Primary electromagnetic field in the sea induced by a moving line of electric dipoles

The analysis of the primary electromagnetic fields caused by steady state or transient electric current flowing along a cable of finite length moving with a constant velocity below the sea surface has several applications. It supports the analysis of submarine physical data and it is useful for protecting ships from the threat of sea mines. The usual approach to describe the primary field starts from the solution of a magnetic vector potential in the frequency domain due to an electric dipole, which is obtained with the method of Green. Subsequent transformation to the time domain employing Laplace transform as well as integration along the cable length allows to describe the time variation of the primary electromagnetic induced field due to a line of electric dipoles. The result is applicable to both shallow and deep sea water environments. Because of the difference in velocity between source and receiver, a careful application of the convolution integral is necessary in order to adapt the source pulse solution to any type of transmitting current waveform. Furthermore it is shown that the influence of the relative velocity between source and receiver is not necessarily negligible. Therefore it has to be considered in the interpretation of the secondary fields scattered by geological features.