A model for the coast-effect

A model for the coast-effect of geomagnetism is presented, in which the horizontal magnetic field induces currents in a circuit including a thin finite ocean. The currents flow horizontally across the ocean, vertically down into the earth, back through the deep interior of the earth, and vertically up to the ocean to complete the current loop. The upper layers of the earth are given non-zero conductivity, allowing the possibility of such current loops.A two-dimensional model involving such currents has been worked out analytically, and it is found that a significant induced magnetic field at the seafloor can be obtained with a reasonable conductivity in the earth's upper layers. A three-dimensional model has also been worked out numerically. It is found that the induced vertical component of magnetic field is of comparable magnitude to the horizontal component induced normal to the coast, whereas the horizontal component parallel to the coast is small. These relations are required to explain the observation of Parkinson arrows.