A modified saddle point method for predicting sound penetration into a rigid-porous ground

Abstract

An approximate analytical formula has been derived for the prediction of sound penetration into a semi-infinite rigid porous ground due to a monopole source. The sound fields can be expressed in an integral form that is amenable to analytical and numerical analyses. A modified saddle point method is applied to evaluate the integral asymptotically that leads to a closed form expression. The validity of the asymptotic formula is confirmed by comparing with the numerical results computed by the fast field formulation and the direct evaluation of the integral. It has been demonstrated that the present analytical formula is sufficiently accurate to predict the penetration of sound into the semi-infinite rigid porous ground. Furthermore, the sound fields predicted by modified saddle point are compared with that computed by the double saddle point method. It is found that these two asymptotic schemes give precise solutions at far fields but the modified saddle method is more accurate at the near field especially when both the source and receiver are close to the air/ground interface. [Research is partially funded by the China Research Scholarship Council.]