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Tsunami flow coupled with the geomagnetic field generates electric currents and associated magnetic fields. Although electromagnetic (EM) tsunami signals can be used for analysis and even forecasting tsunami propagation, the dynamically self-consistent effect of shoaling water depth on the fluid + electrodynamics has not been adequately clarified. In this study, we classify tsunami EM phenomena into three cases based on the ocean depth and find that the deeper ocean results in stronger self-induction due to the increase in both tsunami phase velocity and ocean conductance. In this deep-ocean case, the phase lead of the vertical magnetic variation relative to the sea surface elevation is smaller, while an initial rise in the horizontal magnetic component becomes observable prior to tsunami arrival. Furthermore, we confirm that the enhancement of tsunami height in shallower oceans shifts the ocean depth supplying maximum amplitudes of tsunami magnetic fields from approximately 2.0 km to 1.5 km.