Near-field computation for sound propagation above ground—Using complex image theory

Abstract

In this paper, a very simple method is introduced for the efficient computation of the sound field in the near region above an impedance ground or an extended reaction ground. The procedure is based on complex image theory. Using Prony’s method, the slowly varying factor in the integrand of the Sommerfeld integral is approximated by a short series in terms of complex exponential functions. The result can be exactly evaluated by the Sommerfeld identity. A new closed-form approximate expression of the sound field is obtained, which is represented as the original source, its quasistatic image, and several ‘‘images’’ with complex amplitudes and positions. Avoiding numerical evaluation of the Sommerfeld integral makes these closed-form expressions computationally very efficient. The representation of the field with complex images makes the formula useful in measurement of ground impedance or in other cases requiring repeated mapping of the sound field. Numerical results show that these closed-form Green’s functions are very accurate for the computation of the near field.