Application of the Fast Fourier Transform to the Computation of the Sommerfeld Integral for a Vertical Electric Dipole Above a Half-Space

The fast Fourier transform (FFT) is used in conjunction with analytical techniques to obtain an approximate expression for the Sommerfeld integral associated with a vertical electric dipole above a half-space. The resulting expression, which is an analytic function of the source and observation locations, can be used in lieu of a numerical integration of the Sommerfeld integral. It can be used in either the near zone or the far zone, and it can even be applied for observation angles close to grazing. The accuracy of the expansion directly depends on the number of terms used in the fast Fourier transform. Results obtained using the expansion are compared with those obtained both from a direct numerical integration of the Sommerfeld integral and the reflection coefficient method.