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 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 non-linear and anisotropic. Second, observation points are moving. Nevertheless, our method always computes these volumes, along with estimated uncertainties, when applied to the 2011 Tohoku-Oki Earthquake, even with random selections of only 5% of the 1,000 GPS Earth Observation Network System receivers considered here over Japan. The method can warn of a tsunami event within 15 minutes 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.