ULF/ELF electromagnetic fields generated in a sea of finite depth by a submerged vertically‐directed harmonic magnetic dipole

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Abstract
In this paper we compute the undersea quasi‐static electromagnetic fields of a submerged vertically‐directed harmonic magnetic dipole (VMD), taking into account the presence of a sea floor, for the purpose of evaluating the relative importance of the modes of propagation of the fields at frequencies in the ULF/lower‐ELF bands (frequencies less than 300 Hz). Both the source and the receiver are located at points equidistant between the surface and floor of a sea one skin depth (δ) deep, and the horizontal separation (r) between them is varied over the range 0.1 δ and 100 δ. When the horizontal separation between the receiver and the VMD source is less than about 6 δ, we find that each field component behaves as though the source were in a sea of wholly infinite extent. At larger separations, the ratio of actual field amplitude to the “infinite extent,” or direct, field amplitude increases rapidly and reaches a value exceeding 1036 at a separation of 100 δ, indicating that the fields at such distances have not propagated directly through the sea water. Analysis of the propagation modes reveals that the chief contribution at large separations (r/δ > 20) is the surface mode, and the field amplitudes in this asymptotic regime are independent of sea floor conductivity. At closer ranges (r/δ < 10), the surface and sea‐floor modes are of equal importance. Between these limiting cases (10 < r/δ < 20) is a transitional regime where the first‐order sea floor contribution is sometimes the dominant mode. The changeover between the transitional and the asymptotic regimes moves outward from the source as the sea floor conductivity decreases, and the field components in the asymptotic regime are characteristic of a quadrupole or higher‐order source.