Underwater Acoustic Signal Behavior Prediction in the
Region of Kauai Island
by
Wun Hoa Arthur Jai
B.S., Chinese Naval Academy, Taiwan, Republic of China, 1995
B.S., Virginia Military Institute, 1997
Submitted to the Department of Ocean Engineering and
the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degrees of
Master of Science in Ocean Engineering
and
and
MASSACHUSETTS INS
OF TECHNOt-OGy
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2004
C 2004 Massachusetts Institute of Technology. All rights reserved
E
E
SEP 0 12005
LIBRARIES
Auth or....................................................
4fepartment of Ocean Engineering
May 7, 2004
Certified by .......................................
Arthur B. Baggeroer
Ford Professor of Engineering
Professor of Ocean Engineering
jis4Qnervisor
Certified by............... .
.
...................
i ianahyllos R. Akylas
Professor of Mechanical Engineering
-- IMIX1411ID--er
.WW W
Accepted by...............................
Protessor Am A Sonin
Chairman, Department Committee on Graduate Students
IPejiip~nt &fechanical Engineering
Accepted by..............
Professor Michael S. Triantafyllou
Chairman, Department Committee on Graduate Students
Department of Ocean Engineering
BARKER
Underwater Acoustic Signal Behavior Prediction in the
Region of Kauai Island
by
Wun Hoa Arthur Jai
Submitted to the Department of Ocean Engineering and
the Department of Mechanical Engineering on May 7, 2004,
in partial fulfillment of the requirements for the degrees of
Master of Science in Ocean Engineering
and
Master of Science in Mechanical Engineering
Abstract
Behavior of underwater sound propagation over long-ranges has been studied for
several decades. The purpose of this is to describe sound propagation phenomena in
various ocean environments. The key to understanding and visualizing is
mathematical modeling. In the ocean acoustics community, four major mathematical
techniques have been commonly used to model behavior of acoustic signal in the
ocean environment. And they can be categorized into two different fields,
range-independent and range-dependent. The accuracy of each method is depends on
the environment characteristics. Since the propagating signal can be characterized
through the mathematical modeling, it is then possible to use the propagating signal to
perform beamforming and determine the characteristic of beam output.
Thesis Supervisor: Arthur B. Baggeroer
Title: Ford Professor of Engineering
Professor of Ocean Engineering
Thesis Reader: Triantaphyllos R. Akylas
Title: Professor of Mechanical Engineering
3
Acknowledgments
First, I would like to thank Professor Baggeroer for introducing me to the underwater acoustic community. With his encouragement, patience and guidance, It has
been great pleasure to do research under his supervision. And I would like to thank
Professor Akyla of Mechanical Engineering Department for being willing to provide
his expertise and knowledge to my research. Studying at MIT is a great experience,
doing research under the guidance of Professor Bggeroer and Professor Akyla is even
a privilege.
Thanks to all the staff and students of MIT Ocean Engineering Acoustics Group for
their help through out my research. Thanks to Joseph Sikora III for developing the
complete MatLab package and solving many programming problems. Thanks to Yisan Lai for his patience and knowledge when answering my question and computer
problems. Thanks to Josh Wilson for revising my thesis and providing suggestion.
Also, I would like to thank the friends who has been extremely supportive and
thoughtful during the past two years: Yun-Hua Fan, Jessica Lin, Sandy Chou, and
Tehyen Chu.
I would like to thank the colleagues and superior officers of Taiwan, Republic Of
China Navy for providing me with the chance to study at MIT.
Finally and most importantly, I wish to dedicate this work to my parents for their
endless support and love.
5
6
Contents
23
1 Introduction
Motivation and Methods ........
23
1.2
Problem statement . . . . . . . . .
25
Problem Solution Flow Chart
26
1.2.2
Tools . . . . . . . . . . . . .
27
Overview. . . . . . . . . . . . . . .
28
.
1.2.1
.
1.3
.
1.1
29
2 Formulation
. . . . . . . . . .
29
. .
. . . . . . . . . .
32
2.2
Parabolic Equation . . . . . . .
. . . . . . . . . .
35
2.3
Beamforming
. . . . . . . . . .
. . . . . . . . . .
37
2.3.1
Concept . . . . . . . . .
. . . . . . . . . .
38
2.3.2
Beamforming computation with p(r, z) data from CSNAP or
.
.
Numerical approach
.
.
.
.
.
2.1.1
.
.
.
Normal mode . . . . . . . . . .
2.1
. . . . . . . . . .
.
.
RAM models . . . . . .
41
45
3 Environment
source ..................
...........
45
3.2
Seabed property and bathymetry
. . . . . . . . . .
45
3.3
Sound Velocity Profile (SVP)
.
. . . . . . . . . .
50
3.4
Sonar Array . . . . . . . . . . .
. . . . . . . . . .
50
.
.
.
.
.
3.1
53
4 Results and Discussion
7
53
4.2
T L and p(r, z) . . . . . . . . . . . . . . . . . . . . . . . . . .
58
4.3
Beamform ing . . . . . . . . . . . . . . . . . . . . . . . . . .
58
4.4
Observation ......
60
.
.
.
Transmission Loss from RAM and CSNAP . . . . . . . . . .
............................
Peak shift and Phase slop difference between RAM and CSNAP
60
4.4.2
Resolution . . . . . . . . . . . . . . . . . . . . . . . .
60
4.4.3
Steering Angle
61
.
4.4.1
.
. . . . . . . . . . . . . . . . . . . . .
65
5.1
Grazing Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
5.2
Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
.
Conclusion and Future work
.
5
4.1
A Review of sound propagation in the ocean
67
B Derivation of Wave Equation
69
B.1 W ave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
69
B.1.1
Cylindrical Symmetric Horizontally Stratified Ocean Environm ent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
71
B.2 Normal Mode Method ......
..........................
72
C Beamforming Plots I, Source 75 Hz, receiver depth at 50 meters,
range increment ~ 1 km
77
D Beamforming Plots II, Source 75 Hz, receiver depth at 50 meters,
range increment ~ 5 km
83
E Beamforming Plots III, source 75 Hz, receiver depth at 50 meters,
range coverage range of 5 km
89
F Beamforming Plots V, Source 250 Hz, receiver depth at 50 meters,
range increment ~ 1 km
99
G Beamforming Plots VI, Source 250 Hz, receiver depth at 50 meters,
range increment ~ 5 km
105
8
H Beamforming Plots VI, source 250 Hz, receiver depth at 50 meters,
range coverage range of 5 km
I
111
Beamforming Plots VII, Source 75 Hz, receiver depth at 100 meters,
121
range increment ~ 1 km
J Beamforming Plots VIII, Source 75 Hz, receiver depth at 100 me127
ters, range increment ~ 5 km
K Beamforming Plots IX, source 75 Hz, receiver depth at 100 meters,
133
range coverage range of 5 km
L Beamforming Plots X, Source 250 Hz, receiver depth at 100 meters,
143
range increment ~ 1 km
M Beamforming Plots XI, Source 250 Hz, receiver depth at 100 meters,
149
range increment 2- 5 km
N Beamforming Plots XII, source 250 Hz, receiver depth at 100 meters,
155
range coverage range of 5 km
165
0 Beamforming Contour Plots
9
10
.
..
List of Figures
1-1
Major underwater acoustics modeling methods . . . . . . . . . . . . .
25
1-2
Problem Solution Flow Chart . . . . . . . . . . . . . . . . . . . . . .
26
2-1
zeroth order model for ocean waveguide . . . . . . . . . . . . . . . . .
30
2-2
plane wave propagation in the ocean acoustic waveguide
. . . . . . .
31
2-3
Modes as function of depth . . . . . . . . . . . . . . . . . . . . . . . .
31
2-4
Finite difference mesh approach for normal modes . . . . . . . . . . .
32
2-5
Basic Beamforming schematic . . . . . . . . . . . . . . . . . . . . . .
38
2-6
Angle of propagation direction from array broadside
. . . . . . . . .
40
2-7
Extract p(r, z) data from plot . . . . . . . . . . . . . . . . . . . . . .
42
3-1
NPAL source near Kauai Island . . . . . . . . . . . . . . . . . . . . .
46
3-2
3D plot of the underwater environment near Kauai Island . . . . . . .
47
3-3
2D plot of track from Kauai source . . . . . . . . . . . . . . . . . . .
48
3-4
Bathymetry along the the track . . . . . . . . . . . . . . . . . . . . .
48
3-5
Environmental Paremeters . . . . . . . . . . . . . . . . . . . . . . . .
49
3-6
The SVP near area of 22.5'N -159.5' W . . . . . . . . . . . . . . . . .
50
4-1
TL plot with source at 816 meter, 75Hz by RAM
. . . . . . . . . . .
54
4-2
TL plot with source at 816 meter, 75Hz by CSNAP . . . . . . . . . .
55
4-3
TL plot with source at 816 meter, 250Hz by RAM . . . . . . . . . . .
56
4-4
TL plot with source at 816 meter, 250Hz by CSNAP
. . . . . . . . .
57
4-5
M odeling set up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
4-6
Steering Angle vs range at 75 Hz . . . . . . . . . . . . . . . . . . . .
61
11
4-7
Steering Angle vs range at 250 Hz . . . . . . . . . . . . . . . . . . . .
62
4-8
Steering Angle vs range, when the coverage range is 5 km.
. . . . . .
63
. . . . . . . . . . . . . . . . . . . .
67
B-i Horizontally stratified ocean environment . . . . . . . . . . . . . . . .
71
B-2 Geometry of Cylindrical coordination . . . . . . . . . . . . . . . . . .
72
.
78
A-1 Sound Propagation in the Ocean
C-1 Beamforming, Source 75 Hz, receiver depth 50 m starting at 999 m
C-2 Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
78
C-3 Beamforming, Source 75 Hz, receiver depth 50 m starting at 1998 m .
79
C-4 Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
1998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
C-5 Beamforming, Source 75 Hz, receiver depth 50 m starting at 3000 m .
80
C-6 Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
3000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
C-7 Beamforming, Source 75 Hz, receiver depth 50 m starting at 3999 m .
81
C-8 Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
3999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
81
C-9 Beamforming, Source 75 Hz, receiver depth 50 m starting at 4998 m .
82
C-10 Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
D-1 Beamforming, Source 75 Hz, receiver depth 50 m starting at 4998 m .
84
D-2 Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
D-3 Beamforming, Source 75 Hz, receiver depth 50 m starting at 9999 m .
85
D-4 Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
9999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
D-5 Beamforming, Source 75 Hz, receiver depth 50 m starting at 15000 m
86
12
D-6 Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
86
D-7 Beamforming, Source 75 Hz, receiver depth 50 m starting at 4998 m
87
.
.
15000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D-8 Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
.
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
87
D-9 Beamforming, Source 75 Hz, receiver depth 50 m starting at 24999 m
88
D-10 Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
24999 m .......
..............
....................
88
E-1 Beamforming, Source 75 Hz, receiver depth 50 m covers from 999 m to
.
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
90
E-2 Beamforming, Source 75 Hz, receiver depth 50 m covers from 999 m to
.rceiv
.. . .d. . . . . .c.. . . . . . . . .
.
4998 m
90
E-3 Beamfo rming, Source 75 Hz, receiver depth 50 m covers from 999 m to
4998 m . . . . . . . . . . .
.
91
E-4 Beamforming, Source 75 Hz, receiver depth 50 m covers from 4998 m
91
.
to 9999 m . . . . . . . . .
E-5 Beamforming, Source 75 Hz, receiver depth 50 m covers from 4998 m
. . . .e . . . . . . . .
.
. . . . . . . . .
.
.
to 9999 m . . . . . . . . .
92
E-6 Beamforming, Source 75 Hz, receiver depth 50 m covers from 4998 m
. . . . . .r. . .9 . . .
.
. . . . . . . . .
.
.
to 9999 m. . . . . . . . . .
92
E-7 Beamforming, Source 75 Hz, receiver depth 50 m covers from 9999 m
..
. ..
. ..
. . . . . .
. . . . . . . . . . . .
.
. ...
.
to 15000 m
93
E-8 Beamforming, Source 75 Hz, receiver depth 50 m covers from 9999 m
. . . . . . . . . . . .
.
. . . . . . . . .
.
. . . . . . . .
.
to 15000 m
93
E-9 Beamforming, Source 75 Hz, receiver depth 50 m covers from 9999 m
94
. . . . . . . .
.
to 15000 m
E-10 Beamforming, Source 75 Hz, receiver depth 50 m covers from 15000 m
to 19998 m
..
... .... ... ... ... .. . ... . . ..
13
94
E-11 Beamforming, Source 75 Hz, receiver depth 50 m covers from 15000 m
to 19998 m
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
E-12 Beamforming, Source 75 Hz, receiver depth 50 m covers from 15000 m
to 19998 m. . . . . . . . ..
..
. . . . . . . . . . . . . . . . . . . . .
95
E-13 Beamforming, Source 75 Hz, receiver depth 50 m covers from 19998 m
to 24999 m
. . . . . . . ..
. . . . . . . . . . . . . . . . . . . . . . .
96
E-14 Beamforming, Source 75 Hz, receiver depth 50 m covers from 19998 m
to 24999 m
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
E-15 Beamforming, Source 75 Hz, receiver depth 50 m covers from 19998 m
to 24999 m
. . ..
. . . .. ...
. . . . ..
. . . . . . . . . . . . . .
97
F-1 Beamforming, Source 250 Hz, receiver depth 50 m starting at 999 m . 100
F-2 Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
F-3 Beamforming, Source 250 Hz, receiver depth 50 m starting at 1998 m
101
F-4 Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
1998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
101
F-5 Beamforming, Source 250 Hz, receiver depth 50 m starting at 3000 m
102
F-6 Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
3000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
102
F-7 Beamforming, Source 250 Hz, receiver depth 50 m starting at 3999 m
103
F-8 Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
3999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
103
F-9 Beamforming, Source 250 Hz, receiver depth 50 m starting at 4998 m
104
F-10 Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
104
G-1 Beamforming, Source 250 Hz, receiver depth 50 m starting at 4998 m
106
G-2 Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
106
G-3 Beamforming, Source 250 Hz, receiver depth 50 m starting at 9999 m
107
14
G-4 Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
9999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
107
G-5 Beamforming, Source 250 Hz, receiver depth 50 m starting at 15000 m 108
G-6 Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
15000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
G-7 Beamforming, Source 250 Hz, receiver depth 50 m starting at 4998 m
109
G-8 Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
G-9 Beamforming, Source 250 Hz, receiver depth 50 m starting at 24999 m 110
G-10 Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
110
H-1 Beamforming, Source 250 Hz, receiver depth 50 m covers from 999 m
to 4998 m ........
.................................
112
H-2 Beamforming, Source 250 Hz, receiver depth 50 m covers from 999 m
to 4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
H-3 Beamforming, Source 250 Hz, receiver depth 50 m covers from 999 m
to 4998 m .......
.............
....................
113
H-4 Beamforming, Source 250 Hz, receiver depth 50 m covers from 4998 m
to 9999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
H-5 Beamforming, Source 250 Hz, receiver depth 50 m covers from 4998 m
to 9999 m ........
............
....................
114
H-6 Beamforming, Source 250 Hz, receiver depth 50 m covers from 4998 m
to 9999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
114
H-7 Beamforming, Source 250 Hz, receiver depth 50 m covers from 9999 m
to 15000 m
. . . . .. . . . . .. . . . . . . . . . . . . . . . . . . . .
115
H-8 Beamforming, Source 250 Hz, receiver depth 50 m covers from 9999 m
to 15000 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
115
H-9 Beamforming, Source 250 Hz, receiver depth 50 m covers from 9999 m
to 15000 m
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
15
H-10 Beamforming, Source 250 Hz, receiver depth 50 m covers from 15000
m to 19998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
116
H-II Beamforming, Source 250 Hz, receiver depth 50 m covers from 15000
m to 19998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
117
H-12 Beamforming, Source 250 Hz, receiver depth 50 m covers from 15000
m to 19998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
117
H-13 Beamforming, Source 250 Hz, receiver depth 50 m covers from 19998
m to 24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
118
H-14 Beamforming, Source 250 Hz, receiver depth 50 m covers from 19998
m to 24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
118
H-15 Beamforming, Source 250 Hz, receiver depth 50 m covers from 19998
m to 24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
119
I-1
Beamforming, Source 75 Hz, receiver depth 100 m starting at 999 m .
122
1-2
Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
122
1-3
Beamforming, Source 75 Hz, receiver depth 100 m starting at 1998 m
123
1-4
Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
1998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
123
I-5
Beamforming, Source 75 Hz, receiver depth 100 m starting at 3000 m
124
1-6
Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
3000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
1-7
Beamforming, Source 75 Hz, receiver depth 100 m starting at 3999 m
1-8
Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
1-9
125
3999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
125
Beamforming, Source 75 Hz, receiver depth 100 m starting at 4998 m
126
1-10 Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
J-1
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
126
Beamforming, Source 75 Hz, receiver depth 100 m starting at 4998 m
128
16
J-3
Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
.
J-2
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
128
Beamforming, Source 75 Hz, receiver depth 100 m starting at 9999 m
129
J-4 Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
.
9999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
129
J-5 Beamforming, Source 75 Hz, receiver depth 100 m starting at 15000 m 130
J-6 Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
.
15000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
130
J-7 Beamforming, Source 75 Hz, receiver depth 100 m starting at 4998 m
131
J-8 Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
.
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
131
J-9 Beamforming, Source 75 Hz, receiver depth 100 m starting at 24999 m 132
J-10 Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
.
24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
132
K-1 Beamforming, Source 75 Hz, receiver depth 100 m covers from 999 m
.
to 4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
134
K-2 Beamforming, Source 75 Hz, receiver depth 100 m covers from 999 m
.1 . . . . . . . . . . . . .
.
.
to 4998 m . . . . . . . . . . . . . . . . .
134
K-3 Beamforming, Source 75 Hz, receiver depth 100 m covers from 999 m
.10 . . . .o . . . . . . . . .
.
.
to 4998 m . . . . . . . . . . . . . . . . .
135
K-4 Beamforming, Source 75 Hz, receiver depth 100 m covers from 4998 m
. . . . . . . . . . . . . .
..................
.
to 9999 m ...
135
K-5 Beamforming, Source 75 Hz, receiver depth 100 m covers from 4998 m
to 9999 m . . . . . . . . . . . . . . . . .
.
136
K-6 Beamforming, Source 75 Hz, receiver depth 100 m covers from 4998 m
to 9999 m . . . . . . . . . . . . . . . . .
.
136
K-7 Beamforming, Source 75 Hz, receiver depth 100 m covers from 9999 m
17
. . . . . . . . . . . . . .
.
. . . . . . . . . . . . . . . .
.
to 15000 m
137
K-8 Beamforming, Source 75 Hz, receiver depth 100 m covers from 9999 m
to 15000 m .......
.............................
... 137
K-9 Beamforming, Source 75 Hz, receiver depth 100 m covers from 9999 m
to 15000 m
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
K-10 Beamforming, Source 75 Hz, receiver depth 100 m covers from 15000
m to 19998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
138
K-11 Beamforming, Source 75 Hz, receiver depth 100 m covers from 15000
m to 19998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
K-12 Beamforming, Source 75 Hz, receiver depth 100 m covers from 15000
m to 19998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
K-13 Beamforming, Source 75 Hz, receiver depth 100 m covers from 19998
m to 24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
K-14 Beamforming, Source 75 Hz, receiver depth 100 m covers from 19998
m to 24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
K-15 Beamforming, Source 75 Hz, receiver depth 100 m covers from 19998
m to 24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
141
L-1 Beamforming, Source 250 Hz, receiver depth 100 m starting at 999 m
144
L-2 Magnitude and Phase,Source 250 Hz, receiver depth 100 m starting at
999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
144
L-3 Beamforming, Source 250 Hz, receiver depth 100 m starting at 1998 m 145
L-4 Magnitude and Phase,Source 250 Hz, receiver depth 100 m starting at
1998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
145
L-5 Beamforming, Source 250 Hz, receiver depth 100 m starting at 3000 m 146
L-6 Magnitude and Phase,Source 250 Hz, receiver depth 100 m starting at
3000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
146
L-7 Beamforming, Source 250 Hz, receiver depth 100 m starting at 3999 m 147
L-8
Magnitude and Phase,Source 250 Hz, receiver depth 100 m starting at
3999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
L-9 Beamforming, Source 250 Hz, receiver depth 100 m starting at 4998 m 148
18
L-10 Magnitude and Phase,Source 250 Hz, receiver depth 100 m starting at
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
M-1 Beamforming, Source 250 Hz, receiver depth 100 m starting at 4998 m 150
M-2 Magnitude and phase, source250 Hz, receiver depth 100 m starting at
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
M-3 Beamforming, Source 250 Hz, receiver depth 100 m starting at 9999 m 151
M-4 Magnitude and phase, source250 Hz, receiver depth 100 m starting at
9999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
M-5 Beamforming, Source 250 Hz, receiver depth 100 m starting at 15000 m 152
M-6 Magnitude and phase, source250 Hz, receiver depth 100 m starting at
15000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
M-7 Beamforming, Source 250 Hz, receiver depth 100 m starting at 4998 m 153
M-8 Magnitude and phase, source250 Hz, receiver depth 100 m starting at
4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
M-9 Beamforming, Source 250 Hz, receiver depth 100 m starting at 24999 m 154
M-l0Magnitude and phase, source250 Hz, receiver depth 100 m starting at
24999 m ........
..............................
....
154
N-1 Beamforming, Source 250 Hz, receiver depth 100 m covers from 999 m
to 4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
156
N-2 Beamforming, Source 250 Hz, receiver depth 100 m covers from 999 m
to 4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
156
N-3 Beamforming, Source 250 Hz, receiver depth 100 m covers from 999 m
to 4998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
157
N-4 Beamforming, Source 250 Hz, receiver depth 100 m covers from 4998
m to 9999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
N-5 Beamforming, Source 250 Hz, receiver depth 100 m covers from 4998
m to 9999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
N-6 Beamforming, Source 250 Hz, receiver depth 100 m covers from 4998
m to 9999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
19
N-7 Beamforming, Source 250 Hz, receiver depth 100 m covers from 9999
.
m to 15000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
159
N-8 Beamforming, Source 250 Hz, receiver depth 100 m covers from 9999
.
m to 15000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
159
N-9 Beamforming, Source 250 Hz, receiver depth 100 m covers from 9999
.
m to 15000 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
160
N-10 Beamforming, Source 250 Hz, receiver depth 100 m covers from 15000
.
m to 19998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
160
N-11 Beamforming, Source 250 Hz, receiver depth 100 m covers from 15000
.
m to 19998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
161
N-12 Beamforming, Source 250 Hz, receiver depth 100 m covers from 15000
.
m to 19998 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
161
N-13 Beamforming, Source 250 Hz, receiver depth 100 m covers from 19998
.
m to 24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
162
N-14 Beamforming, Source 250 Hz, receiver depth 100 m covers from 19998
.
m to 24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
162
N-15 Beamforming, Source 250 Hz, receiver depth 100 m covers from 19998
.
m to 24999 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
163
0-1 source=75HZ receiver depth=50M increment=1KM . . . . . . . . . .
166
0-2 source=250HZ receiver depth=50M increment=1KM
. . . . . . . . .
167
0-3 source=75HZ receiver depth=100M increment=1KM
. . . . . . . . .
168
0-4 source=250HZ receiver depth=100M increment=1KM . . . . . . . . . 169
0-5 source=75HZ receiver depth=50M increment=5KM . . . . . . . . . .
170
0-6 source=250HZ receiver depth=50M increment=5KM
. . . . . . . . .
171
0-7 source=75HZ receiver depth=100M increment=5KM
. . . . . . . . .
172
0-8 source=250HZ receiver depth=100M increment=5KM . . . . . . . . .
173
20
List of Tables
Starting Point and Ending Point of the Track
21
. . . . . . . . . . . .
.
3.1
49
22
Chapter 1
Introduction
This thesis describes my research on modeling range-dependent underwater acoustic
propagation behavior in the ocean environment near Kauai Island. The computational results will be used as the prediction for the experiment that will be conducted
as part of the NPAL (North Pacific Acoustics Laboratory) project in September,
2004.
In this chapter I will explain the motivation and goal for this experiment as well as
the suitable methods for solving our problem. Also, I will show the steps to solve our
problem in a flow chart, and explain the tools and concepts that are needed for our
problem.
1.1
Motivation and Methods
Conducting experiments in a very large scale sometimes is time consuming and unpractical, Thus modeling is the solution to overcome that difficulty. To model the underwater acoustic behavior, mathematical methods are the keys in simulating sound
propagation and representing signal characteristics without performing experiment
physically.
In the underwater acoustics community, the major methods that are
common used for modeling sound propagation.Each method has its advantage and
disadvantages when applying in different environment and they are listing as following:
23
1. Ray Tracing :
Advantage : Very useful where computational speed is a critical factor and environmental uncertainty has more severe constrains on accuracy.
Disadvantage: When applying to low frequency problems, it leads to a coarse
approximation in the result.
2. Wavenumber Integration :
Advantage : Is computationally efficient for simple range independent environment.
Disadvantage : Needs to be modified in order to apply to range-dependent
problems.Also takes longer the longest computational time than the other three
methods.
3. Normal Mode:
Advantage : high accuracy when apply to range independent environment with
high mode umber. By dividing the propagation path into a sequence of rangeindependent segments, Normal Mode method can be used to compute a range
dependent problem
Disadvantage:Takes great amount of computational power and memory space,leads
long computation time.
4. Parabolic Equation:
Advantage : can be directly applied to range-dependent environment and requires less computational power than Normal Mode method and Wavenumber
Integration method.
Disadvantage : For shallow water environments, requires more computational
time than Normal Mode method.
The feasibility of each method in various environment is shown in Fig 1-1
24
The blue boxes indicate that the model is applicable and practical, and orange
boxes indicate the model is applicable but with some theoretical limitations.
My modeling requirements are:(1) deep water, (2)low frequency and (3)range dependent. The modeling methods that best meet the environments are the Normal
Mode(NM) method and parabolic equation (PE) method [9].
The codes that use Normal Mode and PE methods are RAM (Range dependent
Acoustic Modeling) and C-SNAP(Coupled SACLANTCEN normal mode propagation loss model).
1.2
Problem statement
The goal for this experiment is to identify how sound wave propagates in the underwater environment with a down slope bathymetry and with that kind of bathymetry
what beam output will be as a function of range, depth and angle with respect to the
source.
,______
APPLICATION
DEEP WATER
SHALLOW WATER
MODEL TYPE
RI
RD
RD
RI
HF
LF
HF
LF
RI
RD
RI
RD
RAY
NORMAL MODE
FAST FIELD (FFP)
PARABOLIC EQ.
LE: LOW FREQUENCY (<500 Hz)
HF: HIGH FREQUENCY (>500 Hz)
RI : RANGE INDEPENDENT
RD: RANGE DEPENDENT
Figure 1-1: Major underwater acoustics modeling methods
25
1.2.1
Problem Solution Flow Chart
Our goal is to determine the signal received by a sonar array as function of range,
depth, and angle in the ocean environment around Kauai island.
A flow chart for calculating the array beamforming output is shown in Fig 1-2 I first
Input I
Bathymetry, SVP, Evironment
I
Range-independent Modeling
RAM & CSNAP
Output I
Input 2
Calculate p(rz) at each sensor in the array
Transmission Loss
Beamforming
Output 2
Received signal as function of range, depth
and angle.
Figure 1-2: Problem Solution Flow Chart
input the bathymetry, Sound Velocity Profile (SVP) and other environmental parameters and use RAM and CSANP to calculate the pressure field p(r, z) and generate
Transmission Loss (TL). The TL plots are to help us to visualize the sound propagation path from source. I will then extract the pressure data p(r, z) at each sensor
26
4669"A"WOM
I .
- -,
II
..
I
I-
. . .
across the sonar array as the inputs for Beamforming. Since the p(r, z) is composed
of real and imaginary number,by using the beamforming algorithm, I will be able to
determine the power of received signal on the towed array as a function of angle, and
by beamforming at different ranges and depths, thus I will be able to determine the
sonar array outputs as functions of range, depth and angle.
1.2.2
Tools
For solving our problem we need modeling codes and the codes that We are going to
use are RAM and CSNAP. These two modeling are written based on the Parabolic
Equation(PE) and Normal Mode (NM) respectively.
Transmission loss
As I mentioned in Section 1.2.1 that the underwater acoustic propagation will be
represented by the Transmission Loss (TL). And transmission loss in the ocean the
transmission can be described as the sum of the a loss due to geometrical spreading (in
my case is cylindrical spreading) and a loss due to attenuation (volume attenuation,
for example) [13]
TL = TL(geometry) + TL(spreading)
(1.1)
and it's given as the ratio in decibels between the acoustic intensity I(rz) at a field
point and the intensity I measured at 1-m distance from the source, thus the transmission loss can be expressed as:
TL = -10 log I(r,
=
I0
-20 log's (rZ)
|p 0|
(1.2)
Beamforming
The purpose of Beamforming is to determine the the location and bearing of the
source. For my case, a linear sonar array is towed by ship. Whenever the propagation direction of signal is aligned with the steering direction of the array, the energy
27
I
MWA"
received by all sensors on the array should be the maximum. Based on this idea, we
can find the bearing of our source (determining range will require more sophisticated
computation). More detail will be explained in Chapter 2.3
1.3
Overview
This thesis will divided into five chapters, the layout of each chapter is as following:
" Chapter 1 Introduction: Gives the general description of the experiment and
concept that this thesis intents to present.
" Chapter 2 Formulation: This chapter will explain Normal Mode and Parabolic
Equation methods. The method for calculating array beamforming will also be
described.
" Chapter 3 Experiment Scenario and Setups : shows the ocean environment,
sound velocity profile and related parameters that will be used in the experiment. Also described are the source and sonar array.
* Chapter 4 Results : This chapter shows the Transmission Loss and Beamforming results generated from the modeling methods and explains the differences
between results.
" Chapter 5 Conclusion : Summarizes the result and gives suggestions on the
experiment and future work.
28
Chapter 2
Formulation
In this chapter, I will give reader some background by introducing the methods and
concepts of Normal Mode, Parabolic Equation and Beamforming, and explain how
these formulation fit into our problem.
A full derivation of Normal Modes and Parabolic Equations can be found in Appendix
B.
2.1
Normal mode
The pressure field p(r, z) in a Horizontally stratified waveguide with a Homogeneous
point source in a cylindrical coordinate system is
p(r.z) =
an(zo)un(z)Rn(r) =
u7r
U(ZO)
HOl(krn0
p(zO)
partl
(Z)
(2.1)
and part 1 is called Normal Modes of waveguide denoted as
pn(r, z) = H,()(knr)un(z)
(2.2)
Here the mode is given by the two point boundary conditions. The modal eigenfunction un(z)is determinted primarily by the boundary condition of the waveguide.
29
Consider a waveguide problem as shown in Fig 2.1 , say this is a homogeneous fluid
Ocean surface
p=0
z =0
r
z7
Receiver (rz)
* Source (0, zo)
pc
SP -0
z=h
&Z
Ocean bottDm
Figure 2-1: zeroth order model for ocean waveguide
d 2 u"(z)
dz 2
+
equation will be
layer with constant density Ldz- = 0, thus the eigenvalue
(2.3)
kznun(z) = 0
assuming pressure release surface and sea bottom, the solution un(z) is
Un(Z) =
psin kznZ, knz =
h
(2.4)
r
, n=1, 2, 3, ...
From Equation 2.1 we know
p(r,z)
=
2iir
h Zsinkznzo sinkznzH1 )(knr)
(2.5)
which is approximately equal to for kn r > 1
p(r, z)
7re 4
h
00
sin k(zn)zo
[ei(kznz+knr)
-
ei(kznz-knr)]
ar
n=1
(2.6)
partl
from the above equation we can interpret part1 as a down and up going plan wave,
as illustrated in Fig 2-2. We know that k2 = k2 (z) - k,. Where kn and knz are the
30
the horizontal and vertical component of k respectively. From Equation 2.4 we can
see that when the mode n increases, the angle 0, will decrease (plan wave propagates
at a steeper angle).
We can also represent modes as function of depth in the waveguide. From Equation
2.4, whenever sin kanz goes to 0, the p(r, z) will also be 0. It implies that there are
points where the pressure contribution of ni mode wave will be zero. If we plot it as
function of depth, it will look like nodes along the z(depth), as shown in Fig 2-3
Ocean surface
z =0
p=0
rI
I
z=h
I
Ocean bottbm
Figure 2-2: plane wave propagation in the ocean acoustic waveguide
Mode
4
Mode
3
Mode
2
Mode
11
-o-
-0-
-0
-
-0
50
-
100
-i 0
I
-oo1
0
100
1
-1
0
1
Figure 2-3: Modes as function of depth
31
100
-I
0
2.1.1
Numerical approach
Now the question is how to formulate Equation 2.3 into a form that can be unmerically
calculated for arbitrary c(z) and p(z)? Recalling that k2 = k 2 (z) - k2 and k(z)
W
=
replace kzn in the Equation 2.3.
d2 u,(z)
2
21
k,2
__-
dz 2
c2(z)
*~l
un(z)
= 0
(2.7)
As shown in Fig 2-4 the waveguide of depth D is divided into N even layers. So
L-
-------------
iLN -
-----
Z = 0
---------
-------- ------
z = LD
Figure 2-4: Finite difference mesh approach for normal modes
h= Q. Notice that, let un(z) = qI(z) and k,, = k, (horizontal wavenumber). So
Equation 2.3 is rewritten as
J (2
T'(z) +
- r] F(z) = 0
(-
(2.8)
+
xpji = Tj + T'h
32
h2
2'! +
'3
+
using Taylor series expansion we have
(2.9)
after rearranging Equation 2.9, we can obtain the forward difference approximation
as
V =4 j++
- jh2 -
,h
-
+
(2.10)
takes only the O(h) and we have
+ Tj
hj+1
h
(2.11)
Inserting Equation 2.8 into Equation 2.10 we have the forward difference approximation
+ Tj
J- +j+1
2
w
h
2
c
h
- 2]
'
(z)
2
(2.12)
For the backward difference approximation, we start with Taylor series expansion as
=h+ 2!
Wy =y -W
h2
3!
h3
(2.13)
---
and through same method we have the O(h) approximation
"Ii
Tjl-
3-~
(2.14)
h
and inserting into Equation 2.8, we get the backward difference approximation
E2
+ - X
h
c2
-
(z)
k2
r
v h-
2
(2.15)
By adding Equation 2.9 and Equation 2.13 we can get the centered difference approximation
W'If
=
'F- - 21Q + Qjl+Oh2
2
l1
'i+i+1+O(h2)
(2.16)
Now, insert Equations 2.12,2.15 and 2.16 into Equation 2.8 we have
c2 (z -
k}2
AFs
+
h2
+
l'j
33
h2
=
0, j=1,...N-1
(2.17)
with boundary conditions
=
TO
'QN+1
0
(2.18)
0
(2.19)
we can see that Equation 2.17 , Equation 2.18 is a eigenvalue problem in the form of
[B
-
(k )I
(2.20)
= 0
and the Equation 2.20 has N eigenvalues k' corresponding eigenvectors pm, where
, so p
IPm is a vector with components of T, TT'
~m(zj) and B is as
d1 e 2
e2
d2
(2.21)
eN-1
dN-1
eN
eN
dN
where the
ej =
w2
h2
1
c2 (z3
)
-2
h
the variable k' can then be solved by tridiagonal solution or by the Kraker method.
Inverse Iteration
Now, since we have k1, we can now use inverse iteration to find the corresponding
eigenvector Tm by using
Wi(zj)
A(kr2)T,+1(zj) =F
34
(2.22)
We choose any arbitrary set of values for the initial eigenvector, say TOim
=
[1, 1, 1, ... , 1].
After sufficient amount of iterations of Equation 2.22, we can find a good approximation for actual value of
Jm.
This sufficient amount can be determined by making
the difference between the actual and approximated
'Jim
small enough.
Mode Normalization
After finding the eigenvector
Nm
=
/c)
WIp
z)
im
we need to normalize the eigenvector by applying
D
/11
-T(z) dz ~
00 + #1 +
02
+
+
ON-1
+
- ON
(2.23)
where
Oj =(2.24)
p(zj)
2.2
Parabolic Equation
The Parabolic Equation (PE) method was first introduced into underwater acoustic community by F.D.Tappert in 1977 [10]. After his initiation of parabolic wave
equation, the PE technique has been widely used for underwater acoustic modeling.
This technique provides an efficient numerical solution scheme based on fast Fourier
transforms for solving range-dependent propagation problems in underwater acoustics. The advantage of the PE is that it assume that the forward scattering dominates
the energy, thus there is no need to consider the backscattering. Therefore, a a oneway wave equation that can be solved by a range-marching technique with proper
starting field.
The standard parabolic equation using the small angle approximation [7] is
1& b
2akr +
192 '
_1V
+ k (n 2 -1)iP=0
(2.25)
For our problem, we can't use Equation 2.25 since it is only considered to be accurate
for propagation angles within 10-15 degree off the horizontal. [13]. Thus, we need
another PE approximation that can handle more wide-angled problems. Recall the
35
Helmholtz equation,
-+p ap_
09r
az paz)
+ k2 p = 0
(2.26)
+ k2
(2.27)
We define X to be an operator given by
X = k-2 p
az p az
insert into Equation 2.26, we have
-
(4r
iko( + X)
) (r
iko(1 + X)ip=O
-
(2.28)
outgoing energy
incoming energy
we assumed that the outgoing energy dominates back-scattered energy, thus
Or
(2.29)
= iko(1 + X)2p
and solution for Equation 2.29 is
p(r + Ar, z) = exp (ikoAr(1 + X)") P(r, z)
where Ar is the range step.
(2.30)
By applying n term rational function expansion to
approximate the (1 + X)2 term, we then have
p(r + Ar, z) = exp(ikoAr) H
p(r, z)
(2.31)
Xp(r, z)
(2.32)
and after partial fraction expansion
p(r + Ar, z) = exp(ikoAr)
where ac,n and
1+ E
j,n are the accuracy and stability constraints.
3
As we mentioned in page35, we need field starter for PE and since we are using RAM
for our problem, the self starter will be used for the Equation 2.30. [5].
36
How do we get a self starter suitable for our environment?
We start by assuming that we have a line source at z = zo and in the plane geometry,
p(r, z) will be satisfied by
-
ax
+
Oz pOz/
+ k 2p = 2i6(x)6(z - zo)
(2.33)
Integrate Equation 2.33 over the distance x from origin we have
lim
x-o0+ 09x
= i6(z - zO)
(2.34)
Insert Equation 2.34 into Equation 2.33 we have
ko(1 + X)2p
=
6(z
-
zO)
(2.35)
Now, plug Equation 2.35 into Equation 2.30 , and Ar = xO, here the range step xO is
on the order of wavelength. Then we have
ikoxo(1 + X) 2
p(X 0 , z) = k 0 ( 1X)! 6(z - zo)
ko(1+ X) -2
(2.36)
However, Equation is not qualified for our case -- "homogeneous point source" and
"cylindrical coordinate". Therefore, we need to modify this p(xo, z) to be suitable for
our environment. The self starter that meets our environment is as.
exp (ikoxo(1 + X)1)
p(X 0 , z) = e(z
k 2 (1
2.3
-
z0)
(2.37)
+X):1
Beamforming
The idea for beamforming is to determine the location of a source that is generating/radiating energy [10]. For our case, we are going to use line array to get information of received signal on array to determine at which direction/bearing where
the strongest power is. This direction estimation mathematically is same as to esti37
mate the spatial Fourier transform of the radiation field. This kind of problem in the
underwater community is called passive sonar problem.
2.3.1
Concept
Assume that a source radiates signal outward into the farfield. When the signal arrives
at our array, the wave can be considered as a plane-wave signal s(t, x) propagating
through medium (in our case is water)at speed c in the direction of L, shown in Fig
2-5 and the mth sensor on the array will receive the wave written as
Directin of propagation
b
Aray direction
-wave from source
z
II
-
/
I
- - - - a
-
1W
Figure 2-5: Basic Beamforming schematic
xm(t) = s t -
TM) + nm(t)
c)
where L is the propagation direction, c is the phase speed of wave, and T
(2.38)
is the
location of mth sensor. L - - is the dot product of - and L implies the projection of L
onto
'.
The total output on the array y(t) is then
y(t)
=
Z amxm(t - 7m)
M
38
(2.39)
where am is the taper function of mth sensor and rm is the time delay for the mth
sensor to receive the incoming signal. Our goal is to obtain the maximum y(t) where
all the delays are compensated, thus the signal are added coherently (no phase difference). When the maximum energy is achieved, the direction (angle) that is needed to
compensate all sensor delays rm is then the direction -ko where the source is located.
Now the field on mth sensor after delay time is compensated can be written as
Xm(t - Tm) = s(t) + nm(t - rm)
(2.40)
and the total output y(t) on the array is then
y(t) = Ms(t) + E nm(t - rm)
(2.41)
m
Here we let the weight am = 1 (every sensor has the same weight).And the total signal
power on array is P(t) = Iy(t)1 2 . From Equation 2.41 the signal power is equal to M 2
(M is the number of sensors) times s(t) (plan-wave signal) on each sensor and here
we assume that the noise on each sensor can is described as mutually uncorrelated
processes, thus we exclude the noise term in our calculation. However, to formulate
the beamforming, we will need to compute the output y(t) in the Frequency Domain
[12][1]. So take Fourier transform on both x(t) and y(t) we have
Xm(f) = S(f) exp
j 27r
(f)
z.
(2.42)
ko
as the Fourier transform of xm(t) and
Y(f, k) = E am exp {j
27r
(f)
zm
k
Xm(f)
(2.43)
as the Fourier transform of y(t). Knowing that zm - k = rm sin 0 and 0 is the
angle of propagation from the array broadside we also know that -A = L. Equation
39
2.43 is then written as
Y(f 1 0)
=
Zm
am exp
-j 27r
(- rm sin
A
part2
9}Xm(f)
(2.44)
artl
partl
Here rm is the distance from the source to the mth sensor on sonar array and let
part 1 be vector X and part 2 be vector A'. The total energy in the beam across
frequency bandwidth is the f IY(f Ir)2 I df, However, since the signal from our source
is a narrow band signal and the frequency that we are interested in is fo, thus the
beam energy P(O) is now
2
P(O) = lY(fo I r)1 2 = I A' X1
(2.45)
Now Equation 2.45 is formulated in matrix form [2] [11] [3]. vector A' is now as
(-j 21r
a1 exp
(-j 27r ()
(-j 27r (A)
a2 exp
am exp (-j
27r
(A
()
sin
o)
sin 01)
sin 02
)
ao exp
rm sin Om)
Propagation diection
Sensors across sonar atray
Figure 2-6: Angle of propagation direction from array broadside
40
(2.46)
since we assume this is a far field problem,
00,01,
02,...
are the same.
As for vector X, it is written as X = caS + ouN,where the -, and a are the power
levels of signal and noise. To simplify our problem, we let a, to be spatially white.
So,
P(9) = [lY(f 10)121 =[A'
X[2]
= [A' X X' A] = A' R A
(2.47)
[15] matrix R = [X X'] is called spatial correlation matrix of sensor outputs. Thus,
by finding matrix A and X we will then be able to perform beaming computation. [6]
Beamforming computation with p(r, z) data from CSNAP
2.3.2
or RAM models
To apply the matrix formulation as shown in Equation 2.46 we have to first compute
the p(r, z) by RAM or CSNAP at a fixed frequency, for our case, we will compute at
75 Hz and 250 Hz. At a given depth, we will perform beamforming with the sonar
array at several ranges R 1 , R 2 , R3 ... , R is the range from the source to 1 8 t sensor of
array at range R. First, we need to extract the p(r, z) data at depth of z and compute
X(f
I r).
The X(f
I r)
vector is the pressure field as function of frequency at the
mth sensor on the sonar array as show in Fig 2-7, thus vector X is
X(f
I rm)
= [Xo(f
I ro), X 1 (f I ri), X 2 (f I r2), ...
Xm(f
I rm)
(2.48)
where rm is the distance from the source to the mth sensor across the sonar array and
f is the frequency that we are interested. So, we can compute the spatial correlation
matrix
XX'
41
(2.49)
RAM - Transmission Loss (dB) - SD=816m,
f=75Hz
500
1000
P(r,z) on Ist sensor
of array at range of
R Xo(f/ra )
1500
2000
2500
w 20
range(km)
Figure 2-7: Extract p(r, z) data from plot
42
Also, the vector of A is equal to Equation 2.46. However, here we will let all am
(weight for each sensor) to be 1. thus we have
ro sin 9)
exp (-j 2-x
(}
(})
()
exp (-j 27r
(}
rm sin 9)
exp (-j 2-7
exp (-j 27
A
=
r1 sin 0
r2
sin 9)
(2.50)
So, plug vector A and X into Equation 2.45 and have directional angle 9 varies
from from 0 to 180, we will obtain the signal power P as function of the "angle
of the direction of propagation from the array broadside" 0, and by looking for the
maximum signal power, we will be able to identify the bearing of the source with
respect to the sonar array.
43
44
Chapter 3
Environment
In this chapter, I will describe the environment where the experiment will take place.
3.1
source
The source for the experiment used to emit the signal is was previously installed and
used by the Acoustic Thermometry of Ocean Climate (ATOC) Project and will be
used for the North Pacific Acoustic Laboratory (NPAL) project. The source is located on the seafloor at a depth of 816 meters, approximately 8 nautical miles (14.8
km) north of Kauai at 22,34.9'N, 159, 56.9'W as shown in Fig 3-1
For my modeling, the source will send out signal at frequencies of 75Hz and 250Hz.
3.2
Seabed property and bathymetry
The underwater environment and bathymetry around the region of Kauai Island is
shown in Figs 3-2, 3-3, and 3-4.
Note that, in Fig 3-2 the yellow dot indicates the location of source.
For my modeling, I only use the area where the seabed has been surveyed in the
precision with a 1/50 mins. The reason is in order to do beamforming suitable for
our needs (3 meters spacing between each sensor across sonar array), we need to have
45
I
22020'
N
22010'
159050, W
159040'
Figure 3-1: NPAL source near Kauai Island
46
-1000
-159.6
-2000-
uJ
-3000
059.4
22.3
22.35
22.4
LATITUDE
Figure 3-2: 3D plot of the underwater environment near Kauai Island
47
-1000
22.5
22.48
22.46
.1500
22.44
22.
-2000
2 2.4
22. 38
.2500
22.
22.34
22.32
-3000
22
-159.45
Longitude (deg)
Figure 3-3: 2D plot of track from Kauai source
Baevywoery
1000
1500
2000
2500
30001
0
5
10
15
range(kmi)
20
25
Figure 3-4: Bathymetry along the the track
48
30
Longitude
Latitude
starting point
22.349
-159.569
ending point
22.5091
-159.343
Table 3.1: Starting Point and Ending Point of the Track
very high precision bathymetry data.
In addition to the 1/50 mins bathymetry data, GEODAS also provides bathymetry
data. However, due to the fact that the data points recorded in the GEODAS are in 2
mins precision. thus, I have choose the 1/50 mins bathymetry data. The disadvantage
for using this data is that the area is very limited (the longest distance from source
to the furthest point is only about 30 km.
The total distance that my modeling covers is 29.251 Km. The starting and ending
points are shown in Table3.1:
and the sediment and water-column property are as following:
Reference velocity
1600 m/s
Source depth
816 m
Source frequency
75 Hz / 250 Hz
Sediment depth
80 m
Sediment density
2 kg/mA3
Sediment attenuation
0.5 dB/lambda
Sediment sound speed
1800 m/s
Highest mode allowed in computation
500
Receiver depth
>50 m
Figure 3-5: Environmental Paremeters
49
3.3
Sound Velocity Profile (SVP)
The SVP used for this modeling is from a measurement taken near 22.5' N, -159.5 W
and is shown in Fig 3-6. It is true that the SVP should change with range, however,
Sound Velocity Profile
0
1000-
2000-
3000-
4000
5000-
500
1510
1520
15 10
1530
4o
Velocity (MIS)
1550
1550
1580
1560
1570
Figure 3-6: The SVP near area of 22.5'N -159.5' W
after comparing other measured SVP, I found that the change is negligible. Thus we
ignore any range dependence to the SVP.
3.4
Sonar Array
For modeling purpose, I set the array at depths of 50 and 100 meters. For the actual
experiment, the array will be towed by a research ship at a depth of approximately
50 meters and will normally be aligned to the source such that the signal arrives from
end-fire direction. The array sensors are spaced 3 meters apart. For my modeling,
each sensor is weighted equally without any taper distribution. In actual experiment,
50
the each sensor will be weighted according to the experiment requirement.
51
52
Chapter 4
Results and Discussion
In this chapter I will present the results of modeling the sound propagation at 75Hz
and 250Hz using two different mathematical codes. The result includes TL at both
frequencies and beamforming with source at both frequencies and receiver (sonar array) at different depths. Also, I will discuss the explanation for the results from my
modeling.
4.1
Transmission Loss from RAM and CSNAP
Following the flow chart in Fig 1-2 the first step is to input the environmental parameters as shown in Fig 3-5. And then to obtain the transmission loss at both frequencies
by RAM and CSNAP. The TL results are shown in Figs 4-1,4-2, 4-3,and 4-4.
From these figures, it is apparent that the lower modes get to travel further by
forming a "bottom bounce" bouncing between the sea floor and surface (see explanation in Appendix A). Also, when the sound propagates into the down slope
bathymetry, the energy spreads out. Since the sediment thickness in my modeling is
only 80 meters, and the sub-bottom has property as rigid bottom, therefore there is
not much energy penetrates into to seabed except for the region near the location of
source.
When comparing Fig 4-1 and Fig 4-3, it is also observed that at higher frequency the
53
RAM - Transmission Loss (dB) - SD=816m, f=75Hz
Above 160
140
500
120
1000
100
0
"a
1500
80
2000
0
40
2500
10
20
15
25
Figure 4-1: TL plot with source at 816 meter, 75Hz by RAM
54
Below 20
CSNAP - Transmission Loss (dB) - SD=816m,f=75Hz
Above 160
140
500
120
1000
100
1500
\80
2000
0
2500
40
5
10
15
range (km)
20
25
Figure 4-2: TL plot with source at 816 meter, 75Hz by CSNAP
55
RAM - Transmission Loss (dB) - SD=816m, f=250Hz
kbove 160
140
500
120
1000
100
1500
'80
2000
60
2500
5
10
20
15
25
range(km)
Figure 4-3: TL plot with source at 816 meter, 250Hz by RAM
56
Below 20
CSNAP - Transmission Loss (dB) - SD=816m,f=250Hz
Above 160
140
00
120
1000
100
E
C1500
80
-8
2000
60
2500
40
5
10
20
15
25
range (km)
Figure 4-4: TL plot with source at 816 meter, 250Hz by CSNAP
57
Below 20
sound field is attenuated more.
4.2
TL and p(r, z)
Following the Flow Chart in Fig 1-2. The pressure p(r, z) data is calculated by RAM
and CSNAP and are used to compute TL as shown in Equation 1.2. Therefore, I can
extract p(r, z) at points where the sensors of linear sonar array locate at while RAM
and CSNAP are computing the TL. The locations of points I need for beamforming
at both 250Hz and 75Hz in various depth and range are tabulated in Fig 4-5
4.3
Beamforming
Following the recipe in Chapter 2.3.2. After the the real part and imaginary part
of p(r, z) are obtained from RAM and CSNAP, they are used as the elements in the
X(f
I rm)
vector of Equation 2.48. Once I obtain the real and imaginary part of
p(r, z), the spatial correlation matrix R can be calculated.
Now, what about the the steering vector A in Equation 2.50?
Since the frequencies, the location of array sensors of are known, I only need to choose
the angle 0 matrix A.
For my modeling, I am interested in the angle between the normal of array and
direction of coming in signal, therefore, I look at angle from -7r
to 7r.
And the
sampling rate for my modeling use is -r/800. Insert into the Equation 2.47, the
beamforming results (in degrees) and phase comparison results by using p(r, z) data
from RAM and CSNAP are plotted in the Appendix C to N.
58
Receiver at depth of 50 meters, range increment is approximately 1 km:
The range that covered by the sonar array (64 sensors with 3 meters spacing)
RAM
999 m-1188m 1998m-2187m 3000m-3189m 3999m-4188m 4998m-5187m
CSNAP
999 m-1188m
1998m-2187m
3000m-3189m
3999m-4188m
4998m-5187m
Receiver at depth of 50 meters, range increment is approximately 5 km:
The range that covered by the sonar array (64 sensors with 3 meters spacing)
RAM
4998m-5178m
9999m-10188m
150OOm-15189m
19998m-20187m
24999m-25188m
CSNAP
4998m-5178m
9999m-10188m
15000m-15189m
19998m-20187m
24999m-25188m
Receiver at depth of 50 meters, range increment is approximately 1 km:
The range that covered by the sonar array (64 sensors with 3 meters spacing)
RAM
999 m-1188m 1998m-2187m 3000m-3189m 3999m-4188m 4998m-5187m
CSNAP
999 m-1188m
1998m-2187m
3000m-3189m
3999m-4188m
4998m-5187m
Receiver at depth of 50 meters, range increment is approximately 5 km:
The range that covered by the sonar array (64 sensors with 3 meters spacing)
RAM
4998m-5178m
9999m-10188m
150OOm-15189m
19998m-20187m
24999m-25188m
CSNAP
4998m-5178m
9999m-10188m
15000m-15189m
19998m-20187m
24999m-25188n
Receiver at depth of 100 meters, range increment is approximately 1 km:
The range that covered by the sonar array (64 sensors with 3 meters spacing)
RAM
999 m-1188m
1998m-2187m 3000m-3189m
3999m-4188m
4998m-5187m
CSNAP
999 m-1188m
1998m-2187m
3999m-4188m
4998m-5187m
3000m-3189m
Receiver at depth of 100 meters, range increment is approximately 5 km:
The range that covered by the sonar array (64 sensors with 3 meters spacing)
RAM
4998m-5178m
9999m-10188m
15000m-15189m
19998m-20187m
24999m-25188m
CSNAP
4998m-5178m
9999m-10188m
15000m-15189m
19998m-20187m
24999m-25188m
Receiver at depth of 100 meters, range increment is approximately 1 km:
The range that covered by the sonar array (64 sensors with 3 meters spacing)
RAM
999 m-1188m
1998m-2187m
3000m-3189m
3999m-4188m
4998m-5187m
CSNAP
999 m-1188m
1998m-2187m
3000m-3189m
3999m-4188m
4998m-5187m
Receiver at depth of 100 meters, range increment is approximately 5 km:
The range that covered by the sonar array (64 sensors with 3 meters spacing)
RAM
4998m-5178m
9999m-10188m
150OOm-15189m
19998m-20187m
24999m-25188m
CSNAP
4998m-5178m
9999m-10188m
150OOm-15189m
19998m-20187m
24999m-25188m
Figure 4-5: Modeling set up
59
Observation
4.4
Peak shift and Phase slop difference between RAM and
4.4.1
CSNAP
From the beamforming plots, it is observed that, the beamforming peak of RAM and
CSNAP are occasionally different at both frequencies. At 75Hz the angle difference
is less than at 250Hz. However, one unusual phenomena in RAM is also observed at
1.99 km,250Hz for both 50 m and 100 m depth. the peak difference deviates from
CSNAP by more than 20 degree. See Figs F-3,L-3.
From the phase plots, it seems that the phase between RAM and CSNAP do not have
the same slope for array length of 189 meters. For example, for source frequency 75
Hz, receiver depth 50 meter set, see Fig C-2,C-4, C-6,C-8, C-10. However, If I extend
the range coverage to 5 km, the phase plots of RAM and CSNAP then have similar
slope, same number of cycle and very close TL, as shown in Fig E-2, E-3 in Appendix
E. Thus, we know that the p(r, z) data obtained from RAM and CSNAP do carry
the same information traveling through the waveguide.
Resolution
4.4.2
After obtaining Beamforming results for different range increments (1 km and 5 km)
at different depth (50 m and 100 m), I use the individual Beamforming results to
construct contour plots of beamforming in order to identify the resolution of the
beam output. The contour plots are shown in the Appendix 0
With the same geological parameters (range and depth).
It is observed that the
beamforming resolution increases when the source frequency increases. (compare Fig
0-1
,
0-2, for example).
Also, with the same frequency and geological parameters, the resolution increases
(peak band is narrower) as the range increment increases (compare Fig 0-4, 0-8, for
example).
60
Steering angle vs Range, 75hz, 50 m
I
0
0)
e 50
I
-RAM
*-*-.-.--~--
-
C
40
0.5
ICSNAP
4.5
4
3.5
3
2.5
2
1.5
1
5
e 8so
50
25
20
Steerind Rngle vs Range, 75A!, 100 m
5
0
R AM
---..
-CSNAP
..
.. . . .. ..
- . . ..
. ..
60 -
-
0
S70
150
-
-RAM
- - CSNAP -.-.
Ca40
0.5
U
80
(D
60 -.
-
-
060-
4.5
4
CSNAP
C 500
0
5
5
M
...
.RA
-.--...
.... . .
-..
.
3.5
3
2.5
2
1.5
1
15
10
20
25
range in km
Figure 4-6: Steering Angle vs range at 75 Hz
4.4.3
Steering Angle
From the geometry relation between the location of the source and sonar array, it
is expected that the steering angle should increase as the range increases due to the
fact that the grazing angle of the received single should be closer to horizontal as the
range goes further, and eventually becomes an end-fire situation. Not surprisingly,
from my modeling, it is observed that the angles does increase as range increases but
the increasing at both 75 Hz and 250 Hz is not steady if the coverage range is only the
length of sonar array (see Figs 4-6 and 4-7). But, regardless the unsteady increasing,
the final grazing angle at ~ 30 km is ~ 75 to 76 degree for both 75 Hz and 250 Hz.
If the coverage range is extended to 5 km, the steering angle for RAM and CSNAP
becomes identical as shown in Fig 4-8. The increasing steering angle can also be
observed from the beamforming contour plots in Appendix 0. The red stripe starts
from between 50 to 60 degree goes down to ~ 80 degree (final grazing angle).
61
Steering angle vs Range, 250hz, 50 m
ID 80r0
-
60
c
-
-
c
20
1
70
-- RAM
CSNAP
1.5
1
0.5
o80
3.5
3
2.5
2
-
--
40
-CSNAP
4.5
4
5
CD
60
25
20
Steeringlhgle vs Range, 256 z, 100 m
5
0
70
-.
-...
.-.
.
-..-..
-.
. .. .
.
-
A
M
-.-.-.-R
. .. .
-.
50 -. . .. .
-
06 0 - . .
-- CSNAP
W40
0)
0.5
1.5
1
3.5
3
2.5
2
4.5
4
5
1)80111
70cO K
601
0
CRAM
5
15
10
20
range in km
Figure 4-7: Steering Angle vs range at 250 Hz
62
25
Steering angle vs Range, with coverage range 5km, 75hz, 50 m
~80
......................
ai60-
-- RAM
0Y)
-
50[
0
ai)
80
_0
70
5D
0D
.C:
C
5
15
.........
..... ....
50'
SIbering angle vs Ra
0
('NA
20
25
--
- --
60 50
10
-
..........
-
Ca
-
-
.
0)
70
0
............
RAM
CSNAP
-
e, with coverage r ge 5km, 250hz, 5 9n
25
80
70
-F
0)
C
60
-
5
10
-
C
50
CD
0
15
RAM-CSNAP
20
25
80
70 -...
600---
-.
-
- - --- --
--
RAM
CSNAP
Ca50'
0
-
CD(D
-
ci)
5
10
15
20
25
range in km
Figure 4-8: Steering Angle vs range, when the coverage range is 5 km.
63
64
U
U
EU
Chapter 5
Conclusion and Future work
5.1
Grazing Angle
Steering Angle vs Range Increment
In this thesis, I used two different modeling methods to find pressure as a function
of range and depth. Then I used those pressure values to perform the Beamforming
.
and determinate the optimal angel for steering the acoustic array
It is found that the best steering angle for the sonar array is about 75-76 degrees
at both 75 Hz and 250 Hz. The steering angles for single frequency with different
range increment (1 km and 5 km) are identical. However, those angles are computed
under the assumption that the sonar array is aligned with the source (or end firing).
Therefor, the angle may be different if the geometrical relation between array and
source becomes broadside or near broadside. In reality, for a ship's towed array, it
is possible that array will not always be at end-fire. The different geometries will
require further study.
Steering Angle vs Range
As shown in Fig 4-6,4-7, 4-8, also the contour plots in Appendix 0, the steering angle
reaches maximum value of 75-76 degree after passing 10 km point. This implies that
the steering becomes independent from range after 10 km. However, due to the fact
65
that the range that I used only covers approximately 30 km, to ensure the assumption
that the steering will not increase over 76 degree will need further study.
5.2
Future work
Although this modeling does provide results in predicting the beam output on sonar
array as a function of range, depth and frequency. There are still some areas that can
be improved and emphasized for more advance research on this subject in the future:
* Result verification with experimental data: The pressure data is obtained by
using computational methods (RAM and CSNAP), there is no "real world"
data to compare with and to determine which computational method gives
more accurate values.
" Extend the range of bathymetry: In this modeling, accurate 1/50 min knowledge
at the bathymetry only extends to a range of 30 km. More accurate knowledge
of longer range bathymetry is needed to compute longer propagation.
" Modify the GEODAS bathymetry data: the 2 min bathymetry from GEODAS
can also be used as the bathymetry data with proper interpolation modification
in order to meet the modeling requirement(3 meter spacing).
" More range point for observing the increasing of grazing angle: If obtaining
finer bathymetry is doable, it is then possible to observe the change of grazing
angle by taking more range points along the waveguide.
66
Appendix A
Review of sound propagation in
the ocean
When sound propagates in various ocean environments, it is effected by four propagation phenomenas. [9]. In Figure A-1, four possible propagation paths are shown.The
RANGE ,km
0
500.
20
60
40
80
too
B
L 1000
z
1500
Figure A-1: Sound Propagation in the Ocean
sound velocity profile (SVP) is shown as a double line. Note the different SVP in
deep and shallow water. Path A is the propagation path from a source located in
shallow depth. Due to the SVP, the sound speed increases with depth up to certain
depth and sound path is refracted toward the surface. Eventually the sound gets
trapped near the surface. This is called surface duct propagation. Paths B,C, and D
all from a source located at 500 meters. The horizontal Path B (with small angle)
67
travels within a channel caused by the SVP(sound velocity increases as depth either
increases and decreases). This is called sound channel propagation. This phenomena
allows sound to travel many thousands of miles. Path C leaves the source with steeper
downward angle but is refracted by the SVP, and interacts with the surface giving a
spatially periodic convergence zone structure. Path D is called bottom bounce path
when sound bounces between the sea bottom and surface. This kind of path has
smaller range period than convergence zone propagation. [13] [9][4]
68
=PI +p'
Appendix B
Derivation of Wave Equation
B.1
Wave Equation
To begin with the derivation of Normal Modes or Parabolic Equations, it is essential
to know the origin of Normal Mode and Parabolic Equation methods: Wave Equation.
The wave equation is derived from the following equations of inviscid, compressible
fluid mechanics without heat conduction,
" Euler's Equation (momentum balance):
p
+ v * VV
V
P(p)
(B.1)
* Equation of Continuity (mass conservation):
ap
--
at
" Adiabatic
(p')2 +-I -+
+ V * pv =0
(B.2)
Equation of State (no heat transfer):
(B.3)
P=PO
I
p 9 ,2
a2P
also we will define
c2
[
69
oPI
(B.4)
where p is the density, c is the speed of sound in ideal fluid. v is the particle velocity,
p is the pressure and the subscript s implies constant entropy.[13] [8]. Since we only
interested in wave equation, linear approximations will be applied and only the lowest
term of Equation B.2 B.1 B.3 will reminded and we have
0
a p'
-po V - V
=
(9 t
(B.5)
0
9V
-
at
-
1
PO
V p'(p)
(B.6)
0
(B.7)
p' = p c2
Wave Equation for Pressure taking the derivative of Equation B.5 with respect to
time.
02 P
1
av
a t2
(B.8)
partl
where partl in Equation B.8 is equal to the left hand side of Equation B.6. Now we
have
(- VP'(p))
2
(B.9)
and from Equation B.7, we have
p
Now insert Equation B.10 into Equation B.9 and let p' a pand po #
(B.10)
p the wave
equation for pressure is obtained.
1 p p =0
Stc2
(B.11)
&i2
,
by taking the Fourier transform
7 oc f(w)e-wt dw
70
(B.12)
f (w)
=
(B.13)
f(t) ejwt dw
the wave equation becomes the Helmholtz Equation
(B.14)
where k(r) =
B.1.1
'
[V2 + k2(r)] 4 (r, w) = f (r, w)
Cylindrical Symmetric Horizontally Stratified Ocean
Environment
We formulate the problem as a boundary value problem. [13]. Thus the ocean acoustic
scenario for the propagation modeling will be set up as shown in Fig B-1 This ocean
r ,x
Bottom layers
IJr
Figure B-1: Horizontally stratified ocean environment
acoustic environment consists of a layered waveguide with paralleled homogeneous
layers. Within each layer, the environment is continuous on the interface and the
boundary conditions are also continuous.
It is also convenient to use a cylindrical coordinate system. As in Fig B-2
71
Where p(z) is the density and c(z) is the sound velocity profile as functions of
depth.
B.2
Normal Mode Method
The Normal Mode method has been used in the underwater acoustic community for
many years. [16]
In a Horizontally Stratified acoustic ocean environment with a homogeneous point
source in cylindrical coordinates, the Helmholtz equation can be written as
po(r)V
[p11 Vp(r, w)] + k 2 (r)p(r, w)
[O
=
p(r)
0
(B.15)
with addition of a point source at the range and depth, this becomes the inhomogeneous Helmholtz equation.
[P1
.p(z)
Vp(r) + k 2 (z)p(r)
=
-47r
J(O) (Z
-
p(z)V
I
p(z)
c(z)
(B.16)
zO)
z=a
r
- -
-
-
-
(0, 0, Z,)
Source
-
-
Receiver
- (r,8z)
-
-
-
-
-
Ix
Z
z=b
Figure B-2: Geometry of Cylindrical coordination
72
where
V = i,
+iO+
r O
-
Vr
[()]
.z
v, we can rewrite Equation B.16 as
and r = (r, 9, z) and wavenumber kz =
V 2 p(r) + p(z)V
(B.17)
tz-
(B.18)
* V p(r) + k 2 (z)p(r) = -47 6(r) 6(0)6(z - zO)
r
where
2
a2
092
az 2
1
(r
V2 =
+2
+
(B.19)
and now since ro = (0, 0, zo)and it is cylindrical symmetry about z axis, thus all 9
terms will disappear and Equation B.18 is now
E
r
10
r Or
p(r, z)
+
2 p(r, z)
2
z
0
a
[
+p(Z) 9z p(z)
0z z) +k 2 (z)p(r, z)
1J10p(r,
= -47r 6 r
)(B.20)
(z-zo)
Now integrate both side of Equation B.20 with respect to 9 from 0 to 27r , we will
have
[
1
r Br
0p(r,z)1
Or
J
+2p(r, z) +p(Z)
+ z2
1
(z
p(z)J
Op(r, z)+k 2 (z)p(r, z)
az
= -2
6
r
6(z-zo)
(B.21)
the solution for Equation B.21 p(r, z) is a separable solution and the components are
eigenfunctions of range, r and depth, z, and can be written as
p(r, z) = E a.(zo) u.(z) Rn(r)
(B.22)
n
when un(z) satisfies the eigenvalue equation with constant density[8].
+ d (1
dz
p (z)
)
1 d2 un(z)
2
p(z) dz
dUn(z)
+k
un(z) = 0
dz
p(z)
(B.23)
Here, k 2 = k 2 (z) - k2, k, is the Horizontal wavenumber and kzn is the Vertical
73
wavenumber. Now, insert Equation B.22 into Equation B.21, we have
(Un(Z) d
Sa
n
Izr)r
d 2Un(z)
+ Rn Mr) I~r
dZ 2
[rd dr(r)]
p(z)
d
(
dun (z)
2
dz + k (z)un(z)
(z))
partl
=
I:
n
-26(r)
( U*(ZO)Un(Z)}
r p (zo)nI
(B.24)
On the right hand side of the Equation B.24 we have applied the closure relation.
Compare Equation B.24 and eigenvalue equation Equation B.23, we can find that
an (ZO) = U* (ZO)
p(zo)
(B.25)
Inserting Equation B.25 into Equation B.24 we have
n
dRn(r) + knRn (r)
+I ,()
dr
u*(z) (1
of- j)r
p(z)
P(Z)
partl
}
=
I
11
2(r)
r p(zo) n(zo)un(z)
part2
(B.26)
Part 1 and part 2 on the either side of Equation B.26 are the same, thus
1
d r dRn(r)
+ kRn(r)]
r dr
dr
2j(r)
r
(B.27)
Equation B.27 is a Bessel's equation and the solution is
Rn(r) = i 7r H01)(knr)
(B.28)
where H(1)(knr) is the Hankel function. We have obtained solution for an(zo) and
Rn(r) and the solution for p(r, z) is
p(r.z) = Zan(zo)un(z)Rn(r) = i7r
u*(zo) H 1)(knr)un(z)
p(zO)
partl
74
(B.29)
and part I is called Normal Modes of waveguide denoted as
(B.30)
pn(r, z) = H(')(knr)un(z)
For far field problem (kr
> 1), the asymptotic approximation to the Hankel function
can be used [14] and the solution is then
p(r, z) ~
v
22eeiknr
e Zu*(zo)un(z)
p(ZO) n= 1
0
75
k r
(B.31)
76
Appendix C
Beamforming Plots I, Source 75
Hz, receiver depth at 50 meters,
range increment ~_ 1 km
The following plots show the beamforming results and the magnitude and phase of
p(r, z) by RAM and CSANP corresponding to different setting parameters.
77
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 9.990000e-01 km
0
~~~~~~- .RAM ..........
~~
.~
..
~. . ..
-20
.....
.
-- CSNAP....
.
0
C
'0 -40
C
2-60
I
-80
-9 0
0
-10
-20
-30
-40
-50
-60
-70
-80
a
0
RAM
CSNAP
-
.
-0.1
-
..
-.-.
...
-...........
-.
-.....-.--.
.
-. .. .-.
-0.3
-...- .
-0.4
-..... .
-%
0
-80
-70
-.
.-...
. . .....
-
-.
-.
.-..
......
....-...
-60
-50
.
- -0.2
-20
-30
-40
0
-10
km
p(r,z) magnitude, source 250Hz receiver location starts at 9.990000e-01
-RAM
C SN AP
-..
-..
.. .
-..
-.. . .
-. .
.
X10-4
a) 6 -. . .
2U4-............
0.95
1.2
1.15
1. 2
---
I
I
.
.
.
.
.
.
..
.
.
.
.
.
.
.
. .
.
.-
.
.
. ...
-..
--.
.
.
-.
-........
.
.........
-.
-200
0 95
...
. .
. .
-CSNAP
.
-.
0
-100
1.15
p(r z) phase
100
e
1.1
1.05
1
.....................
7
...
0
-
Figure C-1: Beamforming, Source 75 Hz, receiver depth 50 m starting at 999 m
1.1
1.05
1
TL
-65
.. .
...
-751onI
0.95
--II
1
1.1
1.05
1.15
-
AM
- RSAP
SNAP
-
..
.
. . . ..
-70
1.2
range in km
Figure C-2: Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at 999
m
78
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 1.998000e+00 km
n
-- RAM
CSNAP
-
2
CO
-80
-90
-20
-30
-40
-50
-60
-70
-80
0
-10
0
0
-RAM
CSNAP
......-............
-0.1
-0.2-
.
--.
- .......
.
-0.3
-0.4
-0.5
-81 0
-30
-40
-50
-60
-70
-20
0
-10
Figure C-3: Beamforming, Source 75 Hz, receiver depth 50 m starting at 1998 m
km
p(r,z) magnitude, source 250Hz receiver location starts at 1.998000e+00
-- RAM
CSNAP
x 10-4
E 12.2
S2
100 -
---RAM
CSNAP.
--
I
-
p(r,z) phase
RAM
-10-
-
-
-
-100-
-
*-
2
2.2
TL
-70
--- RAM
- - CSNAP
..
.
...
. . . . . .
.
. .
. . . . .
.
-8 0 0
-90
-10c
N
2
2.2
range in km
Figure C-4: Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at 1998
m
79
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 3 km
0
M -20
-40
--
-60
-90
RAM
CSNAP
.. . .
-80
-70
-60
.
...
-50
-40
-30
-20
.
C
-10
0
0
RAM
-
CSNAP
-
-2-
-
-
-
-4CD
-
-
-
-8
-
-
-60
-59
-58
-57
-56
-55
0
-54
-
-
-53
-
-6
-
"a
aU
-52
-51
-50
Figure C-5: Beamforming, Source 75 Hz, receiver depth 50 m starting at 3000 m
p(r,z) magnitude, source 250Hz receiver location starts at 3 km
x 10,
-RAM
-- CSNAP
~0.5 [\
....
....
C1
-
-
--
- - - -- -
.
0.
-
E
3
3.1
3.2
3. 3
p(r,z) phase
-1 0 0 3
-.
---.
.
--...
.
-...
-.. . . . . . . . .
-.
-..
. . . . . . . . ..
3.1
.
0 - , , -.
-200
-RAM
- -.CSNAP
. ..
100
-
2001
3.2
-..
3.3
TL
.
-Rn
--
RAM
- CSNAP
-
F
-.... -..
V
-100
-110
-
-
-90
3
3.1
3.2
3.3
range in km
Figure C-6: Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at 3000
m
80
Power(theta) - Normalized, 64 Sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 3.999000e+00 km
0
-50
C
C
-100-
-R
-1501
-9
RAM
-- CSNAP
0
-30
-40
-50
-60
-70
-80
0
-10
-20
0
-
--
-2
-4.
2
RAM
---CSNAP
cd
-6
-
-8
~-
in
-58
-55
-55.5
-56
-56.5
-57
-57.5
-54
-54.5
km
p(r,z) magnitude, source 250Hz receiver location starts at 3.999000e+00
-- RAM
CSNAP
S6 --
E 2
-.
--.
--.-.-.-.
-..
. 4- -
- - -
-
0
3.95
4.1
4.05
4
-
x 10-5
8
-
Figure C-7: Beamforming, Source 75 Hz, receiver depth 50 m starting at 3999 m
p(r
4. 2
4.15
z) phase
200
0-
CSNAP
.. . - . . .
. ... ..
.
100 - -
.-..-..---.
-.-....
.
..-.
--
-
-100 ----
.200
3.95
4.05
4
--
4.1
4.15
4. 2
4.1
4.15
4.2
TL
-85-
-
-
-90
-RAM
100-
P
1NAP
3.95
4
4.05
range in km
Figure C-8: Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at 3999
m
81
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 4.998000e+00 km
u
-20
C
-40
Z,
-60
-80
-9
0
RAM
CSNAP
-80
-50
-40
-30
-20
-10
ia
0
0
RAM
- ....-... ..
-..-...CSNAP
.-..
-.
-
-0.1
-60
-70
- - ....-.-.
.-.....
-
.
-0.2
..-.
.-.
.---..
.--..
.
-.
-0.3-0 .4-
-0.5-80
-70
-60
-50
- -
- - --
----.--
-40
-30
-20
-.-.-----.
-.
-10
0
Figure C-9: Beamforming, Source 75 Hz, receiver depth 50 m starting at 4998 m
-.. . .... . . . . .
--- RAM
C SN A P
. . . -..
.. . . . .
.
-...
- ..........
-.
....--..
--..
..
E 2 - ...
U
4.95
5
5.05
5.1
1400
.......
---
-
.....
.....
.
.
.....
.
..............................
RA
-100
-200 L
4.95
5.2
5.15
p(rz) phase
2 nn
0
-
-..
-~ .
-.
. -.
..
-
.
... .
.
'a 4
...........
- .
6
.
CD
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 km
.
x 10-5
5
yA
5.05
5 .2
5.15
5.1
TL
-80 r-90 1-
-j
-100
-110L
4.95
[- --
5
--
5.05
5.1
5.15
RAM
-- CSNAP
5.2
range in km
Figure C-10: Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
4998 m
82
Appendix D
Beamforming Plots II, Source 75
Hz, receiver depth at 50 meters,
range increment ~ 5 km
The following plots show the beamforming results, the magnitude and phase of p(r, z)
by RAM and CSANP corresponding to different setting parameters.
83
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 4.998000e+00 km
A.
n
I
-20
2-40
-OU
---OSNAP-
-80
-9
-
0
RAM
-80
-70
-60
-50
-40
-30
-20
-10
0
-RAM
-- CSNAP
-0.1
-.
1
-
-0.3
......--.
....
-....--.
.-.
..... ..
.--.
...-..
-..
--.
..
-
-G-0.2
-.
-0.4
-0.5'
-8
0
-70
-60
-50
...-.
.-..-.
.-.
.-..- .-..-.
.-
-40
-30
-20
-10
0
Figure D-1: Beamforming, Source 75 Hz, receiver depth 50 m starting at 4998 m
6
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 krn
x 10-9
. .. . . . -
-
- --
-
C4-
F----RAM
- - CSNAP
. .. . . .
...
-
0
0
2-
. ..........
.....
......
.
4.95
5
5.05
-100
-..
SRAM
-200
5.1
5.15
5.2
5.1
5.15
5.2
p(r z) phase
10
200
-.-
.. *
-- CSNAPj
I
.
4.95
5
5.05
TL
-0
-.
-. ..-...-..-....-.
-.-..
.-..
..
.
-1 00 -
-- RAM
-- CSNAP
4.95
5
5.05
5.1
5.15
5.2
range in km
Figure D-2: Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at 4998
In
84
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 9.999000e+00 km
P------- T-
CD
"a
- -.
-40-
-..-.-.
-
- -.
-20-
RAM
CSNAP ]
- ...
...-.
-.........
.
.
0
. . . . . -.-.
/
-60
-80'
-9 0
0
-10
-20
-30
-40
-50
-60
-70
-80
0
0
-0.1
-
9-0.2
......
-
-
-
-
-
-
.......
-0.3
-0.4
-0.5
-8 0
-60
-70
-30
-40
-50
0
-10
-20
Figure D-3: Beamforming, Source 75 Hz, receiver depth 50 m starting at 9999 m
x 10
p(r,z) magnitude, source 250Hz receiver location starts at 9.999000e+00 km
8
9.95
10
10.1
10.05
10 .2
10.15
p(rz) phase
I
150
0
-- RAM
-- CSNAP
501
10.110-5
9.95
10
10.1
10.05
10
10.15
.2
TL
-an
-85
0
V
-901
-95'
9.95
- RAM
-- CSNAP
10
10.1
10.05
10.15
10.2
range in km
Figure D-4: Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at 9999
m
85
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 15 km
C,--
0I
CSAP
-20
.--.
-.
.-.
.-
-.
l-
-40
-
a
CA
0)s
2
-our..
-80
-90
-80
-70
-50
-60
-40
-30
-10
-20
0
0
0
. .. .
.-.
RAM[]
-CSNAP
............
.
-0.1
M
1-
. -..
.. .
.
-G-0.2
-0.3
-. -.. ..
-.
-
.
-0.4
.-
.-
I
.8
-70
-80
-60
-50
-30
-40
0
-20
-10
0
Figure D-5: Beamforming, Source 75 Hz, receiver depth 50 m starting at 15000 m
-
------
06
-
location starts at
-
15 km
- -
C
-
p(r,z) magnitude, source 250Hz receiver
x 10-5
Z 4
E2
01
15 .2
15.1
p(r,z) phase
15
200
0
-R-AP
-
-200----
-
-
e
15 .2
15.1
TL
15
-95
-
-
-......
.... ...
...............................-
R AM
I
r
15
M
-
-n9r
15.1
range in km
--LSAP]
15.2
Figure D-6: Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
15000 m
86
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 1.999800e+01 km
n
RAM
KCSNAP
-20
.-.
..-
-.
cd
-40
a
-q
-60
-80
-9 0
-60
-70
-80
0
0
RAM
CSNAP
-
'a
-0
-0
-
. - - -
-
-0 .2
.
-- -..
.3 - - . . .
.
M
0
-10
-20
-30
-40
-50
-0
-0 .5-90
-70
-80
0
-10
-20
-30
-40
-50
-60
Figure D-7: Beamforming, Source 75 Hz, receiver depth 50 m starting at 4998 m
km
p(r,z) magnitude, source 250Hz receiver location starts at 1.999800e+01
-
x 10-5
a
~ ~
-~~
'a
CSNAP--
E
19.95
19.9
20.05
p(r,z) phase
20
20.1
20.15
20.2
20 1
20.15
20 .2
2
o
0-
L---
0-
-
00 -
RAM
I
- - CSNAP
-2
19.95
19.9
20.05
20
TL
-i90
-
.. .........
-
-
-
-
-
-
-
-
-
-
-
-
- -
-
-
-
-
-95 -
............
..
..
..
..
..
-
0-100
-105 1
-
19.9
--
... .......... .
RA
.. ..... ......
......
SNAP
19.95
20
20.05
range in km
20.1
20.15
20.2
Figure D-8: Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at 4998
m
87
(
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 2.499900e+01 km
0
RAM
-- CSNAP
\
-..--.-..
--.....-.
...
.....-.
-.
en
-40
..--.
-.
.-.
......-.
-
-60
-
-0I
-90
0
-10
-20
-30
-40
-50
-60
-70
-80
-
0
.C
RAM
CSNAP
-
0.1
---
-
-
-
0 .2
0.30.4 -
-
0.5
-80
-70
-
-
-60
-20
-30
-40
0
-50
-
-
-
-
C-
0
-10
Figure D-9: Beamforming, Source 75 Hz, receiver depth 50 m starting Eat 24999 m
x 10-5
p(r,z) magnitude, source 250Hz receiver location starts at 2.499900e+01 km
1. ---- --RAM
...
...
CSNAP
0 .5
-.-.
.-..--.
-...-.
...
. .. . .
-.
24.95
24.9
25
25.05
p(r,z) phase
25.1
25.15
25. 2
25.15
25..2
200
-
-
100
a
0-100
-20C
24.9
-RAM
CSNAP
24.95
25.1
25.05
TL
25
-qn
-100-
--
-
-
.-
--
-
RAM
-AM
-- CSNAP
-110-12024.9
24.95
25
25.05
range in km
25.1
25.15
25.2
Figure D-10: Magnitude and Phase,Source 75 Hz, receiver depth 50 m starting at
24999 m
88
Appendix E
Beamforming Plots III, source 75
Hz, receiver depth at 50 meters,
range coverage range of 5 km
The following plots show the beamforming results, the magnitude and phase of p(r, z),
and the Transmission Loss by RAM and CSANP corresponding to different setting
parameters.
89
Power(theta) - Normalized, 1334 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 9.990000e-01 km
-- RAM
-CSNAP
.
-
- - -
-
-20 - (D
-40Of
2
-60
-90
-80
-70
-60
-50
-40
-30
-20
0
-10
0
RAM
OSNAP
-
-0.
-
- -0.
~I-0.
Ca
-0.
-A
5-
-80
-70
-60
-50
-40
-30
-20
-10
0
Figure E-1: Beamforming, Source 75 Hz, receiver depth 50 m covers from 999 m to
4998 m
p(r,z) magnitude, source 250Hz receiver location starts at 9.990000e-01 km
0
S6 - .
.
RAM
-..
. .
C S NA P
. . .-.--.
-..
-. . .. . .-..
. -..
.. .
4 j... ..........
.. ---
..
. . . . .
100
0.5
200
-
-
1.5
--
2
/
-10
1
...... ...
.
\.
. .
.
.
. . .
. . .RAA
. . .
.
E22 I
-
x 10~
CSNA
2.5
3
p(r,z) phase
3.5
4
4.5
--
_00 -
5
CNA
ARAM
'0
10
0.5
1
1.5
2
2.5
3
range in kmn
3.5
4
4.5
5
Figure E-2: Beamforming, Source 75 Hz, receiver depth 50 m covers from 999 m to
4998 m
90
1
1.1
1.2 'I~
:.....
01
CD
1.3
SNAP
A
1.5
1.4
1.6
200rnninen
-200
1.7
1.8
1.9
2
I/
C
A
200
2 0
2.1J....... 2.2
2.3
2.4
200
2.5
/........ 2.6 ..
.
3
3.1
3.2
2.8
0
o
CD/-
2.7
.
...
3.3
2.9
3
in L-m
rnna
-CSAP
J
.....
3.4
200
3.5
3.6
n in
r
I
3.7
3.8
3.9
4
-m
A
C
S -200
.4
4.1
4.2
4.3
4.4
4.5
4.6
range in km
4.7
4.8
4.9
5
Figure E-3: Beamforming, Source 75 Hz, receiver depth 50 m covers from 999 m to
4998 m
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 4.998000e+00 km
RAM
CSNAP
-20
-40
-I-)
-80
-9
0
-80
-70
-60
-50
-40
-30
-20
-10
0
0
-1
C
./
. .. .. . .
R-A--70
-=CSNAPJ
I
-69.5
-69
-68.5
-
.
-4
-68
-67.5
-67
Figure E-4: Beamforming, Source 75 Hz, receiver depth 50 m covers from 4998 m to
9999 m
91
km
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00
-RAM
CSNAP
..........
1..........................
E
0
--
-
1
5
4
.............
-
--
-
-
x 10-4
6
7
p(r,z) phase
8
9
0
6
7
TL
8
9
10
20In
100
0
-10 0 -2UU
RAMVI
--
-
CSNA
5
4
-n.
-80
-100
NRAM
--
*
-CSNAP
-120
10
9
8
7
range in km
6
5
4
Figure E-5: Beamforming, Source 75 Hz, receiver depth 50 m covers from 4998 m to
9999 m
200
-200
5
5.1
52
5.3
54
5.5
5.6
57
5.8
5.9
6
200
- - CSNAP
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
2UO
CSNAPI
O"'
-200
7
7.1
7.2
7.3
7.4
7.6
7.5
7.7
7.8
7.9
8
A
200
-200
8
8.1
8.2
8.3
8.4
8.6
8.5
8.7
8.8
8.9
9
CSNAP
9
9.1
9.2
9.3
9.4
9.6
9.5
range in km
9.7
9.8
9.9
10
Figure E-6: Beamforming, Source 75 Hz, receiver depth 50 m covers from 4998 m to
9999 m
92
11 1-1
__'RAM
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 9.999000e+00 km
0 1
-OSNAP
Ca
(D
-o
-60-
-10
-20
-30
-40
-50
-60
-70
-80
-90
0
00
--
RAM
-1 - -
V
C
--
-1.5 --
0)
(U
-2 - -.-.-.-.--
-2.5
-
V
-
-0.5SNAP
-31
-76.5
-75
-75.5
-76
8
Figure E-7: Beamforming, Source 75 Hz, receiver depth 50 m covers from 9999 m to
15000 m
-_...
C6
CSNAP..
km
p(r,z) magnitude, source 250Hz receiver location starts at 9.999000e+00
-RAM
-
9
. .
..
E2 -.
11
10
2n0
.
x 10-5
14
13
12
p(r,z) phase
I
1 5
100
ii
S0
-100
/
-
200'L
9
ilk iIt
/
RAM
-CSNAP
I
10
11
12
TL
13
10
11
12
range in km
13
14
15
V
120
9
14
15
Figure E-8: Beamforming, Source 75 Hz, receiver depth 50 m covers from 9999 m to
15000 m
93
CD
10.3
10.2
10.1
010
200
o
-200
12
200
10.8
10.9
11
AP
200
12.3
12.2
12.1
10.7
10.6
10.5
10.4
12.8
12.7
12.6
10.5
12.4
12.9
11
A
-200C
1
0
. . . . . . ..
..
....
0
o
13
13.1
13.2
13.3
13.4
14
200
14.1
14.2
14.3
14.4
AP
13.6
13.7
13.8
13.9
14
14.6
14.5
range in km
14.7
14.8
14.9
15
13.5
CSA
Figure E-9: Beamforming, Source 75 Hz, receiver depth 50 m covers from 9999 m to
15000 m
Power(theta)
-
Normalized, 1667 sensors, 3 meter spacing, 75
0
receiver at 50m, starting at 15 km
RAM
-
e -20--
hz,
|---RAA
0
-40
-00
-90
-05
- .
-80
-
-50
-60
-70
-40
-30
-20
-10
0
-74.5
-74
N
-
S-1.52-2-
-78
--
--77.5
*
-2.5 -
-77
-76.5
-76
r
-75.5
-75
Figure E-10: Beamforming, Source 75 Hz, receiver depth 50 m covers from 15000 m
to 19998 m
94
p(r,z) magnitude, source 250Hz receiver location starts at 15 km
x 10-5
8
I--RAMI
6-CP
4
E4
0
15
-.
-
.
2
4
17.5
p(r,z) phase
17
16.5
16
15.5
18.5
18
19
200
-
100
15
I
R AM
-CSNAIP
-|--
-100 -200
-
- --
20
19.5
15.5
16
17
16.5
17.5
TL
18
19
18.5
20
19.5
-0
--
- 120 .. . -..
-1401
15
15.5
-
-100 -
- -.
-..
-- RAM
-- CSNAP
17
16.5
16
17.5
range in km
18
20
19.5
19
18.5
Figure E-11: Beamforming, Source 75 Hz, receiver depth 50 m covers from 15000 m
to 19998 M
200
-- RAM
- -CS7NAP
00
15
200
w
15.1
0 - --200
16
200--A
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
16
-CSNAP
-.
-.-.--.
16.1
16.2
16.3
16.4
16.6
16.5
16.7
16.8
16.9
17
RAM
-CSNAP
01
-200
17
200
17.1
17.2
17.3
17.4
17.6
17.5
17.7
17.8
17.9
18
0
-200
18
18.1
18.2
SAP
18.3
18.4
18.6
18.5
18.7
18.8
18.9
19
200
19
-A
19.1
19.2
19.3
19.4
19.6
19.5
range in km
19.7
19.8
19.9
20
Figure E-12: Beamforming, Source 75 Hz, receiver depth 50 m covers from 15000 m
to 19998 m
95
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 75 hz, receiver at 50m, starting at 1.999800e+01 km
RAM
CSNAP
-
-20 -
-.
-.--..--.
C
a
-90
-80
-70
-60
-50
-40
-30
-20
0
1
-2 -
-3--.-.-..-..-.
-.
0
-10
-. -.. -.-
D
-4
-6
- -. :...
- -RAM
CSNAP
-..
-71
-76
-75.9
-75.8
-75.7
-75.6
-75.5
-75.4
-75.3
-75.2
-75.1
-
5-5-
-75
Figure E-13: Beamforming, Source 75 Hz, receiver depth 50 m covers from 19998 m
to 24999 m
x 10-5
4
p(r,z) magnitude, source 250Hz receiver location starts at 1.999800e+01 km
RAM
CSNAP
'a
'E2
CM
Ca
0
19
20
21
22
p(r,z) phase
200
24
25
........
..
..
..
..
....
100
RAM
CSNAP
-D 0
V
Ir
-100
-200
23
it
9
20
21
22
TL
-80
23
24
25
-100
-140
-160
9
20
21
22
range in km
--
-- RAM
-- CSNAP
23
24
-
'0-120
25
Figure E-14: Beamforming, Source 75 Hz, receiver depth 50 m covers from 19998 m
to 24999 m
96
0
-200
20.1
20.2
-200
21
200
21.1
21.2
22
22.1
20
20.3
~
[ 9
/
.........-
20.4
20.5
20.6
20.7
20.8
20.9
21
21.4
21.5
21.6
21.7
21.8
21.9
22
22.6
22.7
22.8
-
A~
AP
200
/-
21.3
RAM
'-
22.3
22.2
22.4
22.5
22.9
23
RAM
SAP
2
23
23.1
23.2
23.3
23.4
-200A
24
24.1
24.2
24.3
24.4
23.6
23.7
23.8
24.6
24.5
range in km
24.7
24.8
23.5
23.9
24
RAM
-CSNAP
24.9
25
Figure E-15: Beamforming, Source 75 Hz, receiver depth 50 m covers from 19998 m
to 24999 m
97
98
Appendix F
Beamforming Plots V, Source 250
Hz, receiver depth at 50 meters,
range increment ~~ 1 km
The following plots show the beamforming results, the magnitude and phase of p(r, z)
by RAM and CSANP corresponding to different setting parameters.
99
0
-RAM
-
- CSNAP
c -20
0-
-90
60
-80
-70
-60
-50
-40
-30
-20
RAM
-
CSNAP
--
--
c -0.5 -
0
-10
..-.
-.-.-.
-....
.
. . . . . --
- 1 .5 -.
S-1
-80
-70
-60
-40
-50
0
-30
-20
Figure F-1: Beamforming, Source 250 Hz, receiver depth 50 m starting at 999 m
x 1o
..
S3 CO
2- -
. ..
.. . . . . .-..
-... .. .
RAM
-.CSNAP
-
p(r,z) magnitude, source 250Hz receiver location starts at 9.990000e-01 km
E
-
0
0.95
1
1.05
1.1
1.15
1.2
p(rz) phase
1 00 -
RAM
C SN A P
.
.
.
.
.
.
200
...
--.
-..-. .-.-...
0 - -.
-100 --10 -/
-200
...
0.95
---
....
1
-
.
7.
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 9.990000e-01 km
.......
..
1.05
IA
1.1
.....
:.+/..
... 1
1.15
1.2
TL
-60
RAM
-- CSNAP
-70
.... ... .
-90C
0.95
1
1..
...
1.05
4--
1.1
L
1.15
1.2
range in km
Figure F-2: Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at 999
m
100
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 1.998000e+00 km
0I
-- RAM
-- CSNAP
-20
... .. ....
...
-40
C
. .. ..
|
.. .
.
ou-90
-80
-70
-60
. ..
-50
-40
-30
-20
-10
8
0
-0.
-0.
-0. 423 -
...-.
.....
-0.
-RAM
CSNAP
-0. 5
-70
-65
-60
-55
-50
-45
-40
-35
Figure F-3: Beamforming, Source 250 Hz, receiver depth 50 m starting at 1998 m
x 1 0-5
p(r,z) magnitude, source 250Hz receiver location starts at 1.998000e+00 km
-
RAM
--
- s
NAP
CS
/
.
-
64
-F
a
N
-
IM
.
8
0
2
p(rz) phase
200
I
2.2
RAM
CSNAP.........
. --..- ....-.-.
-
0-100 - -..
..
-
100 --
../. . . ..
.
..
E2
-200
2
7
-
-
-
-
-90V -100
2.2
TL
-0
-110
RAM
-
-1
Pn
- -CSAP
2
range in km
2.2
Figure F-4: Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
1998 m
101
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 3 km
0
RAM
--
~-60
-
-.
.-.-.
-.-
--
-
--
- 40 -
CSNAP
-
--
- -
-
-
-
-20 -
------
-80,
-90
-70
-80
0
-10
-20
-30
-40
-50
-60
0
0
RAM
-
CSNAP
co -0.5-
~~0
a)a
-66
-67
-68
-69
-70
-65
-64
-63
-60
-61
-62
Figure F-5: Beamforming, Source 250 Hz, receiver depth 50 m starting at 3000 m
X10-,
p(r,z) magnitude, source 250Hz receiver
location starts at
3 km
0 .5 -
-
..
..
-.
..
..
-..
-..
.
RAM
CSNAP
~.
E
0
3.3
3.2
3.1
3
p(r,z) phase
200
F-
100 -
RAM
- - CSNAP
-
-
-
-100
TL
-80
-*
-
3
-.- -.
...
RAM
CSNAP
.-.
..-.
..-.
..
-
-100
3.3
3.2
3.1
3
3.2
3.1
3.3
range in km
Figure F-6: Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
3000 m
102
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 3.999000e+00 km
--
-
-40
..
. . . . .. .
-60..
0L,
-90
-80
-70
.
S-20
RAM
CSNAP
-
-
-60
-50
-40
-30
-20
-10
0
0
Cq
-0.5-
-
-1
RAM
CSNAP
-
3)
C
-1.5 -21
-63
- -
-62.5
-62
--
-61.5
-61
-60.5
0
-60
-59.5
-59
-58.5
-58
Figure F-7 Beamforming, Source 250 Hz, receiver depth 50 m starting at 3999 m
4
X10-5
p(r,z) magnitude, source 250Hz receiver location starts at 3.999000e+00 km
-
......
....
2-
01
3.95
4
.........
.....
..
4.05
RAM
CSNAP
4.1
/
....
4.15
4.2
p(r,z) phase
200
... .. . .
-
10oo R AM
0
S---CSNAP
--
-100B
-2001
3.95
4
4.05
-.
4.1
4.15
4. 2
4.1
4.15
4.2
TL
-90
-95 -
- -.-.
-100-1053.95
-- RAM
-- CSNAP
4
4.05
range in km
Figure F-8: Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
3999 m
103
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 4.998000e+00 kn
\
| ..
...
0
-80
-
AM
-CSNAP
-.-.--.-.-
-
20
--
.............
...
S-40
-80'
-9
-70
-60
-50
-40
-30
-20
-10
0
8
Z
-
-0
I-
2-1. .5 -
.-.
. . .--.-
-
RAM
F-
CSNAP
-73.5
-74
-73
-72.5
-72
-71.5
-71
-70.5
-70
-69.5
-69
Figure F-9: Beamforming, Source 250 Hz, receiver depth 50 m starting at 4998 m
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 km
x 1-5
-RAM
- CSNAP
CO
E=
4.95
5
5.05
5.1
5 .2
5.15
p(r,z) phase
zUU
100
r
-
-
-
-
RAM
CSNAP
'
--
----
-
0
-100- -
-200
4 .95
5
5.05
5.1
5.15
5.2
TL
-80
-90
SN..........
0 -100
- -
-110
--
----
RAM
CSNAP
-120L
4.95
5
5.05
5.1
5.15
5.2
range in km
Figure F-10: Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
4998 m
104
Appendix G
Beamforming Plots VI, Source 250
Hz, receiver depth at 50 meters,
range increment ~ 5 km
The following plots show the beamforming results, the magnitude and phase of p(r, z),
and the Transmission Loss by RAM and CSANP corresponding to different setting
parameters.
105
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 4.998000e+00 knm
0
[=RAM
CSNAP
-...
-.-S-20 ---..
-.-...
..
--.
-.
2-40
- -.
- 60 -
...-
80
-90
-80
-70
--..
-60
-
-.
-50
-40
-30
-20
0
-10
-0.5
-74--73.5
-1
CM
-
1
2-1.5
I-74
RAM
CSNAP
-73.5
-73
-72.5
-72
-71.5
-71
-70.5
-70
-69.5
-69
Figure G-1: Beamforming, Source 250 Hz, receiver depth 50 m starting at 4998 m
4.
x 10F
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 km
RAM
CSNAP
C
c
E
.v ..
..
........ ......
2-
.
0-
4.95
5
5.05
L
5.15
5.1
5. 2
p(rz) phase
20
100
.............
*
-2.5 -.5 -71 -70.5--7 -69.5 -69
I
0-100-iduu
4. 95
.......
-
RAM
CSNAP
...
.........
5
5.05
.......
....................
5.1
5.15
5.2
TL
-80
-90
'a-100
...
.. .. ..
-110
-120.L
4.95
.. .
N
RAM
CSNP
5
5.05
5.1
5.15
5.2
range in km
Figure G-2: Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
4998 m
106
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 9.999000e+00 km
-- -...---
--
-02 0
-RAM
CSNAP
..
0
-
40-
/
-
01
.60
....
.....
. .
A
.
-80
-90
-70
-80
-40
-50
-60
-20
-30
0
RAM
CSNAP
...-.
......
....-.
.--.
---.
.
-
-
0 .5 - -
0
-10
-1 -/
Cm
0)
a
-21
-80
-79
-78
-77
-76
-75
-73
-74
0
-
-
1.5 -
-72L
-71_
-70
Figure G-3: Beamforming, Source 250 Hz, receiver depth 50 m starting at 9999 m
p(r,z) magnitude, source 250Hz receiver location starts at 9.999000e+00 km
x 10-
RAM
CSNAP
CD-
E
0
9.95
10
10. 2
10.15
10.1
10.05
p(r z) phase
200
100200
RM_
-
..........-. -~....
.
-..--.
..
-..
-.
0-
~ CSNAP
p~~r~z) phs
-10010
9.95
10.1
10.05
10. 2
10.15
TL
-0
1100
-90 -
005
-...-
-
T
RAM
SNAP
-100
9.95
10
10.05
10.1
10.15
10.2
range in km
Figure G-4: Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
9999 m
107
RAM
CSNAP
---
20A
1-9
-
-
-
-6
-7
8
.
-3
-2
-1
-20
-10
-
. .
-
-... ..
-40
-90
-
-
-80
-'
-70
-60
-50
-40
-
-60
-30
0
0
0
2Cs
_
-70
-69
-69.5
RAM
CSNAP
- --
-
1.5-
-68.5
-67
-67.5
0
-68
-66.5
-66
-
0.5--
-65
-65.5
Figure G-5: Beamforming, Source 250 Hz, receiver depth 50 m starting at 15000 m
,D
-.
1.5
..
.
.
. . ..
-RAM
. . -....
-..
C SN A P
-
p(r,z) magnitude, source 250Hz receiver location starts at 15 km
x 10-5
Z~ 1
E 0.5
0
15 .2
15.1
p(r,z) phase
15
200
[ZRAM
-
100
-
A
.C.N
..
-
-.
0
.
-100
-200 5
-100
-
15.2
15.1
TL
..
-.
...
-- - -
----- -.. . -..
-. . .....
- - - -... ....
-..
-110
-120
-.
I
15
-15.1
range in km
RAM
-CSNAP|
-
-.
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 15 km
01
15.2
Figure G-6: Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
15000 m
108
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 1.999800e+01 kn
U
-RAM
CSNAP
-2 0~0
ID
~0
-4
0)
(U
-6
-8 0
-90
0
0
-80
-70
-60
RAM
-CSNAP
- -.
-40
-50
-30
-20
0
-10
---
..-.
-.
....-.
. . .. .
--.
..
.
-0. 2 -
-0. 4
-0.
68 -
.
-.
-....
...
-..
..
..
-0. 6
.
. .
_
-75
-74.5
-74
-73.5
-73
-72.5
-72
-71.5
-71
-70.5
-70
Figure G-7: Beamforming, Source 250 Hz, receiver depth 50 m starting at 4998 m
x 10-
p(r,z) magnitude, source 250Hz receiver location starts at 1.999800e+01 km
I
1.5-
-.
..-..-..-
-.
........
-
.
E0.5-
20
20
19.95
19.95
19.9
19.9
20C
-100
20.15
20.05
20.1
20.1
20.15
20.2
20.05
20.1
20 15
20.2
20 05a
p(r,z) phase
RAMI
- CSNAP
-
0
-
o
-100-
-200
19.9
19.95
20
TL
-80
- - RAM
-- CSNAP
-oo
-IAL
I
-0
19.9
19.95
20
20.05
range in km
20.1
20.15
20.2
Figure G-8: Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
4998 m
109
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 2.499900e+01 kn
RAM
CSNAP
0)
C
Z!-40
90 -- 8-
-7-6
50
-0
-0
-50
-40
-30
-
RAM
CSNAP
2
1
-20
-10
-60
-90
-80
-0.5
-70
-60
-
-.-.
-.. -.
-.
00
.. . ..
.
~0
-1
-1.5
I
-
;e
-75
-70
-60
-65
Figure G-9: Beamforming, Source 250 Hz, receiver depth 50 m starting at 24999 m
1.5
x 10-
p(r,z) magnitude, source 250Hz receiver location starts at 2.499900e+01 km
:. -. RAM
0)
--
Ca
-
C-NA
E0.5-
24.9
24.95
25
25.05
p(r,z) phase
52.5
249
24.
25.1
-- RAM
100 -
--
"1
SAP
25.2
25.15
25 .2
'I
-
-
25.15
2.51
-.
-200
24 .9
24.95
25
25.05
TL
-80
25.1
r!s
-
00
- -CSNAP
-
-100
1AfII
24.9
-
$
-120
N
24.95
25
.'
25.05
range in km
25.1
25.15
I
25.2
Figure G-10: Magnitude and Phase,Source 250 Hz, receiver depth 50 m starting at
24999 m
110
Appendix H
Beamforming Plots VI, source 250
Hz, receiver depth at 50 meters,
range coverage range of 5 km
The following plots show the beamforming results, the magnitude and phase of p(r, z),
and the Transmission Loss by RAM and CSANP corresponding to different setting
parameters.
111
Power(theta) - Normalized, 1334 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 9.990000e-01 km
0
-RAM
CSNAP
-20
a
0
-40 -9
-7
-20
-
-6
-
-0
-60
-UA--W
80
-90
-70
-30
-40
-50
-60
0
-10
-20
0
01
0
-1-
-
-1.5 -
-C9AP
-52
-52.5
-53
-53.5
-51
-51.5
0
Figure H-1: Beamforming, Source 250 Hz, receiver depth 50 m covers from 999 m to
4998 m
p(r,z) magnitude, source 250Hz receiver location starts at 9.990000e-01 km
x 10-
3
,
.... ....
....
2
..-.
..
-...
-V-.
.
ED
RAM
CSNAP
- ..
-
4
V0.5
1
1.5
2
3
2.5
p(rz) phase
3.5
4
4.5
5
1.5
2
2.5
3
3.5
4
4.5
5
3
2.5
range in km
3.5
4
4.5
5
200
CSNAP
-
100
(V
-1001
-0 .5
TL
-60
M.
-
.
-120
-140.
0.5
-
.....
- -
RAM
......
CSNAPI
1
1.5
2
Figure H-2: Beamforming, Source 250 Hz, receiver depth 50 m covers from 999 m to
4998 m
112
200
l
Il/
I
11I
NAP
-
.1
4
.2
1 .9
1 .8
1 .7
1 .6
.5
.4
.3
2
-200A
CSAP
4
4.1
200
4.2
4.3
4.4
4.5
2.
range inkcm
.7
28m.
j
A A,
RAM
SNAP
A
Figure H-3: Beamforming, Source 250 Hz, receiver depth 50 m covers from 999 m to
4998 m
Power(theta)
-
Normalized, 1668 sensors, 3 meter spacing, 250
hz,
RAM
km
receiver at 50m, starting at 4.998000e+00
0
-20-
-90
-80
-70
50
-60
-4
30
-20
-10
0
_2-C-NAP
-2
6-4 ----/
-
-
C-6
-80
-76
-75.8
-75.6
-75.4
-75.2
-75
-74.8
-74.6
-74.4
-74.2
-74
Figure H-4: Beamforming, Source 250 Hz, receiver depth 50 m covers from 4998 m
to 999 m
113
-RAM
-..
- CSNAP
...
(D6 -
-
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 km
x10 -5
Ca
E2
0
4
5
6
7
p(rz) phase
8
9
10
5
6
7
TL
8
9
10
7
range in km
8
9
100-
-
S0
-
A
-
-100 -
-
-
-100
- -.....
' -120 -
--
-
-
5
6
-
----140
- - -RAM
-
CSNAP
-101
4
10
Figure H-5: Beamforming, Source 250 Hz, receiver depth 50 m covers from 4998 m
to 9999 m
200
RAP
(.iI2
3
01
-200
05
s
.
/
.
/
I
8
s
.
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
8.
8.
86
8.
9.5
9.6
9.7
200
I
20
8.
.3
2
0
.
. . .....
.....
-200
9.1
9.2
9.3
9.4
range
H-6:
to
9999
/
8
NAP
.
I
9
Figure
/
/
6
.
.
4
-
-200
Beamforming,
Source
250
9.8
9.9
10
in km
Hz,
receiver
m
114
depth
50
m
covers
from
4998
m
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 9.999000e+00 km
0
-4 0 -
-
.-...
.
.. .
--
.
0
C
4)
*0
RAM
c
0)
a
-60
-60
-90
-40
-50
-60
-70
-80
0
-10
-20
-30
0
-/
-0.5
~0
c
4)
*0
C
0)
-1
/-
a
1.5-
I
-
21
-76.5
-76.4
RAM
CSAP
-76.2
-76.3
-75.9
-76
-76.1
e
-75.8
-75.7
-75.5
-75.6
Figure H-7: Beamforming, Source 250 Hz, receiver depth 50 m covers from 9999 m
to 15000 m
X 10-5
p(r,z) magnitude, source 250Hz receiver location starts at 9.999000e+00 km
4
1
1
1-RAM
-- CSNAP
E
9
10
11
12
p(r,z) phase
13
14
15
11
12
TL
13
14
15
13
14
15
100
e
0
-100
- -RAM
CSNAP
-200
10
-80
-100
-
D -120
A
-140
- CSAJ
-160
9
10
11
12
range in km
Figure H-8: Beamforming, Source 250 Hz, receiver depth 50 m covers from 9999 m
to 15000 m
115
ZUL
AM
SIAP
'
-20010
10.1
10.2
10.3
10.4
10.6
10.7
10.8
10.9
11
2~~j~
e
2001.
10.5
1
2SNAP
1t"j
RAAM
0
A
I
hi,
12
12.1
12.2
12.3
I
12.4
12.5
12.6
12.7
g
II~
12.8
RA
-
20
12.9
13
AA
-200
I
14
14.1
14.2
14.3
14.4
-
/
14.5
14.6
range in km
14.7
14.8
14.9
SNAP
15
Figure H-9: Beamforming, Source 250 Hz, receiver depth 50 m covers from 9999 m
to 15000 m
Power(theta) - Normalized, 1667 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 15 km
C
0
[~Th~F7
.
.
-
.
-20
-
'a
C
-40
-60
-80
-9
4
0
-70
-80
-60
-50
-40
-30
A
-20
-10
0
U
~0
C
-0.
51-
-
........- .... - .. -..-... -.... --.-.-
-
a
~0
C
(U
-RAM
-
SNAP
-..
.C
-.
...
..-.
..-..
-1 .5 -. . . . . . . ... .-....-..
-77
-76.5
-76
-75.5
0
-75
-74.5
-74
Figure H-10: Beamforming, Source 250 Hz, receiver depth 50 m covers from 15000 m
to 19998 m
116
p(r,z) magnitude, source 250Hz receiver location starts at 15 km
x 10-5
RAM
. . .. .. .
. .. . .
..
.
.
.
.
2
I13
- - CSNA
100
15
15.5
16
16.5
17
17.5
p(r,z) phase
18
18.5
19
19.5
20
19.5
20
0
TL
-80
-100
999I 1m
T
,
t00
Ii
-120.AP
RAAP
RAM
15
15.5
16
15
15.5
1 6
IV
CSNAP
16.5
1 .
5.
.3
1
17
17.5
range in km
1
1.5
18
1
18.5
19
81. 151919. 2
-0
A
Figure H-12: Beamforming,
Source 250 Hz, receiver depth 50 m covers from 15000 m
to 19998 m
1I1.1
1
.2
1
.
165
1lj
1
15.5
15.6
.7
1
1/.'
1
15.7
15.8
15.9
16
-RAM
16.7
16.8
16.9
17
-200
15
200
15.1
15.2
15.3
1
-200
16
200/1-A
~
16.1
16.2
15.4
~
16.3
I~
/A/
16.4
1
16.5
16.6
CSNAP
/
-200
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
18
18
18.1
18.2
18.3
18.4
18.5
18.6
18.7
18.8
18.9
19
19
19.1
19.2
19.3
19.4
19.5
19.6
range in kmn
19.7
19.8
19.9
20
/
17
200~
Figure H-12: Beamforming, Source 250 Hz, receiver depth 50 m covers from 15000 m
to 19998 m
117
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 250 hz, receiver at 50m, starting at 1.999800e+01 km
ROSAP
--
CC
0
CO
c
0
-
-1 .
- 8
-
-
-
-77
-76.8
70
-
6
-5
-
-4
-30-
- 20
-1-
--.-.-.-.-.-
-76.6
-76.4
-76.2
-76
-758
-75.6
-75.4
-752
-75
Figure H-13: Beamforming, Source 250 Hz, receiver depth 50 m covers from 19998 m
to 24999 m
~0
6. -
-
17
p(r,z) magnitude, source 250Hz receiver
2x 0a 1.5 -
7 .-7 I. 7 . 7 7 . 7 .7 . -7 . --
-
location starts at
1 .999800e+01 km
-
X 10-5
19
~~~~~~~p(r,z)
20
- - CSNAP..980e0
phntdsuc
oansatsa
2Ozrcie
21
22
23
21
22
23
24
25
0.
200
-
-- CSNAP
01-100 19 -1R-100
00TL
100
S-120I
-8 0
19
-I
--
AM-- 20- A
-
CSA
-
CNA
24
I
25
tillI
-
100
20
21
range n
2325
Figure H-14: Beamforming, Source 250 Hz, receiver depth 50 m covers from 19998 m
to 24999 m
118
20
20.1
20.2
20.3
20.4
20.5
20.6
20.7
20.8
20.9
21
-200
-20021
200C
21.1
21.2
21.3
21.4
21.5
21.6
21.7
21.8
21.9
22
-200
22
200~..
22.1
'/
22.2
22.3
/
23
24
-
0
2204
23.1
24.1
23.2
24.2
23.3
24.3
22.4
~
22.5
22.6
22.7
-RAM
22.8
22.9
'
23
A
CSNAP
-CE'NAP]
A
*~~
23.4
24.4
RAP
A
23.5
23.6
24.5
24.6
rageink
23.7
24.7
23.8
24.8
23.9
24.9
24
25
-
2
N-AP
2
Figure H-15: Beamforming, Source 250 Hz, receiver depth 50 m covers from 19998 m
to 24999 m
119
120
Appendix I
Beamforming Plots VII, Source 75
Hz, receiver depth at 100 meters,
range increment ~ 1 km
The following plots show the beamforming results, the magnitude and phase of p(r, z)
by RAM and CSANP corresponding to different setting parameters.
121
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 100m, starting at 9.990000e-01 km
A
RAM
-- CSNAP]
-20
.....- . ..
-40
-.....-.
.
-80
-91 0
-80
- .......
-..-.
.
...--.-.
- -.
-60
.-.-
-70
-60
-50
-40
-30
-20
-10
0
a
0
I-RAM
I
-0.1
0
-
-0.2
-.
. .-.
-0.3-
...
.. ..
-..
--
-
(
0.U F
-04'
-80
-70
-60
-50
-40
-30
0
-20
-10
0
Figure I-1: Beamforming, Source 75 Hz, receiver depth 100 m starting at 999 m
x 10-4
p(r,z) magnitude, source 250Hz receiver location starts at 9.990000e-01 km
--
1,6
CSNAP[
01
(U
1.0.95
1
1.05
1.1
1.15
1 .2
p(rz) phase
200
-
-- RAM
-~
CSNAP
-
-
-
I
.
I
-
..-.-.-
100-
.-
0..- -... --
.
-100-200
0.95
1
1.05
1.1
1.15
1 .2
TL
75...................
-
-o -75
..
.......... ..............
.....
-80 -.........
.. ....
.
.
-
0.95
1I
1.05
1.1
-..............-..
..
1.15
AM
- CSNAP
1 .2
range in km
Figure 1-2: Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at 999
m
122
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75
n
hz,
receiver at 1 QOm, starting at 1.998000e+00 km
-4
CO
2
-60V
-80'
-91
F--- R-AM1
-- CSNAP
0
-80
-70
-60
-50
-40
-30
-20
-10
0
RAM
CSNAP
-
-0.11-
-..
-
-0.2
-
0
-
...
a
-0.3
-
-0.4[
4
-80
-70
-60
-50
-40
-30
-20
-10
0
Figure 1-3: Beamforming, Source 75 Hz, receiver depth 100 m starting at 1998 m
x
p(r,z) magnitude, source 250Hz receiver location starts at 1.998000e+00 km
10-
2RAM
-- CSNAP
E
02
2.2
p(r,z) phase
203
.
0r
I
/
-100
-200-
-
-
-
--
-
-
------
.......
CSNAP
-
.
100
2
2.2
TL
-80k
'a-85-F
,-
RAM
CSNAP
2.2
2
range in km
Figure 1-4: Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at 1998
m
123
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 100m, starting at 3 km
0
-. . . . .
rn -20
-RAM
CSNAP
-
.........-..
... .....
-40
'D:
Cm
as
Cu
-.... -.....-
-60
-00
-80
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
0
-RAM
-CSNAP
-
-0.1
.....-..........
.G-0.2'0) -0.3
-
'a
-0.4-
-70
-60
-50
-40
0
-30
-20
-10
0
Figure 1-5: Beamforming, Source 75 Hz, receiver depth 100 m starting at 3000 m
x 10-
p(r,z) magnitude, source 250Hz receiver location starts at 3 km
81
-RAM
6
-
6
.. ............
..... ... ...................... ...... ................ L
24
0
- -
-
A
-
~
3
3.1
3.2
100 -.
0 --
3.3
p(r,z) phase
200
...
.
..
RAM
- --... CSNAP
-
C
E
....-.-.
-CSNAP
-.
- 1 00 - ...........................
-2003
3.1
TL
-80
3.2
3.3
* -RAM
-90
- 1 0 0 - . .. . ..-
3
-
APj
-S
.
. . . .. . . .. . . . . . .
3.1
3.2
3.3
range in km
Figure 1-6: Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at 3000
m
124
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 100m, starting
at 3.999000e+00 kmr
I
V
-20
-40
CO
-60
-IRAM
-- SNAP
-90
-80
-70
-60
-50
00
-40
-30
-20
-10
0
0
-2-
_4
-6 -
-
-8 -
--
-10
-60
-
-
-
-
RAM
-- CSNAPJ
--- .
-59
-58
-57
-56
-55
0
-. -
-54
-
-53
-
-
0)
C
-52
-51
-50
Figure 1-7: Beamforming, Source 75 Hz, receiver depth 100 m starting at 3999 m
x 10-5
p(r,z) magnitude, source 250Hz receiver location starts at 3.999000e+00 km
8
I
--- RAMI
a)6 -
.
. ..
-.
-. .
4 -
-.--...
CSNAP .-
..
E 2.-.-
........
0
3.95
4
4.05
4.1
4.15
4. 2
p(r,z) phase
2001
-- RAM
-..
.-..
...
..
....CSNAP
-
100 a)
0-100-
-.
-
-200
3.95
4
4.05
4.15
4. 2
4.1
4.15
4.2
-
-100-
.........
-
3.95
--.-.-.....
4.1
TL
-80
-90 -
.
2
4
RAM
-- CSNAP
4.05
range in km
Figure 1-8: Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at 3999
m
125
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 1
n
00m,
starting at 4.998000e+00 kmn
-RAM
-- CSNAP
:
-.
........
.....
-
-20
~0 -40
C
2
-.-
..-.
.-
---.
\.
-60
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
I
0I
.
8
RAM
SNAP
-0.1
1
-0.2
\
-0.3
.-
Ca
-0.4f
-U.!11
-80
-70
-60
-50
-40
0
-30
-20
-10
0
Figure 1-9: Beamforming, Source 75 Hz, receiver depth 100 m starting at 4998 m
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 krn
-- RAM
CSNAP
0
, 6
c4
-
x 10-5
-.-.-.-.--.-.-..~. ........
0
4.95
5
5.05
5.1
-
E 2
5.15
5.2
p(rz) phase
200
100
0
-100
-
-200
4. 95
-
-
-
-
5
R-RAM
5.05
-..
ACSNAP
.
CD
5.1
5.2
5.15
TL
an
-
-90
-110-
-- RA M
-
-. -.-.-.-.-
-
-120
4.9 5
5
5.05
5.1
5.15
-
-100-
- CSNAP
5.2
range in krn
Figure I-10: Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
4998 m
126
.
......
......
i
Appendix J
Beamforming Plots VIII, Source
75 Hz, receiver depth at 100
meters, range increment
km
The following plots show the beamforming results and the magnitude and phase of
p(r, z) by RAM and CSANP corresponding to different setting parameters.
127
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 1 00m, starting at 4.998000e+00 knm
Cr
SNAP
C
2n
- --- .. -.
....
-..
..--..
.
...... ....
-40
...-..
.. ............-. ... .....
-.
......
-7:
an
-90
-80
-8
-70
-60
0
-50
-40
0
-30
-20
0
-10
I
i
-- RAM
-CSNAP
......
.
-0.11-0.2 --
.
.... -.
-
-0.3
-0.41
'
-0. I
-80
-70
-60
-50
-40
-30
-20
-10
0
Figure J-1: Beamforming, Source 75 Hz, receiver depth 100 m starting at 4998 m
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 km
-
, Cm6
0
4 .95
RAM
-.- CSNAP
5
5.05
-
X 10-5
5.1
5.15
5. 2
5.1
5.15
5. 2
p(r z) phase
200
100
-100
CSNAP
-200
4 .95
5
5.05
TL
-0
-90
-.
---.- -..-
S-100
-110
-120
4 .95
-
5
5.05
5.1
5.15
RAM
- CSNAP
5.2
range in km
Figure J-2: Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
4998 m
128
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 1 00m, starting at 9.999000e+00 kr
RAM
CSNAP
-
-2 0-
~0C
-4
or
a
---
0-
cc
-6
-8 01
.0
RAM
CSNAP
-0.1
-/
-
-
-0.3 -
-0.4
-I
-
-A .0
C
-80
-70
-60
-
C
-
-0.2 -
-50
-40
-30
-20
-10
0
Figure J-3: Beamforming, Source 75 Hz, receiver depth 100 m starting at 9999 m
x 10-5
p(r,z) magnitude, source 250Hz receiver location starts at 9.999000e+00 km
10r
-RAM
-- CSNAP
8
CO
E 6
4L9.95
10
10.05
10.1
10.15
10.2
p(r,z) phase
10050-0
-50
-
-RAM
- - CSNAP
-19.95
10
10.1
10.05
10.2
10.15
TL
-- RAM
CSNAP
-
-82
9.95
-
10
- -
10.1
10.05
-
-84-
10.15
10.2
range in km
Figure J-4: Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
9999 m
129
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 1 00m, starting at 15 km
,
a
-- RAM
-CSNAP
- ...-.
M -20
-
......
-
.....
--..
--..-
--.-.-.-.-.--.-.-.-
-40
-80
-90
-...--.
..-.
-.
....
-80
-
-.
-60
-70
-60
-50
-40
-30
-20
-10
0
0
-- RAM
.
-0.1
..-.
- ..- ...-.
.. -.
..-...-CSNAP
-.
-
--
-
-
......
....
.-..
.-..
.... .. ..
-
..
-.... ... -.-.
-.-.
.-.
.-.
.-.
-60
-50
. -. -..
...-.
.
0.3
.
.
.
-0.2' . -
-0.4-0.5'
-8
0
-70
-40
-20
-30
-10
0
Figure J-5: Beamforming, Source 75 Hz, receiver depth 100 m starting at 15000 m
x 10-5
p(r,z) magnitude, source 250Hz receiver location starts at 15 km
-
4r
(D
-.
................
~..
.
2
E
-
0
'
-RAM
-- CSNAP
15 .2
15.1
p(r,z) phase
15
200
100
e
0
.......
~
~-... ... . ~.. ~CSNAP~
........
-.
-100
-200'
15
15 .2
15.1
TL
-
-
-
~0
--100 -
15
-
-
15.1
range in km
-
- ---- --
-RAM
CSNAP
-
-
-95
-
-90
15.2
Figure J-6: Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
15000 m
130
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 75 hz, receiver at 1 00m, starting at 1 .999800e+01 km
V
RAM
CSNAP
-
-20CD
'0
-40 -
--
-..--.
CM
0a
0)
-60-
-80
-90
-70
-60
-50
0
-40
0
-30
1
1
-40
-30
-20
0
-10
RAM
CSNAP
-0.1
. I
-0.2
as
-0.3
*1
-0.4
-0.5
-8
0
-70
-60
-50
-20
-10
0
Figure J-7: Beamforming, Source 75 Hz, receiver depth 100 m starting at 4998 m
p(r,z) magnitude, source 250Hz receiver location starts at 1.999800e+01 km
x 10-5
-CSNAP
a
V
1
1
---RAM
-
4
0
19.95
1 0-
- -
100-
-------RAM
-
---
20
20.05
p(r,z) phase
20.1
-
20.15
20..2
.
19.9
100
- -
--
-
2--
-
-10
-
-
-
a
E
-......
.......
-- CSNAP
19.9
19.95
20.05
TL
20
20.1
20 .2
20.15
--85
AM
I---
Ca
-95-
.
.............. .... ..... ........... .................................-
-------inn ,---
19.9
- -- - - - - -- - - -
-19.95
20.05
20
20.1
20.15
20.2
range in km
Figure J-8: Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
4998 m
131
Power(theta) - Normalized,
n
64 sensors, 3 meter spacing, 75 hz,
receiver at 1 00m, starting at 2.499900e+01 km
-20
--..-.-.
-.
.
.........
-
-.
-40
0)
-60
RAMj
CNAP
F-80'
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
08
RAM
CSNAP
-
V
C
a)
V
--
-
-
-0 .1
-.--
-.
-.-.-
0I
0
-0 2L_
-80
-70
-30
-40
0
-50
-60
-20
-10
0
Figure J-9: Beamforming, Source 75 Hz, receiver depth 100 m starting at 24999 m
2
e
p(r,z) magnitude, source 250Hz receiver location starts at 2.499900e+01 km
x 1-5
-
1.5 -
-.
-
-Aj
-
C
01-
25
24.95
24.9
25.05
p(r,z) phase
25.1
200
-RAM
-
100 --
CD
0-
--
-100 --
-
-200-24.9
25.2
25.15
-
24.95
-~
25.05
25
25.1
25.15
TL
!
-90
-100 --
-
-110
-120
24.9
CSNAP
---
--
I
25
RAM
CSNAP
25.05
range in km
25.1
25.15
25.2
1
25.2
Figure J-10: Magnitude and Phase,Source 75 Hz, receiver depth 100 m starting at
24999 m
132
Appendix K
Beamforming Plots IX, source 75
Hz, receiver depth at 100 meters,
range coverage range of 5 km
The following plots show the beamforming results, the magnitude and phase of p(r, z),
and the Transmission Loss by RAM and CSANP corresponding to different setting
parameters.
133
Power(theta) - Normalized, 1334 sensors, 3 meter spacing, 75 hz, receiver at I00m, starting at 9.990000e-01 km
0
-..----...
....
- 20 - -.
CO
- 40 -
-...
-..-.-.
.-.-.
..
-.
-..
-.
.
.
-..
Z1
- 60 - - -90
-80
-.-
- - .-. -..
-. -..
..
-70
-60
-50
-40
-30
..-
-20
0,
--
- -
RAM
CSNAP
-
- -
.
-0.1
0
-10
0.2
-
-0.3
-0.4-0.5 L
-80
-70
-60
-50
-40
-30
-20
-10
0
Figure K-1: Beamforming, Source 75 Hz, receiver depth 100 m covers from 999 m to
4998 m
p(r,z) magnitude, source 250Hz receiver location starts at 9.990000e-01 km
x 10-4
--...-..
..
....
.
-
2 -
-
.
.
.
.
. . . ..
4 E
-RAM
AP
~..~-..
~~~~
......~ .....CSN
a)'
V
0.5
1
1.5
2
3
2.5
p(r,z) phase
3.5
1.
I
4
4.5
5
100~
0-
I
-
CNP
w
I
Il
-100
-200
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
4
4.5
5
TL
-60
-RAM~
------
--
CSNAP
-140
0. 5
1
1.5
2
3
2.5
range in km
3.5
Figure K-2: Beamforming, Source 75 Hz, receiver depth 100 m covers from 999 m to
4998 m
134
RAM
20C
01
<D
1.1
1.2
1.3 ///....
/..1.4
200
1.5
1.6....
in
rn
I.,1.7
V
1.8
1.9
2
Lem
-200
CSNA
O
e
20>n
--
2~
3.1
23
3.2
3.3
3.4
200
3.5
in
r
3.6
RAM
A
-
3.7
3.8
RAM
3.9
4
4.9
5
Lm
-200'
0
20I,
4
na
4.1
4.2
4.3
4.4
I
nL
4.5
4.6
range in km
:
>.
4.7
1AP
4.8
Figure K-3: Beamforming, Source 75 Hz, receiver depth 100 m covers from 999 m to
4998 m
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 75 hz, receiver at 1 00m, starting at 4.998000e+00 km
A,
0
RAM
-CSNAPj
-S
-
m -20
1
~0
-40
C
.q
2-60~
-8 0
-90
-80
-70
1
-60
-50
-40
-30
1
-20
1
-10
0
0I-RAM!
-
.. .. .
...
- CSAP
-
5
0
-0.
-'a
5
-
0)
-
.-.
..-.
-... -...... -..... -..--.-..-.-.-.-..-
-80
-70
-60
-50
-40
-30
-20
-10
0
Figure K-4: Beamforming, Source 75 Hz, receiver depth 100 m covers from 4998 m
to 9999 m
135
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 km
X 104
1*
2
-- RAM
CSNAP
CDI
1-
E
0
4
5
6
7
p(r,z) phase
200
8
9
-
1G0
0
-100
--200
5
4
N
6
7
I
TL
8
91
0
-
- 80 -
.
-.
..-...-...
M'0
....
.......RAM
-120 --140'
--
---
---
-
-100 -
-
4
5
6
-
7
range in km
-
8
9
10
Figure K-5: Beamforming, Source 75 Hz, receiver depth 100 m covers from 4998 m
to 9999 m
5
5.1
5.2
200
5.3
5.4
5.5
5.6
5.7
5.8
5.9
6
200
NAP
200
.
..
0
6
0
6.1
6.2..
..
6.3
6.4
65
6.6.
6.7
6.8
69
7
ZI-NAP
200 7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
CSAP
8
- 200'A
9
81
82
CD~~
0
9.1
9.2
8.3
8.6
8.7
8.8
8.9
9
9.6
9.5
range in km
9.7
9.8
9.9
10
8.5
8.4
I...CN
9.3
9.4
Figure K-6 Beamforming, Source 75 Hz, receiver depth 100 m covers from 4998 m
to 9999 m
136
-
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 75 hz, receiver at 1 00m, starting at 9.999000e+00 km
0RAM
CSNAP
C
VE
Cl
80
-90
0-
C
--
-6-
-
10-
-
C
01
a
CSNAP
-
-
-
-4-
-o
RAM
-
-2 --
*0
0
-10
-20
-30
-40
-50
-60
-70
-80
-30
-40
-50
-60
-70
-80
-20
0
-10
0
Figure K-7: Beamforming, Source 75 Hz, receiver depth 100 m covers fr om 9999 m
to 15000 m
km
p(r,z) magnitude, source 250Hz receiver location starts at 9.999000e+00
X 10-4
0.5-
--
RAM
-CSNAP
-
Ca
1
E
01
12
p(r,z) phase
11
10
9
13
14
1 5
13
14
15
14
15
1
200
.
10 0 . ..
-.
-.
-
-.
0 --100 - -
RAM
-- CSNAP
0
-
12
TL
11
-0
-100
- -
I~
-.
.. .T.
-.
V
. . . . . . . . . .V
I
V
I
*0
-- ..
-120 -.
-RAM
-CSNAP
9
10
11
12
range in km
13
Figure K-8: Beamforming, Source 75 Hz, receiver depth 100 m covers from 9999 m
to 15000 m
137
200
CSAP
-200
10
200
10.1
10.2
10.3
10.4
10.5
10.7
10.8
I
10.9
11
--
-200
11.1
11
200
11.2
11.3
11.4
11.5
0
12
12.1
-
-
--
-
S -
-200
10.6
11.6
11.7
11.8
11.9
L5
-
12
0
12.2
12.3
12.4
NAP
12.5
12.6
12.7
12.8
12.9
13
20
-200
13
-20
... .......
13.1
13.2
13.3
13.4
~.
13.5
-- RAM
- CSNAP
~-..
/..
.
........
0
RAM
CSNAP
13.6
13.7
13.8
13.9
14
200
A
14
14.1
14.2
14.3
14.4
14.5
14.6
range in km
14.7
14.8
14.9
15
Figure K-9: Beamforming, Source 75 Hz, receiver depth 100 m covers from 9999 m
to 15000 m
Power(theta) - Normalized, 1667 sensors, 3 meter spacing, 75 hz, receiver at 1 00m, starting at 15 km
Ca
-
-
-20
-
-
RAM
CSNAP
-40-60
-80
-90
cc
-50
-60
-70
-30
-40
-20
-10
0
00
0
-2 -
---
RAM
-4-
-
............
-.....-..
...
.
2
...........
. .....................
......
_4....
-6
-8
.
0i
-80
-79
-78
-77
0
-76
-75
-74
-73
Figure K-10: Beamforming, Source 75 Hz, receiver depth 100 m covers from 15000 m
to 19998 m
138
p(r,z) magnitude, source 250Hz receiver location starts at 15 km
S6 -
E 2A
' N.
.
.
-
4-
RAM
CSNAP
-.
-.
-
x10-5
.I
0
15
15.5
16
16.5
17
17.5
p(rz) phase
18
18.5
19
19.5
20
17
17.5
TL
18
18.5
19
19.5
20
18
18.5
19
19.5
20
200
-
-200
RAM
-- CSNAP
&
-100
15
15.5
16.5
16
..
-100
- 12
0
--
--.
-..
--.-.-.-..-.-.-....
-.
15.5
15
.
-80
16
17
16.5
17.5
range in km
Figure K-11: Beamforming, Source 75 Hz, receiver depth 100 m covers from 15000 m
to 19998 m
R.M
200
..
..
..
5.1...
......
..
.
0
-200
15
200
15.1
15.2
15.3
15.4
15.5
-
15.6
15.7
15.8
15.9
16
AP
-1
ISNAP
-20016
200
16.9
17
17.6
17.7
17.8
17.9
18
18.6
18.7
18.8
18.9
19
16.3
16.4
16.5
16.6
17
17.1
17.2
17.3
17.4
17.5
18
18.1
18.2
18.3
18.4
18.5
200
-200
16.8
16.2
0
M1
-200
16.7
16.1
..
I
2CSNAP
-200-
19
A
19.1
19.2
19.3
19.4
19.6
19.5
range in km
19.7
19.8
19.9
20
Figure K-12: Beamforming, Source 75 Hz, receiver depth 100 m covers from 15000 m
to 19998 m
139
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 75 hz, receiver at 100m, starting at 1.999800e+01 km
-
-2 0 --
Ca
-..---.-.
..
..- . . -.
-4 0 -
.
-90
-80
.
-..
-. -.
-
RAM
CSNAP
-.-..
-.
V
-70
-60
-50
-40
-30
-20
0
-10
CO
(D
0
--
M
SNAP
-2
-4
- -
....
-.-.-.-.--.-
cc
a
.
-8.......-6n
-80
-79.5
-7
-8.
-79
-78.5
-
-78
-7.
-7
-77.5
-77
----76.
-76.5
-76
-5.
-75
-76
-75.5
-75
Figure K-13: Beamforming, Source 75 Hz, receiver depth 100 m covers from 19998 m
to 24999 m
p(r,z) magnitude, source 250Hz receiver location starts at 1.999800e+01 km
x 10-5
4-RAM
CSNAP
(D
0
19
20
21
22
p(r z) phase
21
22
200
-
100
0|
100
-
24
215
24
25
232
.. ..
.V
RA-M-- I.AMf
- 'SNAP I
/
019
23
20
I,,II
21
22
TL
23
-80
-- CSNAP
20
21
22
range in km
23
24
25
Figure K-14: Beamforming, Source 75 Hz, receiver depth 100 m covers from 19998 m
to 24999 m
140
200
!-
A
-- CSNAP
-RAM
200,,.--~
CD
020-/
200
0 -200
21
200
-200
22
200--
o
0
20.1
20.5
20.4
1--
21.1
21.3
21.2
20.6
20.8
20.7
21
-
--
- -- --
-
21.6
21.5
21.4
21.8
21.7
21.9
22
22.1
22.3
22.2
22.4
22.6
22.5
22.8
22.7
22.9
23
-
..
....
0-~..
200
23.1
23.2
.
..
-
:1.
23.3
-
.....
23.4
23.5
23.6
23.7
23.8
23.9
24
RA
-CSNAP
24
-RA
-
-200
A
-- CSNAP
-RAM
- --CSNAP
-<
23
200
-20.3--
20.2
-
0
I
20.9
-
-200
24.1
24.2
24.3
24.4
24.6
24.5
range in km
24.7
24.8
24.9
- - CSNAP
25
Figure K-15: Beamforming, Source 75 Hz, receiver depth 100 m covers from 19998 m
to 24999 m
141
142
Appendix L
Beamforming Plots
Source 250
Hz, receiver depth at 100 meters,
range increment ~ 1 km
The following plots show the beamforming results, the magnitude and phase of p(r, z)
by RAM and CSANP corresponding to different setting parameters.
143
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 1 00m, starting at 9.990000e-01 km
A.
0
RAM
-- CSNAP
-.
-.-.
.
..-.
..-.
-.
..-.-.-.-.-.-.-.-20 - .....- ...
Ca
C
-40
C
-.
....... .-.
..-..
..-..
.-
-80
-70
-60
-90
-60
-50
-40
-30
-20
0
-10
AM
RCSNAP
-
-0.5 ..............
C
4)
-1 -.. .
-
-
-.-.-.
-.
C
-1.5
-54
-55
-52
-53
-51
-50
-49
-48
-47
-46
-45
Figure L-1: Beamforming, Source 250 Hz, receiver depth 100 m starting at 999 m
4
p(r,z) magnitude, source 250Hz receiver location starts at 9.990000e-01 km
x 10-4
ICD
3 --
CD
2 -
RAM
CSNAP-
-......
-
E
0
0.95
1
1.05
1.1
1.15
1. 2
1.1
1.15
1.2
1.15
1.2
p(r,z) phase
2
--
100 -
RAM
CSNAP
0
.
....
.......
....
.. .A
-100
-200
0. 95
1
1.05
TL
-70-
-75
-
(n -80
-85
RAM
CSNAP
-
-90
0.95
1
:
1.1
1.05
range in km
Figure L-2: Magnitude and Phase,Source 250 Hz, receiver depth 100 m starting at
999 m
144
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 100m, starting at 1.998000e+00 km
0
-RAM
-/CSNAP
C -20k
*-40
2-60
-80
-70
-80
-9
0
-10
-20
-30
-40
-50
-60
0
1
/
-0.
2-1-0. 31
-RAM
-0.
o_ -60
CSNAP
-54
-56
-58
-40
-42
-44
-46
-48
-50
-52
Figure L-3: Beamforming, Source 250 Hz, receiver depth 100 m starting at 1998 m
p(rz) magnitude, source 250Hz receiver location starts at 1.998000e+00 km
__R M
x 10-5
8
7,
CSNA7
E2-
.
. .
..
N
-~
.
-
6
2.2
2
p(r,z) phase
200
L
RAM
CSAP.......
0- --
.......
-100..........
I.
......
...
..... ..
..
...
.
~ ~
..
...
-202
/I
.
....
/.I,
.
.
..
.
100
2.2
TL
Qn
-100
-120-140
-CSNAP
2.2
range in km
Figure L-4: Magnitude and Phase,Source 250 Hz, receiver depth 100 m starting at
1998 m
145
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 100m, starting at 3 km
0i
-- CSNIAP
.
.
. . . . .. . . . . .-..-.
-.-.
.
-.
.-.
-.
.-.
.-..
.....
...
-
.
-.
-40
C
.
.
. . .-.
. .
o -20
2-60
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
0-0.
Z
0)
cc
2
-1.- -RAM
CSNAP
-1.5
-70
-69
-68
-66
-67
-65
-63
-64
-62
-61
-60
Figure L-5: Beamforming, Source 250 Hz, receiver depth 100 m starting at 3000 m
E
i dI
pr z)0 magntu
..
250H
e0j , sOVur
%'&eee ocV nl sw ir a" =ml
- -. -..
-
k
t t
ti
- .
..
-AM
F-.. CSNAP
1
-
8
S6 -
-5
-
x 10
0
3. 3
3.2
3.1
3
p(r,z) phase
200
RAM
3
............-..... /
.
-........
100
3. 3
3.2
3.1
TL
-n.
RAMI
-90
.
......
........... .
-1001
-1 1 01
3
3.2
3.1
3.3
range in km
Figure L-6: Magnitude and Phase,Source 250 Hz, receiver depth 100 m starting at
3000 m
146
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 1 00m, starting at 3.999000e+00 km
0I
NCSNAP
m -20 -
RAM
-.-.
....-
V
- ...- ...
--..-.
-.
.
--.
..
--.
.
..-.
-
, -40
CO
.......---------.
-.
-Ou
-90
-
a
-80
-70
-60
-50
-40
-30
-20
0
-10
0
0
RAM
CSNAP
-
-
--
- --
--
-
-
0 .5 -
II)
-1 -
-
C
-60
-59
-58
---
--
- -
--
1 .5 -
-57
-56
-55
-54
-53
-52
-51
-50
Figure L-7: Beamforming, Source 250 Hz, receiver depth 100 m starting at 3999 m
p(r,z) magnitude, source 250Hz receiver location starts at 3.999000e+00 km
x 10-5
--- RAM
-- CSNAP
06-
c
aM
3.95
3.95
I
44
4.05
4.05
-
N
I
4.1
-
-
-:
-
I
4.2
4.2
4.15
4.15
4.1
-
N
I
p(r,z) phase
2nn
e
100 -
- - CSNAP
0 -
-
.
................
-
-100
4
3.95
- .....
-.-
--
-.-
-
4.05
4.1
-
-
-- RAM
.-
4.15
4.2
TL
-90
-..
-90 -
-110 3.95
...
-.-.-
-.
4
4.05
4.1
4.15
-
-100 -
-- RAM
-. CSNAP-
4.2
range in km
Figure L-8: Magnitude and Phase,Source 250 Hz, receiver depth 100 m starting at
3999 m
147
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 100m, starting at 4.998000e+00 km
11
CSNAP
-
-
--
-
~- ~~
S-40
0Y)
Ca
2-60
-50
-60
-70
-80
-90
0
-
*0
AM
CSNAP
-
-
-0.5 -
0
-10
-20
-30
-40
--
-1 - - --1.5 ----2
-70
-63
-64
-65
0
-66
-67
-68
-69
-61
-62
-60
Figure L-9: Beamforming, Source 250 Hz, receiver depth 100 m starting at 4998 m
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 krn
x 10-5
-
RAM
CSNAP
-
2 -
01
5.1
5.05
5
4.95
p(r,z) phase
200
/
-
.
-.
5.15
5. 2
:7
.-.
--
- -
RAM
- - CSNAP
---
..........
.
-100 4.95
-20C
.
5. 2
5
-
100 0
. . .
5.15
5.05
I
5.1
TL
-RAM
- CSNAP-
-95'-100/
-105-
-14.
4.95
5
5.1
5.05
5.15
5.2
range in km
Figure L-10: Magnitude and Phase,Source 250 Hz, receiver depth 100 m starting at
4998 m
148
Appendix M
Beamforming Plots XI, Source 250
Hz, receiver depth at 100 meters,
range increment ~5 km
The following plots show the beamforming results and the magnitude and phase of
p(r, z) by RAM and CSNAP corresponding to different setting parameters.
149
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 1 00m, starting at 4.998000e+00 km
0
(I
RAM
-CSNAP
Co
*~-40
-
---.
.-.-.-.
.-.-. .-.-.-.-
-60
-90
-90
-80
-70
I
-60
-50
-40
-30
-20
-10
I
0
-RAM
-CSNAP
/
.....
- - -.-.-.-.-.-.
-..
-
.
-0.5
00
-q
-1
-1.5--
-
C
-70
-69
-68
-67
-66
-65
-64
0
-63
-62
-61
-60
Figure M-1: Beamforming, Source 250 Hz, receiver depth 100 m starting at 4998 m
4
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 km
x 10-5
RAM
CSNAP
Cu
2-
C
0
Cu
E
04.95
5
5.05
5.1
5.2
5.15
p(r,z) phase
/0.
2
.
100
..................
- RAM'
- --CSNAP
0
-100 -.-2U0
.. . .
4 .95
n
.........................
.-.-
.-.
5
5.05
C1
5.1
5.2
5.15
TL
- V
.
RAM
CSNAP
...
.
.....
-
-95
.-...
-.-
-100--105-110.4.95
5
5.05
5.1
5.15
5.2
range in km
Figure M-2: Magnitude and phase, source250 Hz, receiver depth 100 m starting at
4998 m
150
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 1 00m, starting at 9.999000e+00 km
-RAM
CSNAP
-20
V
0
V
-40-
C
0)
CU
-801.
-90
-
-
-60 --
-80
-70
-60
-50
-40
-30
-20
0
-10
0
RAM
-
-SNAP
~0
-0 .5 -
...
......
... .. ..
..
-..
.......
0
-1 -
.-.
-
*0
C
0)
CU
-1.5 -
--
-80
-79
-78
-77
-76
-75
-74
-73
-72
-71
-70
Figure M-3: Beamforming, Source 250 Hz, receiver depth 100 m starting at 9999 m
x 10-
5
p(r,z) magnitude, source 250Hz receiver location starts at 9.999000e+00 km
RAM
-- CNA
._..
..-.
-.-...-.
'E 2
Cm
E
0
9 .95
10
10.05
10.1
10.15
10 .2
10.1
10.15
10.2
p(rz) phase
20C
CSNAP
- -
S 0 -1
-
-
100
-
--
-1001-
-
-
-200
9.95
10.05
10
....... ....... .... ......
9
-
-
-
-
.
-1 10 -...........
....
-1: 20-
AMj
-.-.
---
.
.
.
.
.
.
9C
-1 00
-
TL
-
- CSNAP
-1.
9.95
10
10.05
10.1
10.15
10.2
range in km
Figure M-4: Magnitude and phase, source250 Hz, receiver depth 100 m starting at
9999 m
151
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at loom, starting at 15 km
0
.
.... AM..
M-20
.
CD
~ ~
~
~
~
...
-
CSNAP.
.
..-..
..-..
-..--..
---.
..-
_4
|
C
0)_
-90
-80
-70
-60
-50
-40
-20
-30
-10
0
00
-0.5
CY
-
-1.5 -
RAM
CSNAP
-2
-75
-74
-73
-72
-71
-70
-69
-68
-67
-66
-65
Figure M-5: Beamforming, Source 250 Hz, receiver depth 100 m starting at 15000 m
x 10-5
1
p(r,z) magnitude, source 250Hz receiver location starts at 15 km
CD
0)
cc
....... ......
E 0.5
F
0
15.1
p(r,z) phase
15
......
RAM
CSNAP
15 .2
200
100
0
-100
--- CSNAP
-200
RAM.
15.1
TL
5
15.2
-Qn
--
RA M
-- CSNAP
1gn
15
15.1
range in km
15.2
Figure M-6: Magnitude and phase, source250 Hz, receiver depth 100 m starting at
15000 m
152
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 100m, starting at 1.999800e+01 km
-
RAM
-CSNA
-20
-0
S-40
.
-80
-9
;
0
-80
0
-
.
-
-1 .5
--
-
-80
-79
/
-D
1
0
-10
RAM
CSNAP
-0 .5 -
-20
-30
-40
-50
-60
-70
-
-DU
-72
-73
-74
-75
-76
-77
-78
-70
-71
Figure M-7: Beamforming, Source 250 Hz, receiver depth 100 m starting at 4998 m
x 1C5
p(r,z) magnitude, source 250Hz receiver location starts at 1.999800e+01 km
1
C
-
RAM
-- CSNAP]
I
0.5
01
19.9
20
19.95
20.05
p(r,z) phase
20.1
20. 15
20.2
20.1
20.15
20.2
200
-
-
- C.N
.
.
100
-
0
-100
19.9
19.95
20.05
TL
20
-90
-- OSNAP
-100
-110
-120'
19.9
19.95
20
20.05
range in km
20.1
20.15
ii
20.2
Figure M-8: Magnitude and phase, source250 Hz, receiver depth 100 m starting at
4998 m
153
Power(theta) - Normalized, 64 sensors, 3 meter spacing, 250 hz, receiver at 100m, starting at 2.499900e+01 km
.
n.
-
RAM
SNAP
-..-.
-...
-..-.-.-.-.
......
--.
-..
..
-20
-.
-.
.-.
.-.
...-.
..-.
.
-40
-
-60
-80
-90
--.
--
-70
.. -.-.-.
-60
-50
-30
-40
0
-10
-20
RAM
-
CSNAP
.0.5 -
---
---
-
-
- 1 -(M
Z
--
-
--
-
-1.5 - -I
-80
-76
-77
-78
-79
-71
-72
-73
-74
-75
-70
Figure M-9: Beamforming, Source 250 Hz, receiver depth 100 m starting at 24999 m
X10-6
8
(D6-
-
p(r,z) magnitude, source 250Hz receiver location starts at 2.499900e+01 km
CNA
.
..
..........
4F....
.E
E2
...................
........
24.9
25
24.95
25.
25.05
p(r,z) phase
25.1
......
25.2
251
25.2
25.15
0A
AP
100 --
-
-
-100
24.9
25.1
25.15
25.2
25.05
range in km
25.1
25.15
25.2
-100
-
-110-120
: -
1'-4.9
:
24.95
RAM
-
SNAP
25
I-
25.05
TL
25
24.95
-
V-.
I
Figure M-10: Magnitude and phase, source250 Hz, receiver depth 100 m starting at
24999 m
154
Appendix N
Beamforming Plots XII, source 250
Hz, receiver depth at 100 meters,
range coverage range of 5 km
The following plots show the beamforming results, the magnitude and phase of p(r, z),
and the Transmission Loss by RAM and CSANP corresponding to different setting
parameters.
155
Power(theta) - Normalized, 1334 sensors, 3 meter spacing, 250 hz, receiver at 100m, starting at 9.990000e-01 km
Al
01
RAM
CSNAP
-.
..
.
.
...
...
.
....
-20
0
C
Cu
~0
- .....-...
J
-40
-..........
CC
CU
-60*
0'
0
-9
-80
-70
-60
-50
-40
-30
-20
-10
0
-0.
-0. 4 -
. ..
--.-.-.-.-.
-
RAM
-C
6
-CSNAPI
C-0.
-
6 --
-
---
--
-0.
.... . . . .. . .
. .
-
. . ...
.
81
-60
-59
-58
-57
-56
-55
0
-54
-53
-52
-51
-50
Figure N-1: Beamforming, Source 250 Hz, receiver depth 100 m covers from 999 m
to 4998 m
p(r,z) magnitude, source 250Hz receiver location starts at 9.990000e-01 km
x 10-4
-.
S3 -..
.. . . . . . .. . . . . . . .
RAM
CSN A P
-
4
Ca
E
0
0.5
1
1.5
2
2.5
3
p(r,z) phase
3.5
4
4.5
5
2001
RAM
-CAP
I'
-
100
-
0
-100
-2000
.5
1
1.5
2
2.5
3
3.5
4
4.5
5
3.5
4
4.5
5
TL
-60
-80
Co
-100-120[
-140
0. 5
-..-
-RAM
-CSNAP
1
1.5
2
2.5
3
range in km
Figure N-2: Beamforming, Source 250 Hz, receiver depth 100 m covers from 999 m
to 4998 m
156
CSNAP
:A
1
1.1
1.2
1.3
1.5
1.4
1 .6
1.8
1.7
2
1.9
W
AP
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
-200A
4
4.1
4.2
4.3
4.4
4.6
4.5
range in km
4.7
4.8
4.9
5
Figure N-3: Beamforming, Source 250 Hz, receiver depth 100 m covers from 999 m
to 4998 m
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 250 hz, receiver at 100m, starting at 4.998000e+00 km
0
-RAM
-
.
-.
-...
-40 -
CSNA
---
--
.
M-20 - - ----
-
~-2O
-60
-80
-90
-80
-30
-40
-50
-60
-70
-20
0
-10
A
0
-RAM
OSNAP
-G -0.4
-
--
-
-
-
M
-0.2-
-
-0.6
-0.8-76
-75.8
-75.6
-75.4
-75.2
-75
-74.8
-74.6
-74.4
-74.2
-74
Figure N-4: Beamforming, Source 250 Hz, receiver depth 100 m covers from 4998 m
to 9999 m
157
p(r,z) magnitude, source 250Hz receiver location starts at 4.998000e+00 km
X 10-5
8
-- RAM
...
CSNAP
-.--...
-
S6 -ooi
Z4 . .. .. . .. .
.. ..
20:
4
0
-
40
)ph...s..
1,l 1
I
5
API
6
7
5
6
71
_
-10:_____
_
JiTL
....
....
0 Al
9
8
0
_
-
120
-140
CSNAP
5
4
6
8
7
range in km
9
10
Figure N-5: Beamforming, Source 250 Hz, receiver depth 100 m covers from 4998 m
to 9999 m
200,
RAM
il
2
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
-200
6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
NAP
-
RAP
6
-200
200
-
7
RAM
7
7.1
7.2
8
8.1
8.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
8
8.3
8.4
8.5
8.6
8.7
8.8
8.9
9
9.9
10
200
I IT:'
Y
I2CSNAP
I
-200
9
9.1
9.2
9.3
9.4
9.6
9.5
range in km
9.7
9.8
Figure N-6: Beamforming, Source 250 Hz, receiver depth 100 m covers from 4998 m
to 9999 m
158
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 250 hz, receiver at l00m, starting at 9.999000e+00 km
1,
0
-
-I-
IL
RAM
CSNAP
-20
- .
C
V
-40
-60
-90
-80
-70
-50
-60
-40
-30
-20
0
-10
-0.2-
-
- -0.4k-
-0.6
-0.8
-77
-77.5
-78
-75.5
-76
-76.5
-75
Figure N-7: Beamforming, Source 250 Hz, receiver depth 100 m covers from 9999 m
to 15000 m
p(r,z) magnitude, source 250Hz receiver location starts at 9.999000e+00 km
10-5
4
--
SNAP
Ca
0
11
10
20 9
12
13
14
15
12
13
14
15
13
14
15
p(r,z) phase
100
0
0
..
~
....
. . . . . . ....
-100
-200
9-
10
11
TL
-80 r--100-
-120IRA
9
10
11
12
range in kmn
Figure N-8: Beamforming, Source 250 Hz, receiver depth 100 m covers from 9999 m
to 15000 m
159
RAM
oI
-201
10
10.1
/
,
10.2
10.3
20C
/I
//
10.4
10.5
10.6
10.7
~
I
I
10.8
10.9
11
-RAM
0 0P
-200
11
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
12
RAM
0
-2
14
14.1
14.2
14.3
14.4
14.5
14.6
14.7
14.8
14.9
AP
15
to 15000 m
-20
-
-
AM
-CSNAP
- .
-
Power(theta) - Normalized, 1667 sensors, 3 meter spacing, 250 hz, receiver at I00m, starting at 15 km
CO
--
-
-80
-70
-
---
-60
-80
-90
-
.
-
-40
-60
-50
Ca
0
-40
-30
-20
-10
0
-2
-
.............
.
-4
-
.
.
(D
-6
-8
-101
-70
-69.9
I
II
-69.8
RAM
CSNAP
-69.7
I
-69.6
I
-69.5
-69.4
-69.3
-69.2
-69.1
-69
Figure N-10: Beamforming, Source 250 Hz, receiver depth 100 m covers from 15000
m to 19998 m
160
p(r,z) magnitude, source 250Hz receiver location starts at 15 km
X 10-5
4r
155
15.5
015
15
I
I
1j65
16
-100
-00
~)pae118
1
17
16.5
17.5
p(r,z) phase
1
I
I
8.
18.5
19
19
95
19.5
2
20
18.5
19
19.5
20
A
15.5
15
-140
-
A
-
18
17.5
TL
17
16.5
16
-
Figure N-il: Beamforming, Source 250 Hz, receiver depth 100 m covers from 15000
m to 19998 m
WAP
-200
I
-
-1200
-2 0
-260 15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
16
16
16.1
16.2
16.3
16.4
range in km
16.6
16.5
16.7
16.8
16.9
17
17
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
18
18
18.1
18.2
18.3
184
185
186
187
18.8
189
19
19
19.1
19.2
19.3
19.4
195enk
19.6
19.7
19.8
19.9
20
-20
-1A
APIl
Figure N-12: Beamforming, Source 250 Hz, receiver depth 100 m covers from 15000
m to 19998 m
161
Power(theta) - Normalized, 1668 sensors, 3 meter spacing, 250 hz, receiver at loom, starting at 1.999800e+01 km
SAP
-
0
*0
a)
40
~0
0)
(U
60-'
-80
-90
-80
-70
-60
-40
-50
-20
-30
-10
0
CSAP
-
0
.. ..
.
0 .4 - -.
a 0.6C-
0.8-
/
-76.9
-77
-76.8
-76.7
-76.6
-76.5
-76.4
-RAM
-76.3
-76.2
CN AP]
-76
-76.1
Figure N-13: Beamforming, Source 250 Hz, receiver depth 100 m covers from 19998
m to 24999 m
p(r,z) magnitude, source 250Hz receiver location starts at 1.999800e+01 km
X 10-5
1
2
(D
--
RAM
1 .5
0 .5 -
--
-
c
0
19
21
22
p(r,z) phase
23
242
20
20
21
22
TL
23
24
24
25
25
20
21
22
range in km
23
24
25
20
5
2
100
S0
-100
RAM
19
19
of%
-100
-120
RAM
140'
9
Figure N-14: Beamforming, Source 250 Hz, receiver depth 100 m covers from 19998
m to 24999 m
162
A
200
CNAP
o
200.
-200
20
20
--
/AP
/*
i
20.1
21.2
21.3
21.4
21.5
20.6
21.7
20.8
20.9
21
20.1
20.2
20.3
20.4
20.5
20.6
20.7
20.8
20.9
21
.
A-
-
RAM
NAP
2
21
21.1
2:: 23.
200
-200
23
21.2
21.3
21.4
23.2
233
2.4
/
21.6
21.5
range-RAM
k 22.6
23.5
21.7
21.8
21.9
22
22.7
22.8
22.9
23
7~~
,
23.3
23.2
23.1
kn-A
200~rng
23.4
23.6
23.5
in~
23.7
23.8
23.9
24
/
from 19998
Figure N-15: Beamforming, Source 250 Hz, receiver depth 100 m covers
m to 24999 m
163
164
Appendix 0
Beamforming Contour Plots
The plots will show the beamforming contour at different frequency and range increment.
165
RAM BEAMFORMING CONTOUR PLOT ,50M,75 Hz 1 km increment
-10
-20
-20
-30
0)
-40
-40
-D
-50
-60
1
1.5
2
2.5
3
range in km
3.5
4
-70
4.5
CSNAP BEAMFORMING CONTOUR PLOT ,50M,75Hz 1km increment
-10
0
-20
-20
r
a)-40
I
-30
-40
-50
* -60
-60
-80
1
1.5
2
2.5
3
range in km
3.5
4
4.5
Figure 0-1: source=75HZ receiver depth=50M increment=1KM
166
-70
RAM BEAMFORMING CONTOUR PLOT 50M,250hz 1 km increment
0
-10
-20
-20
I I
-30
-40
-)
-40
-60
-50
-60
-80
1
1.5
2
2.5
3
range in km
3.5
4
-70
4.5
CSNAP BEAMFORMING CONTOUR PLOT ,50M,250Hz, 1km increment
0
0
-10
-20
-20
I
-40
I-30
-40
-60
-50
-60
-80
1
1.5
2
2.5
3
range in km
3.5
4
4.5
Figure 0-2: source=250HZ receiver depth=50M increment=1KM
167
-70
RAM BEAMFORMING CONTOUR PLOT ,100M,75 Hz 1 km increment
0
-10
-20
-20
-30
-40
-40
-50
-60
-60
-80
1
1.5
2
2.5
3
range in km
3.5
4
4.5
-70
CSNAP BEAMFORMING CONTOUR PLOT ,100M,75Hz 1km increment
.10
0
-20
-20
-30
V)
a)
-40
(D
-40
-60
-50
-60
-80
1
1.5
2
2.5
3
range in km
3.5
4
4.5
Figure 0-3: source=75HZ receiver depth=100M increment=lKM
168
-70
RAM BEAMFORMING CONTOUR PLOT 100M,250hz 1 km increment
-10
-20
-30
U)
U)
U)
V
-40
0
-50
-60
1
1.5
2
2.5
3
range in km
3.5
4
-70
4.5
CSNAP BEAMFORMING CONTOUR PLOT ,100M,250Hz, 1km increment
-10
0
-20
-20
-30
a)
r
M-40
a)
I
-40
-50
-60
-60
-80
1
1.5
2
2.5
3
range in km
3.5
4
4.5
Figure 0-4: source=250HZ receiver depth=100M increment=lKM
169
-70
RAM BEAMFORMING CONTOUR PLOT ,50M,75Hz, 5 km increment
0
-10
-20
-20
>-40
-40
x -60
-50
-60
-80
6
8
10
12
14
16
range in km
18
20
22
24
-70
CSNAP BEAMFORMING CONTOUR PLOT ,50M,75Hz, 5 km increment
-10
-20
-30
U)
U)
0)
U)
V
C
-40
-50
-60
6
8
10
12
14
16
range in km
18
20
22
24
Figure 0-5: source=75HZ receiver depth=50M increment=5KM
170
-70
RAM BEAMFORMING CONTOUR PLOT 250 HZ, 50M, 5 km increment
-10
0
-20
-20
-30
-40
-40
-50
-60
-60
-80
6
8
10
12
14
16
range in km
18
20
22
24
-70
CSNAP BEAMFORMING CONTOUR PLOT with 5 km increment
-10
0
-20
-20
(D
a)
C
-40
-40
-50
-60
-60
-80
6
8
10
12
14
16
range in km
18
20
22
24
Figure 0-6: source=250HZ receiver depth=50M increment=5KM
171
-70
RAM BEAMFORMING CONTOUR PLOT ,100M,75Hz, 5 km increment
-10
0
-20
-20
-30
)-4
-60
-50
-60
-80
8
6
10
12
16
14
range in km
18
20
22
24
-70
CSNAP BEAMFORMING CONTOUR PLOT ,100M,75Hz, 5 km increment
-10
0
-20
-20
-30
c-40
-40
-50
-60
-60
-80
6
8
10
12
16
14
range in km
18
20
22
24
Figure 0-7: source=75HZ receiver depth=100M increment=5KM
172
-70
RAM BEAMFORMING CONTOUR PLOT 100M 250Hz, 5 km increment
0
-10
-20
-20
a)
a)
0)-4U
-30
40
-60
-50
a)
-60
-80
6
8
10
12
14
16
range in km
18
20
22
-70
24
CSNAP BEAMFORMING CONTOUR PLOT, 100M 250Hz, 5 km increment
0
-10
-20
-20
r
CD
-40
U)
_0
.C
-60
-30
1
-40
-50
-60
-80
6
8
10
12
14
16
range in km
18
20
22
24
Figure 0-8: source=250HZ receiver depth=100M increment=5KM
173
-70
174
Bibliography
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176
~-~cNo