Applied Research Laboratory, University of Texas at Austin, Austin, Texas 78713-8029, USA.
J Acoust Soc Am. 2012 Jan;131(1):54-68. doi: 10.1121/1.3662049.
Scattering by pressure-release sinusoidal surfaces in three dimensions is analyzed using the Fresnel phase approximation and realistic source and receiver directivity approximations. Geometrical shadowing and second-order scattering are explicitly included to explore the validity of the Kirchhoff approximation. No restrictions on the surface heights and slopes are made. The "goodness" of the resulting expressions is verified by requiring the pressure scattered by a sinusoidal surface to reduce to the image solution as the surface amplitude goes to zero. The first-order scattered pressure achieves a very good approximation to the image solution, and the second-order scattered pressure goes to zero, as expected, under this requirement. The theory is compared with available experimental scattering measurements, and the agreement is good. Because the slopes on the experimental surface are very steep, shadowing corrections are indispensible to achieving accurate first and second order scattering results. Shadowing has a greater impact on the scattering prediction than the second-order scattering contribution. This suggests that the Kirchhoff approximation may be more robust when incorporated into a theory including a detailed shadowing treatment as well as the Fresnel phase approximation and a good directivity approximation.
使用菲涅耳相位近似和实际源和接收器指向性近似，分析了三维压力释放正弦曲面的散射。明确包括几何阴影和二阶散射，以探索基尔霍夫近似的有效性。不对表面高度和斜率施加任何限制。通过要求由正弦曲面散射的压力随着表面幅度趋于零而减小到镜像解，来验证所得表达式的“正确性”。一阶散射压力非常好地逼近镜像解，并且二阶散射压力在这种要求下预期为零。该理论与可用的实验散射测量结果进行了比较，并且一致性很好。由于实验表面的斜率非常陡峭，阴影校正对于实现准确的一阶和二阶散射结果是必不可少的。阴影对散射预测的影响比二阶散射贡献更大。这表明，当将包括详细的阴影处理以及菲涅耳相位近似和良好的指向性近似的理论纳入其中时，基尔霍夫近似可能更稳健。
