The marine controlled-source electromagnetic method has become a popular technique for mapping the electrical resistivity structure of the seafloor. Electromagnetic fields, produced by an electric dipole transmitter, diffuse through the earth and are recorded on the seabed by nodal or cable based electric dipole receivers. Accurate information on transmitter and receiver geometry is extremely important for proper interpretation; errors in the position and orientation of the transmitter and/or the receivers propagate into errors in the predicted seafloor resistivity. We consider the special situation where a receiver cable is towed in the vicinity of a transmitter which is located on the seafloor with a known position and orientation. We theoretically and numerically examine the response of this system for a selection of 1D, 2D, and 3D models, and show that although the electromagnetic field recorded at early times contains information about the subsurface resistivity, the late time decay of the transient response is only a function of the seawater conductivity and receiver position for all the models we consider. In fact, the shape of the late time decay is almost exactly the same as that of a dipole in a wholespace having the same resistivity as seawater. This shows that late time transient information can be used to determine the position of the receiver cable, whereas early time information can be used to determine the resistivity structure of the seafloor.