Starting with a previous formalism, a method is developed for computing the tangential magnetic field on the surface of an inhomogeneous spherical earth for excitation by a plane wave. The model consists of a two-section earth which is piecewise homogeneous. As has been shown before, the line integral approximation for the pattern function may be evaluated in terms of various representations for the pattern function and the groundwave attenuation functions for homogeneous earth. In the present paper, the results are cast in a form suitable for numerical work. This involves some nontrivial transformations of the relevant contour integral representations. Some specific examples for 50 and 100 kHz show that a marked recovery effect takes place as the receiving antenna is moved from land to sea.