Apparatus for determining the distribution of the electric polarization of a vessel in water, comprises an array of electric potential sensors (22) which are located in the water beneath the vessel and each generates a signal corresponding to the amplitude of the electric potential at the sensor as effected by the vessel, a signal processor unit (48) and cables (42) connecting each sensor (22) to the signal processor unit (48) to deliver each respective signal to the signal processor unit, the signal processor unit (48) serving to determine the potential difference between respective pairs of sensors (22) from the respective signals they generate, and the signal processor unit (48) processing multiple such potential difference determinations to deduce the distribution of electric polarization in the vessel which would cause said electric potential at each of the electric potential sensors (22). In addition, the electrical field and corrosion related magnetic field can be deduced from the distribution of electric polarization.