Michael J. White
U.S. Army Construction Eng. Res. Lab., P.O. Box 9005, Champaign, IL 61826-9005
Y. L. Li
Univ. of Illinois, Urbana, IL 61801
A very simple and accurate method is introduced for the computation of the sound field above an impedance ground or a porous half-space. The procedure is based on complex image theory. Using Prony's method, the slowly varying part of the integrand in the Sommerfeld integral is approximated by a short series in terms of complex exponential functions. Combining the series of exponential functions and the remaining integrand, the resulting integral can be exactly evaluated by the Sommerfeld identity. A new closed-form expression of the sound field is represented as the original source, its quasistatic image, and three ``images'' with complex amplitudes and positions. Avoiding numerical evaluation of the Sommerfeld integral makes these closed-form expressions computationally very efficient. Numerical results show that these closed-form Green's functions are very accurate for the computation of the near and intermediate fields.