文章目录
- 前言
- 一、预备内容
- 二、水平海底波导（水平海底）
- 1、海底水平的深海波导中的声线
- ①、环境文件
- ②、Matlab 命令
- ③、执行结果
- 2、海底水平的深海波导中的本征声线
- ①、环境文件
- ②、Matlab 命令
- ③、执行结果
- 3、海底水平的深海波导中的相干传播损失
- ①、环境文件
- ②、Matlab 命令
- ③、执行结果
- 4、到达接收器处的脉冲响应
- ①、环境文件
- ②、Matlab 命令
- ③、执行结果
- 三、高斯海山（变化的海底）
- 1、海底形状文件
- 2、环境文件
- 3、Matlab 代码
- 3、执行结果
- 四、变化的边界（变化的海底和海面）
- 1、海面形状文件
- 2、海底形状文件
- 3、环境文件
- 4、Matlab 代码
- 5、执行结果
- 五、分段线性边界（Dickins 海山）
- 1、海底形状文件
- 2、环境文件
- 3、Matlab 代码
- 4、执行结果
- 六、曲线拟合边界（抛物线海底）
- 1、海底形状文件
- 2、环境文件
- 3、Matlab 代码
- 4、执行结果
- 七、资源自取
- 总结
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：
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
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
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
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
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
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)=5001+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
'C'
1001
-0.250000 0.000000
-0.249975 5.000000
-0.249900 10.000000
-0.249775 15.000000
-0.249600 20.000000
-0.249375 25.000000
-0.249100 30.000000
-0.248775 35.000000
-0.248400 40.000000
-0.247975 45.000000
-0.247500 50.000000
-0.246975 55.000000
-0.246400 60.000000
-0.245775 65.000000
-0.245100 70.000000
-0.244375 75.000000
-0.243600 80.000000
-0.242775 85.000000
-0.241900 90.000000
-0.240975 95.000000
-0.240000 100.000000
-0.238975 105.000000
-0.237900 110.000000
-0.236775 115.000000
-0.235600 120.000000
-0.234375 125.000000
-0.233100 130.000000
-0.231775 135.000000
-0.230400 140.000000
-0.228975 145.000000
-0.227500 150.000000
-0.225975 155.000000
-0.224400 160.000000
-0.222775 165.000000
-0.221100 170.000000
-0.219375 175.000000
-0.217600 180.000000
-0.215775 185.000000
-0.213900 190.000000
-0.211975 195.000000
-0.210000 200.000000
-0.207975 205.000000
-0.205900 210.000000
-0.203775 215.000000
-0.201600 220.000000
-0.199375 225.000000
-0.197100 230.000000
-0.194775 235.000000
-0.192400 240.000000
-0.189975 245.000000
-0.187500 250.000000
-0.184975 255.000000
-0.182400 260.000000
-0.179775 265.000000
-0.177100 270.000000
-0.174375 275.000000
-0.171600 280.000000
-0.168775 285.000000
-0.165900 290.000000
-0.162975 295.000000
-0.160000 300.000000
-0.156975 305.000000
-0.153900 310.000000
-0.150775 315.000000
-0.147600 320.000000
-0.144375 325.000000
-0.141100 330.000000
-0.137775 335.000000
-0.134400 340.000000
-0.130975 345.000000
-0.127500 350.000000
-0.123975 355.000000
-0.120400 360.000000
-0.116775 365.000000
-0.113100 370.000000
-0.109375 375.000000
-0.105600 380.000000
-0.101775 385.000000
-0.097900 390.000000
-0.093975 395.000000
-0.090000 400.000000
-0.085975 405.000000
-0.081900 410.000000
-0.077775 415.000000
-0.073600 420.000000
-0.069375 425.000000
-0.065100 430.000000
-0.060775 435.000000
-0.056400 440.000000
-0.051975 445.000000
-0.047500 450.000000
-0.042975 455.000000
-0.038400 460.000000
-0.033775 465.000000
-0.029100 470.000000
-0.024375 475.000000
-0.019600 480.000000
-0.014775 485.000000
-0.009900 490.000000
-0.004975 495.000000
0.000000 500.000000
0.005025 505.000000
0.010100 510.000000
0.015225 515.000000
0.020400 520.000000
0.025625 525.000000
0.030900 530.000000
0.036225 535.000000
0.041600 540.000000
0.047025 545.000000
0.052500 550.000000
0.058025 555.000000
0.063600 560.000000
0.069225 565.000000
0.074900 570.000000
0.080625 575.000000
0.086400 580.000000
0.092225 585.000000
0.098100 590.000000
0.104025 595.000000
0.110000 600.000000
0.116025 605.000000
0.122100 610.000000
0.128225 615.000000
0.134400 620.000000
0.140625 625.000000
0.146900 630.000000
0.153225 635.000000
0.159600 640.000000
0.166025 645.000000
0.172500 650.000000
0.179025 655.000000
0.185600 660.000000
0.192225 665.000000
0.198900 670.000000
0.205625 675.000000
0.212400 680.000000
0.219225 685.000000
0.226100 690.000000
0.233025 695.000000
0.240000 700.000000
0.247025 705.000000
0.254100 710.000000
0.261225 715.000000
0.268400 720.000000
0.275625 725.000000
0.282900 730.000000
0.290225 735.000000
0.297600 740.000000
0.305025 745.000000
0.312500 750.000000
0.320025 755.000000
0.327600 760.000000
0.335225 765.000000
0.342900 770.000000
0.350625 775.000000
0.358400 780.000000
0.366225 785.000000
0.374100 790.000000
0.382025 795.000000
0.390000 800.000000
0.398025 805.000000
0.406100 810.000000
0.414225 815.000000
0.422400 820.000000
0.430625 825.000000
0.438900 830.000000
0.447225 835.000000
0.455600 840.000000
0.464025 845.000000
0.472500 850.000000
0.481025 855.000000
0.489600 860.000000
0.498225 865.000000
0.506900 870.000000
0.515625 875.000000
0.524400 880.000000
0.533225 885.000000
0.542100 890.000000
0.551025 895.000000
0.560000 900.000000
0.569025 905.000000
0.578100 910.000000
0.587225 915.000000
0.596400 920.000000
0.605625 925.000000
0.614900 930.000000
0.624225 935.000000
0.633600 940.000000
0.643025 945.000000
0.652500 950.000000
0.662025 955.000000
0.671600 960.000000
0.681225 965.000000
0.690900 970.000000
0.700625 975.000000
0.710400 980.000000
0.720225 985.000000
0.730100 990.000000
0.740025 995.000000
0.750000 1000.000000
0.760025 1005.000000
0.770100 1010.000000
0.780225 1015.000000
0.790400 1020.000000
0.800625 1025.000000
0.810900 1030.000000
0.821225 1035.000000
0.831600 1040.000000
0.842025 1045.000000
0.852500 1050.000000
0.863025 1055.000000
0.873600 1060.000000
0.884225 1065.000000
0.894900 1070.000000
0.905625 1075.000000
0.916400 1080.000000
0.927225 1085.000000
0.938100 1090.000000
0.949025 1095.000000
0.960000 1100.000000
0.971025 1105.000000
0.982100 1110.000000
0.993225 1115.000000
1.004400 1120.000000
1.015625 1125.000000
1.026900 1130.000000
1.038225 1135.000000
1.049600 1140.000000
1.061025 1145.000000
1.072500 1150.000000
1.084025 1155.000000
1.095600 1160.000000
1.107225 1165.000000
1.118900 1170.000000
1.130625 1175.000000
1.142400 1180.000000
1.154225 1185.000000
1.166100 1190.000000
1.178025 1195.000000
1.190000 1200.000000
1.202025 1205.000000
1.214100 1210.000000
1.226225 1215.000000
1.238400 1220.000000
1.250625 1225.000000
1.262900 1230.000000
1.275225 1235.000000
1.287600 1240.000000
1.300025 1245.000000
1.312500 1250.000000
1.325025 1255.000000
1.337600 1260.000000
1.350225 1265.000000
1.362900 1270.000000
1.375625 1275.000000
1.388400 1280.000000
1.401225 1285.000000
1.414100 1290.000000
1.427025 1295.000000
1.440000 1300.000000
1.453025 1305.000000
1.466100 1310.000000
1.479225 1315.000000
1.492400 1320.000000
1.505625 1325.000000
1.518900 1330.000000
1.532225 1335.000000
1.545600 1340.000000
1.559025 1345.000000
1.572500 1350.000000
1.586025 1355.000000
1.599600 1360.000000
1.613225 1365.000000
1.626900 1370.000000
1.640625 1375.000000
1.654400 1380.000000
1.668225 1385.000000
1.682100 1390.000000
1.696025 1395.000000
1.710000 1400.000000
1.724025 1405.000000
1.738100 1410.000000
1.752225 1415.000000
1.766400 1420.000000
1.780625 1425.000000
1.794900 1430.000000
1.809225 1435.000000
1.823600 1440.000000
1.838025 1445.000000
1.852500 1450.000000
1.867025 1455.000000
1.881600 1460.000000
1.896225 1465.000000
1.910900 1470.000000
1.925625 1475.000000
1.940400 1480.000000
1.955225 1485.000000
1.970100 1490.000000
1.985025 1495.000000
2.000000 1500.000000
2.015025 1505.000000
2.030100 1510.000000
2.045225 1515.000000
2.060400 1520.000000
2.075625 1525.000000
2.090900 1530.000000
2.106225 1535.000000
2.121600 1540.000000
2.137025 1545.000000
2.152500 1550.000000
2.168025 1555.000000
2.183600 1560.000000
2.199225 1565.000000
2.214900 1570.000000
2.230625 1575.000000
2.246400 1580.000000
2.262225 1585.000000
2.278100 1590.000000
2.294025 1595.000000
2.310000 1600.000000
2.326025 1605.000000
2.342100 1610.000000
2.358225 1615.000000
2.374400 1620.000000
2.390625 1625.000000
2.406900 1630.000000
2.423225 1635.000000
2.439600 1640.000000
2.456025 1645.000000
2.472500 1650.000000
2.489025 1655.000000
2.505600 1660.000000
2.522225 1665.000000
2.538900 1670.000000
2.555625 1675.000000
2.572400 1680.000000
2.589225 1685.000000
2.606100 1690.000000
2.623025 1695.000000
2.640000 1700.000000
2.657025 1705.000000
2.674100 1710.000000
2.691225 1715.000000
2.708400 1720.000000
2.725625 1725.000000
2.742900 1730.000000
2.760225 1735.000000
2.777600 1740.000000
2.795025 1745.000000
2.812500 1750.000000
2.830025 1755.000000
2.847600 1760.000000
2.865225 1765.000000
2.882900 1770.000000
2.900625 1775.000000
2.918400 1780.000000
2.936225 1785.000000
2.954100 1790.000000
2.972025 1795.000000
2.990000 1800.000000
3.008025 1805.000000
3.026100 1810.000000
3.044225 1815.000000
3.062400 1820.000000
3.080625 1825.000000
3.098900 1830.000000
3.117225 1835.000000
3.135600 1840.000000
3.154025 1845.000000
3.172500 1850.000000
3.191025 1855.000000
3.209600 1860.000000
3.228225 1865.000000
3.246900 1870.000000
3.265625 1875.000000
3.284400 1880.000000
3.303225 1885.000000
3.322100 1890.000000
3.341025 1895.000000
3.360000 1900.000000
3.379025 1905.000000
3.398100 1910.000000
3.417225 1915.000000
3.436400 1920.000000
3.455625 1925.000000
3.474900 1930.000000
3.494225 1935.000000
3.513600 1940.000000
3.533025 1945.000000
3.552500 1950.000000
3.572025 1955.000000
3.591600 1960.000000
3.611225 1965.000000
3.630900 1970.000000
3.650625 1975.000000
3.670400 1980.000000
3.690225 1985.000000
3.710100 1990.000000
3.730025 1995.000000
3.750000 2000.000000
3.770025 2005.000000
3.790100 2010.000000
3.810225 2015.000000
3.830400 2020.000000
3.850625 2025.000000
3.870900 2030.000000
3.891225 2035.000000
3.911600 2040.000000
3.932025 2045.000000
3.952500 2050.000000
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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。
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)。
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。
我的qq：2442391036，欢迎交流！
