We formulate a mathematical model of generation and propagation of seismo-electromagnetic (EM) signals in the basin of a marginal sea with an arbitrary 2D geological structure of the bottom, including the transfer of seismic and EM energy from lithosphere to hydrosphere and EM emission into atmosphere. In case of a model basin which is a 2D scheme of the central part of the basin of the Sea of Japan, the first magnetic signal is generated in the conductive (0.02 S/m) upper mantle layer M where weak seismic displacements (SD) are supposed to arise at the moment t = 0. The amplitude and duration of a SD were of order of a few centimetres and a few seconds and differ in different simulations. The primary signal from M with the amplitude about 50 pT reaches for the sea bottom at the moment t = 3.5 sec. Magnetic diffusion into the conductive sea water is too slow and thus EM signal in atmosphere originates due to geomagnetic field induction in the vertically moving water column Q_s located above the area of the initial contact of the seismic P wave (from M) with the sea bottom. Because of the structure of the seismohydrodynamic field and the EM field conjugation conditions at the sea-atmosphere interface the horizontal component B_2 of the seismo-hydrodynamic magnetic field is being generated, at first, in a thin water layer under the top of Q_s at the sea surface, whereas the vertical component B_1 is being generated everywhere in Q_s. After the spreading of the magnetic signals, B_1 is up to 250 and 150 pT at the sea surface and at the height of 10 km respectively at t = 10 sec Magnetic signals are represented by oscillations of the same low frequency range (0.1 to 10 Hz) as the SD. The computed long hydrodynamic wave's amplitude, caused by the SD, is not more then 20 cm. Therefore the waves transferring seismic energy can be discovered far from the coast by low-frequency EM observations.
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