The electromagnetic field generated by a progressive ocean wave in a horizontally stratified ocean is a sum of a transverse electric type field, a transverse magnetic type field, and an electrostatic type field. Seawater velocity components in a vertical plane containing the direction of wave propagation generate the transverse electric part of the field, and the velocity component normal to the plane generates the transverse magnetic part of the field, which vanishes above an ocean surface. The electrostatic part of the field results from surface charges that half vertical electric currents at an ocean surface. Gradients of magnetic fields generated at the surface by both surface and internal waves provide sensible signals for recently developed magnetic gradiometers based on the Josephson effect, provided surface speeds exceed 1 cm/s or so. Vertically spaced measurements of noise spectra of magnetic field gradients above an ocean surface offer a unique and promising means of obtaining a measure of surface and internal wave spectra for three reasons: (1) magnetic field strengths above the surface are proportional to a weighted average of seawater speed over an ocean depth, which provides a response depending on the mode structure of internal waves: (2) field strengths decrease exponentially with height above the surface as ekh, where k denotes wave number, which provides means of wave number discrimination, and together with frequency discrimination, offers means of resolving internal wave spectra mode by mode; and (3) noise spectra of magnetic field gradients are effectively cross sepctra and so provide directional information on wave spectra from an effective point measurement.