FDTD Modeling of Scattered Ultra-Low Frequency Electromagnetic Waves From Objects Submerged in the Ocean

The skin depth of electromagnetic (EM) waves in ocean water is on the order of 160 m at 3 Hz and just 50 m at 30 Hz. The detection of objects in the ocean using EM waves is, thus, very challenging due to the high attenuation rate of the EM fields. We propose the usage of ultra-low frequencies (ULF: <3 Hz) to detect submerged objects due to the larger skin depths (1.5 km at 0.03 Hz) at those frequencies. Using the finite-difference time-domain (FDTD) method, ULF scatterings from objects submerged in the ocean are obtained. This is achieved by running the FDTD model in the scattered-field-only regime, in which EM field components in a 3-D FDTD grid are excited by a hard source, i.e., the electric field components are set to a sinusoid at ULF to represent the scatterings from the object. The propagation attenuation versus distance from the source (object) is recorded and compared to the propagation attenuation as predicted by the plane wave theory. A total round-trip propagation attenuation is estimated for ULF waves originating in the air region above the ocean. Frequencies ranging from 0.01 to 2 Hz are tested.