A method for signal communication between a well drilling instrument and the Earth's surface includes generating an electromagnetic field in an instrument disposed in drill string used to drill a wellbore. The electromagnetic field includes encoded measurements from at least one sensor associated with the instrument. A signal corresponding to an amplitude of the electromagnetic field is measured and the measurements from the measured signal are decoded. The signal comprises a voltage measured across electrodes or a voltage induced in an electromagnetic receiver disposed at a selected depth below the Earth's surface. The selected depth is at least the depth of a formation below the water table having a highest resistivity within 500 meters of the surface.