### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 3aPAa13. Complex image theory for sound propagation above ground.

**Michael J. White
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*U.S. Army Construction Eng. Res. Lab., P.O. Box 9005, Champaign, IL
61826-9005
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**Y. L. Li
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*Univ. of Illinois, Urbana, IL 61801
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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.