In geophysical probing, a borehole is often drilled in the earth, and the environment probed with electromagnetic waves. When such a borehole transverses a complex geological environment, the effect of the inhomogeneous medium on the propagation of electromagnetic waves needs to be understood. In this paper we present two methods with which the effect could be assessed in a two-dimensional inhomogeneous environment. The first technique illustrates a generalized Hankel transform method. The second technique shows the use of the semianalytic method to solve a two-dimensional inhomogeneity problem. Comparison with the finite element method showed 200 times improvement in computational speed. The method is general and may be extended to application in the field of optics, microwaves and millimeter waves.