Bellhop 海底地形起伏条件下的传播特性

Gnep@97

发布于 2023-08-10 10:53:19

5260

发布于 2023-08-10 10:53:19

文章被收录于专栏：Gnep's_Technology_BlogGnep's_Technology_Blog

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

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 \sqrt{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

'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 
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 -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 
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 -0.081900 410.000000 
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 -0.004975 495.000000 
 0.000000 500.000000 
 0.005025 505.000000 
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 1.130625 1175.000000 
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 1.166100 1190.000000 
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 1.190000 1200.000000 
 1.202025 1205.000000 
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 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 
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 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 
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 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 
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 1.766400 1420.000000 
 1.780625 1425.000000 
 1.794900 1430.000000 
 1.809225 1435.000000 
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 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 
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 2.045225 1515.000000 
 2.060400 1520.000000 
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 2.121600 1540.000000 
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 2.278100 1590.000000 
 2.294025 1595.000000 
 2.310000 1600.000000 
 2.326025 1605.000000 
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 2.358225 1615.000000 
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 2.606100 1690.000000 
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 2.640000 1700.000000 
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 2.674100 1710.000000 
 2.691225 1715.000000 
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 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 
 3.973025 2055.000000 
 3.993600 2060.000000 
 4.014225 2065.000000 
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 4.097225 2085.000000 
 4.118100 2090.000000 
 4.139025 2095.000000 
 4.160000 2100.000000 
 4.181025 2105.000000 
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 24.750000 5000.000000

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。