前言
由于水下声信道课程大作业的需要，因此本节专门研究海底地形起伏条件下的声传播特性。
一、预备内容
在所有实例中，我们均采用 Munk 深海声速剖面，界于 0 到 5000m 深度之间，声源频率 50Hz，位于 1000m 深度，声线步距 100m，声线70根，出射角扇面为 -13°~ 13°，海底声速1600m/s，海底密度 1.8g/cm3，海底衰减系数 0.8 dB/λ，海洋环境如下图所示：
应用的深海场景示意图
二、水平海底波导（水平海底）
注：波导含义：海洋波导可以理解为声波在海洋中传播的通道，比如经典的深海 Munk 剖面，声波会被限制在一定范围内的通道远距离传播,这个通道就可以理解为海洋波导
我们以从 0 到 101km 之间简单的声线轨迹（计算）作为开始。
下面是 Matlab 代码，分别绘制了海底水平的深海波导中的声线轨迹、海底水平的深海波导中的本征声线、海底水平的深海波导中的相干传播损失、到达声线（脉冲响应）
clc; clear; close all; global units; units = 'km'; bellhop flatwav_R % Runtype = 'R' figure; plotray flatwav_R % 海底水平的深海波导中的声线 bellhop flatwav_E % Runtype = 'E' figure; plotray flatwav_E % 海底水平的深海波导中的本征声线 bellhop flatwav_C % Runtype = 'C' figure; plotshd flatwav_C.shd % 海底水平的深海波导中的相干传播损失 bellhop flatwav_A % Runtype = 'A' % [ Arr, Pos ] = read_arrivals_asc( ARRFile, Narrmx ) [ Arr, Pos ] = read_arrivals_asc( 'flatwav_A.arr' ); % plotarr( filename, irr, ird, isd ) plotarr( 'flatwav_A.arr', 1, 1, 1 ) % 到达接收器处的脉冲响应
接下来我们会对上面代码分别进行讲解
1、海底水平的深海波导中的声线
①、环境文件
有关环境文件的具体讲解可以参考我之前的博客-> Bellhop 从入门到上手
flatwav_R.env
'Munk profile/Flat waveguide/Ray trace' % TITLE 50.0 % FREQ (Hz) 1 % NMEDIA 'SVW' % SSP-TOP-WATER-OPT 51 0.0 5000.0 % NMESH SIGMA Z(NSSP) 0.0 1548.52 / % Z() CP() CS() RHO() AP() AS() 200.0 1530.29 / 250.0 1526.69 / 400.0 1517.78 / 600.0 1509.49 / 800.0 1504.30 / 1000.0 1501.38 / 1200.0 1500.14 / 1400.0 1500.12 / 1600.0 1501.02 / 1800.0 1502.57 / 2000.0 1504.62 / 2200.0 1507.02 / 2400.0 1509.69 / 2600.0 1512.55 / 2800.0 1515.56 / 3000.0 1518.67 / 3200.0 1521.85 / 3400.0 1525.10 / 3600.0 1528.38 / 3800.0 1531.70 / 4000.0 1535.04 / 4200.0 1538.39 / 4400.0 1541.76 / 4600.0 1545.14 / 4800.0 1548.52 / 5000.0 1551.91 / 'A' 0.0 % BOTOPT SIGMA 5000.0 1600.00 0.0 1.8 .8 0.0 % ZB CPB CSB RHOB APB ASB 1 % NSD 1000.0 / % SD(1:NSD) (m) 1 % NRD 1000.0 / % RD(1:NRD) (m) 1 % NRR 101.0 / % RR(1:NRR ) (km) 'R' % OPTION: 'R/E/C/A/I/S 70 % NBEAMS ISINGLE -13.0 13.0 / % ALPHA(1:NBEAMS) (°) 100.0 5500.0 102.0 % STEP (m) ZBOX (m) RBOX (km)
②、Matlab 命令
bellhop flatwav_R % Runtype = 'R' figure; plotray flatwav_R % 海底水平的深海波导中的声线
一旦 Bellhop 完成计算，可以查验是否创建了两个文件：第一个是flatwav_R.prt，包含波导特性、出射角数目、计算时间等相关的综合信息；第二个是 flatwav_R.ray，它是包含射线坐标的 ASCII 码文件，并可用 M-文件 plotray.m 来绘进行图。
③、执行结果
海底水平的深海波导中的声线轨迹
2、海底水平的深海波导中的本征声线
将 OPTIONS3(1) = ‘R’ 改为 OPTIONS3(1) = ‘E’，和前面同样地运行程序，可以得到本征声线。
①、环境文件
将上面 flatwav_R.env 第 41 行的 ‘R’ 改为 ‘E’ 即可
'Munk profile/Flat waveguide/Eigenrays' 50.0 1 'SVW' 51 0.0 5000.0 0.0 1548.52 / 200.0 1530.29 / 250.0 1526.69 / 400.0 1517.78 / 600.0 1509.49 / 800.0 1504.30 / 1000.0 1501.38 / 1200.0 1500.14 / 1400.0 1500.12 / 1600.0 1501.02 / 1800.0 1502.57 / 2000.0 1504.62 / 2200.0 1507.02 / 2400.0 1509.69 / 2600.0 1512.55 / 2800.0 1515.56 / 3000.0 1518.67 / 3200.0 1521.85 / 3400.0 1525.10 / 3600.0 1528.38 / 3800.0 1531.70 / 4000.0 1535.04 / 4200.0 1538.39 / 4400.0 1541.76 / 4600.0 1545.14 / 4800.0 1548.52 / 5000.0 1551.91 / 'A' 0.0 5000.0 1600.00 0.0 1.8 .8 0.0 1 1000.0 / 1 1000.0 / 1 101.0 / 'E' 70 -13.0 13.0 / 100.0 5500.0 102.0
②、Matlab 命令
bellhop flatwav_E % Runtype = 'E' figure; plotray flatwav_E
③、执行结果
海底水平的深海波导中的本征声线
3、海底水平的深海波导中的相干传播损失
计算相干传播损失需要对输入文件做点小修改。首先，设置OPTIONS3(1) = ‘C’；其次，需要考虑是在 501×501 点的距离-深度矩形网格上计算传播损失。最后，我们设置 nbeams = 0，让 Bellhop 自行决定所需的射线根数。
①、环境文件
flatwav_C.env
'Munk profile/Flat waveguide/Coherent transmission loss' 50.0 1 'SVW' 51 0.0 5000.0 0.0 1548.52 / 200.0 1530.29 / 250.0 1526.69 / 400.0 1517.78 / 600.0 1509.49 / 800.0 1504.30 / 1000.0 1501.38 / 1200.0 1500.14 / 1400.0 1500.12 / 1600.0 1501.02 / 1800.0 1502.57 / 2000.0 1504.62 / 2200.0 1507.02 / 2400.0 1509.69 / 2600.0 1512.55 / 2800.0 1515.56 / 3000.0 1518.67 / 3200.0 1521.85 / 3400.0 1525.10 / 3600.0 1528.38 / 3800.0 1531.70 / 4000.0 1535.04 / 4200.0 1538.39 / 4400.0 1541.76 / 4600.0 1545.14 / 4800.0 1548.52 / 5000.0 1551.91 / 'A' 0.0 5000.0 1600.00 0.0 1.8 .0 .0 / 1 1000.0 / 501 0.0 5000.0 / 501 0.0 101.0 / 'C' 0 -14.0 14.0 / 100.0 5500.0 102.0
②、Matlab 命令
bellhop flatwav_C % Runtype = 'C' figure; plotshd flatwav_C.shd
运行 Bellhop，我们得到名为 flatwav_C.shd 的二进制文件，它实际上包含了经过相干计算的声压。我们用 M-文件 plotshd.m 来绘制传播损失图。
③、执行结果
海底水平的深海波导中的相干传播损失
4、到达接收器处的脉冲响应
修改 flatwav_C.env 设置 OPTIONS3(1)=‘A’
①、环境文件
flatwav_A.env
'Munk profile/Flat waveguide/Arrive' 50.0 1 'SVW' 51 0.0 5000.0 0.0 1548.52 / 200.0 1530.29 / 250.0 1526.69 / 400.0 1517.78 / 600.0 1509.49 / 800.0 1504.30 / 1000.0 1501.38 / 1200.0 1500.14 / 1400.0 1500.12 / 1600.0 1501.02 / 1800.0 1502.57 / 2000.0 1504.62 / 2200.0 1507.02 / 2400.0 1509.69 / 2600.0 1512.55 / 2800.0 1515.56 / 3000.0 1518.67 / 3200.0 1521.85 / 3400.0 1525.10 / 3600.0 1528.38 / 3800.0 1531.70 / 4000.0 1535.04 / 4200.0 1538.39 / 4400.0 1541.76 / 4600.0 1545.14 / 4800.0 1548.52 / 5000.0 1551.91 / 'A' 0.0 5000.0 1600.00 0.0 1.8 .0 .0 / 1 1000.0 / 1 1000.0 / 1 101.0 / 'A' 101 -14.0 14.0 / 100.0 5500.0 102.0
②、Matlab 命令
bellhop flatwav_A % Runtype = 'A' % [ Arr, Pos ] = read_arrivals_asc( ARRFile, Narrmx ) [ Arr, Pos ] = read_arrivals_asc( 'flatwav_A.arr' ); % plotarr( filename, irr, ird, isd ) plotarr( 'flatwav_A.arr', 1, 1, 1 )
运行 Bellhop 之后，得到名为 flatwav_A.arr 的 ascii 码文件，其中包含到达接收器位置的射线的振幅和传播时间（我们仅指一个位置点，该模型能够计算到达阵列块中所有阵列点的声线的传播时间和振幅）。包含在 *.arr 文件中的数据可以使用 M-文件 read_arrivals_asc.m 读取。
③、执行结果
到达接收器处的脉冲响应
三、高斯海山（变化的海底）
本小节描述针对不平海底应用 Bellhop 计算声线的算例。应用高斯函数生成一个理想化的海山， 并写入文件 seamount.bty。
1、海底形状文件
seamount.bty
'L' % 插值类型 101 % 点数 0 4997.16 % r( ) z( ) 1.01 4997.15 2.02 4997.15 3.03 4997.14 4.04 4997.12 5.05 4997.1 6.06 4997.07 7.07 4997.01 8.08 4996.93 9.09 4996.81 10.1 4996.64 11.11 4996.38 12.12 4996.01 13.13 4995.48 14.14 4994.74 15.15 4993.7 16.16 4992.26 17.17 4990.3 18.18 4987.66 19.19 4984.12 20.2 4979.45 21.21 4973.35 22.22 4965.48 23.23 4955.43 24.24 4942.75 25.25 4926.94 26.26 4907.46 27.27 4883.73 28.28 4855.18 29.29 4821.26 30.3 4781.43 31.31 4735.28 32.32 4682.48 33.33 4622.87 34.34 4556.49 35.35 4483.61 36.36 4404.74 37.37 4320.69 38.38 4232.57 39.39 4141.73 40.4 4049.81 41.41 3958.67 42.42 3870.3 43.43 3786.84 44.44 3710.38 45.45 3642.97 46.46 3586.5 47.47 3542.59 48.48 3512.54 49.49 3497.24 50.5 3497.16 51.51 3512.31 52.52 3542.22 53.53 3586 54.54 3642.36 55.55 3709.66 56.56 3786.04 57.57 3869.45 58.58 3957.77 59.59 4048.9 60.6 4140.82 61.61 4231.68 62.62 4319.84 63.63 4403.93 64.64 4482.85 65.65 4555.8 66.66 4622.25 67.67 4681.93 68.68 4734.79 69.69 4781.01 70.7 4820.89 71.71 4854.87 72.72 4883.47 73.73 4907.24 74.74 4926.77 75.75 4942.61 76.76 4955.32 77.77 4965.39 78.78 4973.28 79.79 4979.4 80.8 4984.08 81.81 4987.63 82.82 4990.28 83.83 4992.25 84.84 4993.69 85.85 4994.73 86.86 4995.48 87.87 4996.01 88.88 4996.38 89.89 4996.64 90.9 4996.81 91.91 4996.93 92.92 4997.01 93.93 4997.07 94.94 4997.1 95.95 4997.12 96.96 4997.14 97.97 4997.15 98.98 4997.15 99.99 4997.16 101 4997.16
2、环境文件
seamount_R.env
'Munk profile/Sea Mountain/Ray trace' % TITLE 50.0 % FREQ (Hz) 1 % NMEDIA 'SVW' % SSP-TOP-WATER-OPT 51 0.0 5000.0 % NMESH SIGMA Z(NSSP) 0.0 1548.52 / % Z() CP() CS() RHO() AP() AS() 200.0 1530.29 / 250.0 1526.69 / 400.0 1517.78 / 600.0 1509.49 / 800.0 1504.30 / 1000.0 1501.38 / 1200.0 1500.14 / 1400.0 1500.12 / 1600.0 1501.02 / 1800.0 1502.57 / 2000.0 1504.62 / 2200.0 1507.02 / 2400.0 1509.69 / 2600.0 1512.55 / 2800.0 1515.56 / 3000.0 1518.67 / 3200.0 1521.85 / 3400.0 1525.10 / 3600.0 1528.38 / 3800.0 1531.70 / 4000.0 1535.04 / 4200.0 1538.39 / 4400.0 1541.76 / 4600.0 1545.14 / 4800.0 1548.52 / 5000.0 1551.91 / 'A*' 0.0 % BOTOPT SIGMA 5000.0 1600.00 0.0 1.8 .0 0.0 % ZB CPB CSB RHOB APB ASB 1 % NSD 1000.0 / % SD(1:NSD) (m) 1 % NRD 1000.0 / % RD(1:NRD) (m) 1 % NRR 101.0 / % RR(1:NRR ) (km) 'R' % OPTION: 'R/E/C/A/I/S' 71 % NBEAMS ISINGLE -14.0 14.0 / % ALPHA(1:NBEAMS) (°) 100.0 5500.0 102.0 % STEP (m) ZBOX (m) RBOX (km)
3、Matlab 代码
下面是 Matlab 代码，分别绘制了高斯海山深海波导中的声线轨迹、高斯海山的深海波导中的本征声线、高斯海山的深海波导中的相干传播损失。
clc; clear all; close all; global units; units = 'km'; a=5; sigma=1; x=linspace(0,10.1,101); y=(1/((sqrt(2*pi))*sigma))*exp(-((x-a).^2)/(2*sigma.^2)); y = 4997.1624 - y / max(y) * 1500; fid = fopen('seamount.bty','wt'); fprintf(fid,'%1s%1s%1s\n',char(39),'L',char(39)); fprintf(fid,'%3d\n',length(y)); for mi = 1 : length(y) fprintf(fid,'%g %g \n',x(mi)*10,y(mi)); end fclose(fid); subplot(321); bellhop('seamount_R'); plotray('seamount_R');ylim([0 5000]) hold on; grid on; plot(x*1e1,y,'b','LineWidth',1.5); subplot(323); bellhop('seamount_E'); plotray('seamount_E');ylim([0 5000]) hold on; grid on; plot(x*1e1,y,'b','LineWidth',1.5); subplot(325); bellhop('seamount_C'); plotshd('seamount_C.shd');ylim([0 5000]) hold on; plot(x*1e1,y,'y','LineWidth',1.5); subplot(322); bellhop('seamount_R'); plotray('seamount_R');ylim([0 5000]) plotbty('seamount_R'); grid on; subplot(324); bellhop('seamount_E'); plotray('seamount_E');ylim([0 5000]) plotbty('seamount_E'); grid on; subplot(326); bellhop('seamount_C'); plotshd('seamount_C.shd');ylim([0 5000]) plotbty('seamount_C');
仿照之前的例子，将 OPTIONS3(1) = 'R’改为 OPTIONS3(1) = 'E’和 OPTIONS3(1) =‘C’，就能够分别计算得到本征声线和相干传播损失，因此这里其他环境文件不再一一列举。
3、执行结果
上图从上到下，从左到右依次为：高斯海山的深海波导中的声线轨迹、高斯海山的深海波导中的本征声线、高斯海山的深海波导中的相干传播损失。
注：左图和右图的区别在于右边图使用已有的 .bty 文件进行绘制
四、变化的边界（变化的海底和海面）
Bellhop 不仅能够处理变化的海底，还能够同时处理海面、海底都起伏变化的场景。
1、海面形状文件
波浪海面形状文件 varbounds.ati
'L' % 插值类型 101 % 点数 0 41.2215 % r( ) z( ) 1.01 69.0983 2.02 100 3.03 130.902 4.04 158.779 5.05 180.902 6.06 195.106 7.07 200 8.08 195.106 9.09 180.902 10.1 158.779 11.11 130.902 12.12 100 13.13 69.0983 14.14 41.2215 15.15 19.0983 16.16 4.89435 17.17 0 18.18 4.89435 19.19 19.0983 20.2 41.2215 21.21 69.0983 22.22 100 23.23 130.902 24.24 158.779 25.25 180.902 26.26 195.106 27.27 200 28.28 195.106 29.29 180.902 30.3 158.779 31.31 130.902 32.32 100 33.33 69.0983 34.34 41.2215 35.35 19.0983 36.36 4.89435 37.37 0 38.38 4.89435 39.39 19.0983 40.4 41.2215 41.41 69.0983 42.42 100 43.43 130.902 44.44 158.779 45.45 180.902 46.46 195.106 47.47 200 48.48 195.106 49.49 180.902 50.5 158.779 51.51 130.902 52.52 100 53.53 69.0983 54.54 41.2215 55.55 19.0983 56.56 4.89435 57.57 0 58.58 4.89435 59.59 19.0983 60.6 41.2215 61.61 69.0983 62.62 100 63.63 130.902 64.64 158.779 65.65 180.902 66.66 195.106 67.67 200 68.68 195.106 69.69 180.902 70.7 158.779 71.71 130.902 72.72 100 73.73 69.0983 74.74 41.2215 75.75 19.0983 76.76 4.89435 77.77 0 78.78 4.89435 79.79 19.0983 80.8 41.2215 81.81 69.0983 82.82 100 83.83 130.902 84.84 158.779 85.85 180.902 86.86 195.106 87.87 200 88.88 195.106 89.89 180.902 90.9 158.779 91.91 130.902 92.92 100 93.93 69.0983 94.94 41.2215 95.95 19.0983 96.96 4.89435 97.97 0 98.98 4.89435 99.99 19.0983 101 41.2215
2、海底形状文件
varbounds_R.bty
'L' 101 0 4997.16 1.01 4997.15 2.02 4997.15 3.03 4997.14 4.04 4997.12 5.05 4997.1 6.06 4997.07 7.07 4997.01 8.08 4996.93 9.09 4996.81 10.1 4996.64 11.11 4996.38 12.12 4996.01 13.13 4995.48 14.14 4994.74 15.15 4993.7 16.16 4992.26 17.17 4990.3 18.18 4987.66 19.19 4984.12 20.2 4979.45 21.21 4973.35 22.22 4965.48 23.23 4955.43 24.24 4942.75 25.25 4926.94 26.26 4907.46 27.27 4883.73 28.28 4855.18 29.29 4821.26 30.3 4781.43 31.31 4735.28 32.32 4682.48 33.33 4622.87 34.34 4556.49 35.35 4483.61 36.36 4404.74 37.37 4320.69 38.38 4232.57 39.39 4141.73 40.4 4049.81 41.41 3958.67 42.42 3870.3 43.43 3786.84 44.44 3710.38 45.45 3642.97 46.46 3586.5 47.47 3542.59 48.48 3512.54 49.49 3497.24 50.5 3497.16 51.51 3512.31 52.52 3542.22 53.53 3586 54.54 3642.36 55.55 3709.66 56.56 3786.04 57.57 3869.45 58.58 3957.77 59.59 4048.9 60.6 4140.82 61.61 4231.68 62.62 4319.84 63.63 4403.93 64.64 4482.85 65.65 4555.8 66.66 4622.25 67.67 4681.93 68.68 4734.79 69.69 4781.01 70.7 4820.89 71.71 4854.87 72.72 4883.47 73.73 4907.24 74.74 4926.77 75.75 4942.61 76.76 4955.32 77.77 4965.39 78.78 4973.28 79.79 4979.4 80.8 4984.08 81.81 4987.63 82.82 4990.28 83.83 4992.25 84.84 4993.69 85.85 4994.73 86.86 4995.48 87.87 4996.01 88.88 4996.38 89.89 4996.64 90.9 4996.81 91.91 4996.93 92.92 4997.01 93.93 4997.07 94.94 4997.1 95.95 4997.12 96.96 4997.14 97.97 4997.15 98.98 4997.15 99.99 4997.16 101 4997.16
3、环境文件
varbounds_R.env
'Munk profile/Variable boundaries/Ray trace' % TITLE 50.0 % FREQ (Hz) 1 % NMEDIA 'SVW *' % SSP-TOP-WATER-OPT 51 0.0 5000.0 % NMESH SIGMA Z(NSSP) 0.0 1548.52 / % Z() CP() CS() RHO() AP() AS() 200.0 1530.29 / 250.0 1526.69 / 400.0 1517.78 / 600.0 1509.49 / 800.0 1504.30 / 1000.0 1501.38 / 1200.0 1500.14 / 1400.0 1500.12 / 1600.0 1501.02 / 1800.0 1502.57 / 2000.0 1504.62 / 2200.0 1507.02 / 2400.0 1509.69 / 2600.0 1512.55 / 2800.0 1515.56 / 3000.0 1518.67 / 3200.0 1521.85 / 3400.0 1525.10 / 3600.0 1528.38 / 3800.0 1531.70 / 4000.0 1535.04 / 4200.0 1538.39 / 4400.0 1541.76 / 4600.0 1545.14 / 4800.0 1548.52 / 5000.0 1551.91 / 'A*' 0.0 % BOTOPT SIGMA 5000.0 1600.00 0.0 1.8 .0 0.0 % ZB CPB CSB RHOB APB ASB 1 % NSD 1000.0 / % SD(1:NSD) (m) 1 % NRD 1000.0 / % RD(1:NRD) (m) 1 % NRR 101.0 / % RR(1:NRR ) (km) 'R' % OPTION: 'R/E/C/A/I/S' 71 % NBEAMS ISINGLE -14.0 14.0 / % ALPHA(1:NBEAMS) (°) 100.0 5500.0 102.0 % STEP (m) ZBOX (m) RBOX (km)
4、Matlab 代码
下面是 Matlab 代码，分别绘制了波浪海面和高斯海山的深海波导中声速剖面、声线轨迹、本征声线、传播损失。
clc; clear all; close all; global units; units = 'km'; %======= Sea Surface ============ xs = linspace(0,10*pi,101); ys = 100 + sin(xs - pi/5) * 100; xs = xs / max(xs) *101; %======= Write the Sea Surface file ============ % fid = fopen('varbounds_R.ati','wt'); % fprintf(fid,'%1s%1s%1s\n',char(39),'L',char(39)); % fprintf(fid,'%3d\n',length(ys)); % for mi = 1 : length(ys) % fprintf(fid,'%g %g \n',xs(mi),ys(mi)); % end % fclose(fid); %======= Sea Bottom ============ a = 5; sigma = 1; x = linspace( 0,10.1,101 ); y = (1/((sqrt(2*pi)) * sigma)) * exp(-((x-a).^2)/(2*sigma.^2)); y = 4997.1624 - y / max(y) * 1500; %======= Write the Sea Bottom file ============ % fid = fopen('varbounds_R.bty','wt'); % fprintf(fid,'%1s%1s%1s\n',char(39),'L',char(39)); % fprintf(fid,'%3d\n',length(y)); % for mi = 1 : length(y) % fprintf(fid,'%g %g \n',x(mi)*10,y(mi)); % end % fclose(fid); %======= Calculating and Plotting ============ subplot(3,6,2.5:6); bellhop('varbounds_R'); plotray('varbounds_R');ylim([0 5000]) hold on; grid on; plotati('varbounds_E');plotbty('varbounds_E') % plot(x*1e4,y,'b','LineWidth',1.5); % plot(xs*1e3,ys,'b','LineWidth',1.5); subplot(3,6,8.5:12); bellhop('varbounds_E'); plotray('varbounds_E');ylim([0 5000]) hold on; grid on; plotati('varbounds_E');plotbty('varbounds_E'); xlabel(''); % plot(x*1e4,y,'b','LineWidth',1.5); % plot(xs*1e3,ys,'b','LineWidth',1.5); subplot(3,6,14.5:18); bellhop('varbounds_C'); plotshd('varbounds_C.shd');ylim([0 5000]) hold on; grid on; plotati('varbounds_E');plotbty('varbounds_E') % plot(x*1e4,y,'y','LineWidth',1.5); % plot(xs*1e3,ys,'y','LineWidth',1.5); %======= Other Plottings ============ subplot(3,6,[1 7 13]);plotssp('varbounds_C.env')
仿照之前的例子，将 OPTIONS3(1) = 'C’改为 OPTIONS3(1) = 'E’和 OPTIONS3(1) =‘R’，就能够分别计算得到本征声线和相干传播损失，因此这里其他环境文件不再一一列举。
5、执行结果
从左到右，从上到下分别绘制了波浪海面和高斯海山的深海波导中的声速剖面、声线轨迹、本征声线、传播损失。
五、分段线性边界（Dickins 海山）
Dickins 海山场景：先将海底测深理想化为 3000m 深度的平面，在距离 20km 的地方，升起一座海山，山顶延伸至海深 500m 处，海山模拟成三角形，底边 20km。
1、海底形状文件
DickinsB.bty
'L' 5 0 3000 10 3000 20 500 30 3000 100 3000
- 第 1 行指明“分段线性拟合”设为“L”，“曲线拟合”设为“C”。因为我们打算模拟一座三角形的海山，所以选择“分段线性拟合”。
- 第 2 行是测深点的数目，后续各行是以“距离-深度”来定义的“海底测深”
2、环境文件
DickinsB.env
'Dickins seamount' ! TITLE 230.0 ! FREQ (Hz) 1 ! NMEDIA 'CVW' ! SSPOPT (Analytic or C-linear interpolation) 525 0.0 3000.0 ! DEPTH of bottom (m) 0 1476.7 / 38 1476.7 / 50 1472.6 / 70 1468.8 / 100 1467.2 / 140 1471.6 / 160 1473.6 / 170 1473.6 / 200 1472.7 / 215 1472.2 / 250 1471.6 / 300 1471.6 / 370 1472.0 / 450 1472.7 / 500 1473.1 / 700 1474.9 / 900 1477.0 / 1000 1478.1 / 1250 1480.7 / 1500 1483.8 / 2000 1490.5 / 2500 1498.3 / 3000 1506.5 / 'A*' 0.0 3000.0 1550.0 0.0 1.5 0.5 / 1 ! NSD 18.0 / ! SD(1:NSD) (m) 201 ! NRD 0.0 3000.0 / ! RD(1:NRD) (m) 1001 ! NR 0.0 100.0 / ! R(1:NR) (km) 'CB' ! 'R/C/I/S' 0 ! NBEAMS -89.0 89.0 / ! ALPHA1,2 (degrees) 0.0 3100.0 101.0 ! STEP (m), ZBOX (m), RBOX (km)
第 4 行：我们看到顶端选项（针对声速剖面、海面以上半空间、海洋水体的设定）为“CVW”。“C”表示我们希望以“分段线性”方式对声速 c 进行插值。“V”是将海洋表面设置为“标准真空”的选项。“W”表示将衰减单位设定
为 dB/λ（波长），这是用于环境描述的单位。
第 5 行：水深设定为 3000m。在这种海底测深随距离变化的场景中，该深度值不是直接使用的，不过，因为它是海洋声速剖面定义的一部分，因此该深度值必须深到足以覆盖测深文件中随距离而变化的最深深度。
第 36 行中：我们看到“海底选项”设置为“A*”。“A”表示海底是“声学弹性”半空间，这是典型的设置。这里引入“*”，作为标志，是告诉 BELLHOP 要读取一个附加的测深文件“Dickins.bty”，来标识海深是随距离变化的。
3、Matlab 代码
clc; clear all; % close all global units ; units = 'km'; bellhop( 'DickinsB' ) plotshd( 'DickinsB.shd', 2, 1, 1 ) caxisrev( [ 70 120 ] ) plotbty 'DickinsB' % 绘制海深曲线 ram plotshd( 'RAM.shd.mat', 2, 1, 2 ) caxisrev( [ 70 120 ] ) plotbty 'DickinsB' % bellhop DickinsB_oneBeam % plotshd DickinsB_oneBeam.shd % caxisrev( [ 70 120 ] ) % plotbty 'DickinsB' TL = load('tl.line'); plot(TL(:,1)/1000,TL(:,2)); axis ij;
4、执行结果
Dickins 海山场景下的传播损失，从上到下依次为应用 Bellhop 、 应用RAM(抛物线方程模型)
上半图板是 BELLHOP 的计算结果，下半图板是我们当做参考解的 RAM PE 的计算结果。
两者的一致性是令人满意的；不过，人为的海山尖顶导致了大量的能量衍射。通过在不连续的测深点附近插入额外的测深点，这种情况可以得到进一步改善。
六、曲线拟合边界（抛物线海底）
我们考虑了 McGirr 等人所描述的抛物线型海底剖面，其深度由 D ( r ) = 500 1 + 4 r D(r) = 500 \sqrt{1+4r}D(r)=500
1+4r
给出，其中距离 r 单位为公里，深度 D 单位为米。声源位于焦点并作为原点，这是最理想的情况。
1、海底形状文件
ParaBot.bty
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2、环境文件
'Parabolic bottom profile' ! TITLE 10.0, ! FREQ (Hz) 1, ! NMEDIA 'CVW *', ! SSPOPT (Analytic or C-linear interpolation) 525 0.0 5100.0 ! DEPTH of bottom (m) -5100 1500.0 / 5100 1500.0 / 'A~' 0.0 5100.0 5000.0 0 1.0 0.0 0.0 / 1 ! NSD, 0.0 / ! SD(1:NSD) (m) 201 ! NRD 0.0 5000.0 / ! RD(1:NRD) (m) 501 ! NR, 0.0 20.0 / ! R(1:NR) (km) 'R' ! 'R/C/I/S' 50 ! NBEAMS -89.0 89.0 / ! ALPHA1,2 (degrees) 0 5100.0 25.1, ! STEP (m), ZBOX (m), RBOX (km)
3、Matlab 代码
clc; clear all; close all global units; units = 'km'; % linear boundary interpolation make_bdry( 'L' ) % the rays: bellhop ParaBot subplot(211); plotray ParaBot; axis( [ 0 20 -5000 5000 ] ) plotati 'ParaBot' % superimpose an altimetry plot plotbty 'ParaBot' % superimpose a bathymetry plot bellhop ParaBothl subplot(212); plotray ParaBothl; axis( [ 0 20 0 5000 ] ) plotbty 'ParaBot' % linear boundary interpolation make_bdry( 'C' ) bellhop ParaBot figure; subplot(311); plotray ParaBot; axis( [ 0 20 -5000 5000 ] ) plotati 'ParaBot'; plotbty 'ParaBot' bellhop ParaBothc subplot(312); plotray ParaBothc; axis( [ 0 20 0 5000 ] ) plotbty 'ParaBot' bellhop ParaBothcC subplot(313); plotshd ParaBothcC.shd; axis( [ 0 20 0 5000 ] ) plotbty 'ParaBot'
4、执行结果
从底部反射的声线应该与表面平行，就像手电筒中的反射面所产生的均匀光束一样。当我们超出 20 公里的距离时，声线的位置对底部各块小面元的倾斜非常敏感。我们每增加 25m 海深就进行一次测深采样，并将“测深插值”选项设置为“分段线性插值”，就得到下图所示的声线轨迹。下图中不规则的声线结构明显揭露了该方法的缺陷。
分段线性拟合边界反射的声线
为了获得更加平滑的声线轨迹，我们只需将测深文件内的第一个字母更改为“C”，即设置成“曲线拟合”选项，就可实现。这种改进的边界插值提供了一组完美的平行射线(在眼睛所能辨识的范围内)。
曲线拟合边界插值的抛物线测深剖面；从上到下依次是声线轨迹、声线轨迹、相干传播损失。
七、资源自取
CSDN 链接：https://download.csdn.net/download/qq_41839588/87855407?spm=1001.2014.3001.5503
总结
这就是文章的全部了，案例中详细讲解了水平海底、变化的海底、Dickins 海山以及抛物线海底场景下的声传播特性。
