Vecherin Sergey N, Albert Donald G
United States Army Cold Regions Research and Engineering Laboratory, 72 Lyme Road, Hanover, New Hampshire 03755, USA.
J Acoust Soc Am. 2018 Oct;144(4):2383. doi: 10.1121/1.5064467.
Predicting a full waveform of an acoustic broadband signal propagating over different impedance surfaces is a stringent test of both the method used in the modeling of propagation and the surface impedance models. It has been shown that predicted waveforms might be sensitive to the fractional travel time, when the propagation time of the pulse does not equal an integer number of computational time steps. A method overcoming this issue is developed and demonstrated for different propagation conditions: a pulse propagating over a snow layer, frozen ground, and their combinations along the propagating path with homogeneous and vertically stratified atmosphere for a range of 60 m. For the numerical simulations, a conventional one-way parabolic equation with the Crank-Nicholson numerical algorithm is modified to improve computational efficiency and insure that the experimental time of arrival and spatial location of the receiver are matched exactly to the digital grids used in the simulations. The results are in a good agreement with experimental measurements and prior knowledge, and confirm that physical properties of a snow layer, sublayer ground, atmospheric conditions, and the order of range dependent ground properties affect the pulse waveforms.
预测在不同阻抗表面上传播的声学宽带信号的完整波形，是对传播建模中使用的方法和表面阻抗模型的严格测试。研究表明，当脉冲的传播时间不等于计算时间步长的整数倍时，预测波形可能对分数传播时间敏感。针对不同的传播条件，开发并演示了一种克服此问题的方法：一个脉冲在雪层、冻土及其沿传播路径的组合上传播，传播路径上的大气为均匀且垂直分层的，范围为60米。对于数值模拟，对采用克兰克-尼科尔森数值算法的传统单程抛物线方程进行了修改，以提高计算效率，并确保接收器的实验到达时间和空间位置与模拟中使用的数字网格精确匹配。结果与实验测量和先验知识吻合良好，并证实雪层、下层地面的物理性质、大气条件以及与距离相关的地面性质的顺序会影响脉冲波形。
