Time-domain calculations of sound interactions with outdoor ground surfaces

A time-domain formulation for sound propagation in rigid-frame porous media, including waveform attenuation and dispersion, is developed. The new formulation is based on inversion of the relaxation functions from a previous model [Wilson DK, Ostashev VE, Collier SL. J Acoust Soc Am 2004;116:1889–92], thereby casting the convolution integrals in a form amenable to numerical implementation. Numerical techniques are developed that accurately implement the relaxational equations and transparently reduce to previous results in low- and high-frequency limits. The techniques are demonstrated on calculations of outdoor sound propagation involving hills, barriers, and ground surfaces with various material properties. We also compare the relaxation formulation to a widely applied phenomenological model developed by Zwikker and Kosten. The two models can be made equivalent if the resistance constant, structure constant, and compression modulus in the ZK model are allowed to be weakly frequency dependent. But if the ZK parameters are taken to be constant, as is typically the case, the relaxation model provides more accurate calculations of attenuation by acoustically soft porous materials such as snow, gravel, and forest litter.