The electromagnetic response of a layered earth is expressed in rectangular coordinates and the solution is obtained as a double inverse Fourier transform. This simplifies the theoretical development for any EM source, grounded or not, and the fast Fourier transform algorithm may be used to evaluate the fields. In some cases where complicated source geometries are used and where the fields are required over a large area or volume, the procedure may lead to a substantial reduction in computation costs. The standard problems of the numerical fast Fourier transform algorithm may be overcome by using correction techniques such as pre-aliasing. An analysis of the ground-wire EM source shows that the infinite line is a poor approximation to the long grounded line due to the strong component of galvanic current in the ground.