the acoustic wave generated by a tsunami onto TEC levels is nonlinear and anisotropic. Second, observation points are moving. Third, the measured data are not uniformly distributed in the targeting range. Nevertheless, our method always computes the electron density depression volumes, along with estimated uncertainties, when applied to the 2011 Tohoku-Oki earthquake, even with random selections of only 5 % of the 1000 GPS Earth Observation Network System receivers considered here over Japan. Also, the statistically estimated TEC depression area mostly overlaps the range of the initial tsunami, which indicates that our method can potentially be used to estimate the initial tsunami. The method can warn of a tsunami event within 15 min of the earthquake, at high levels of confidence, even with a sparse receiver network. Hence, it is potentially applicable worldwide using the existing GNSS network