Adding Decibels
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Transcript of Adding Decibels
Adding DecibelsAdding Decibels
Speed of Sound in WaterSpeed of Sound in WaterD
epth
Dep
th
Dep
thD
epth
Dep
thD
epth
SalinitySalinity PressurePressure TemperatureTemperature
Medium Effects: Elasticity and DensityMedium Effects: Elasticity and Density
Salinity Pressure Temperature Salinity Pressure Temperature
Variable Effects of:Variable Effects of:
Speed of Sound Factors
• Temperature
• Pressure or Depth
• Salinity
speedin increase m/s 1.3 salinity in increaseppt 1
speedin increase m/s 1.7 depth of meters 100
speedin increase m/s 3 turein tempera increase C 1
Temperature, Pressure, and Salinity 2 2 4 3 2 2c t, z,S 1449.2 4.6t 5.5x10 t 2.9x10 t 1.34 10 t S 35 1.6x10 z
with the following limits:
0 t 35 C
0 S 45 p.s.u.
0 z 1000 meters
Sound Speed Variations with Temperature and Salinity (z = 0 m)
13801400142014401460148015001520154015601580
0 5 10 15 20 25 30 35 40
Temperature (C)
So
un
d S
pe
ed
(m
/s)
0
30
35
40
ppt salinity
Class Sound Speed Data
Class Sound Speed in Water Data
y = 0.0004x3 - 0.0807x2 + 6.2061x + 1393.4
1400
1420
1440
1460
1480
1500
1520
0 5 10 15 20 25
Temp (C)
So
un
d S
pee
d (
m/s
)
Series1
Poly. (Series1)
More Curve Fitting
2 2 4 3 6 4 9 5o
4 6 2 7 31
32 3 22
0 1 2 3
P Pressure from Leroy Formula
c 1402.388 5.03711t 5.80852x10 t 3.3420x10 t 1.478x10 t 3.1464x10 t
c 0.153563 6.8982x10 t 8.1788x10 t 1.3621x10 t 6.1185 1.362
c = c + c P+ c P + c P + AS+ BS + CS
10 4
5 6 8 2 10 3 12 42
9 10 12 23
2 3o 1 2 3
5 5 8 2 8 31
1x10 t
c 3.126x10 1.7107x10 t 2.5974x10 t 2.5335x10 t 1.0405x10 t
c 9.7729x10 3.8504x10 t 2.3643x10 t
A A A P A P A P
A 9.4742x10 1.258x10 t 6.4885x10 t 1.0507x10 t 2.01
10 4
7 9 10 2 12 32
10 12 13 23
2 5 5 7
6 3
22x10 t
A 3.9064x10 9.1041x10 t 1.6002x10 t 7.988x10 t
A 1.1x10 6.649x10 t 3.389x10 t
B = -1.922x10 -4.42x10 t 7.3637x10 1.7945x10 t P
C = -7.9836x10 P+1.727x10
3 6 2 4P 1.0052405 1 5.28 10 sin z 2.36 10 z 10.196 10 Pa
- latitude in degrees
z - depth in meters
Chen and Millero
Leroy
Expendable BathythermographExpendable Bathythermograph
LAUNCHER
RECORDER
Wire Spool
Thermistor
PROBE (XBT)
Canister Loading Breech
TerminalBoard
Stantion
Launcher RecorderCable (4-wireshielded)
Alternating Current PowerCable (3-wire)
OptionalEquipment
Depth/TemperatureChart
Canister Loading Breech
Typical Deep Ocean Sound Velocity Profile (SVP)
Typical Deep Ocean Sound Velocity Profile (SVP)
Sonic LayerDepth (LD)
Deep SoundChannel Axis
T PC
Refraction
A
B
D1
E
2
1 BD c t
2 AE c t
11cos
BD c t
AD AD
22cos
AE c t
AD AD
1 2
1 2
cos cos 1
c t c t AD
High c1
Low c2
1
1 2
1 2
cos cos
c c
Multiple Boundary Layers
1234
1
2
3
4
where c1 < c2 < c3 < c4 and 1 > 2 > 3 > 4
constant
cccc n
n
3
3
2
2
1
1
cos
....coscoscos
1234
1234
c1 c2 c3 c4
depth
Simple Ray Theory
1
1
c c cgradient g
z z z
z
c
(c,z)(c1,z1)
1c c gz
1
1
1
1 1
cos cos
c c
cos cos
c c gz
Snell’s Law
1
1
cR
g cos
1z R cos cos
Ray Theory Geometry
Positive gradient, g
z1
z2
x1 x2
c1
c2
1
2
R
The z (Depth) and x (Range) Directions
I=20
csurface=1500 m/s
1z R cos cos
1
1
cR
g cos
dz R sin d
z
x
1 1
z
zdz R sin d
1 1z z R cos cos
The z (Depth) and x (Range) Directions
I=20
csurface=1500 m/s
1z R cos cos
1
1
cR
g cos
dz R sin d
z
x
1 1 1 1
x z
x z
dz sin ddx R R cos d
tan tan
dztan
dx
1 1x x R sin sin
Why is R = Radius?
Positive gradient, g
z1
z2
x1 x2
c1
c2
1
2
R
1 1z z R cos cos
1 1x x R sin sin
px x R sin
p 1 1x x R sin
pz z R cos
p 1 1z z R cos
11R cos
1R sin p px , z
2 2 2 2 2 2p px x z z R sin R cos
2 2 2p px x z z R
Summary
Positive gradient, g
z1
z2
x1 x2
c1
c2
1
2
R
1 1x x R sin sin
1 1z z R cos cos
1
1
cR
g cos
1
1
cos cos
c c
1
1
c c cg
z z z
Negative Gradient
Negative gradient, g
z1
z2
x1 x2
c1
c2
1
2
R
1 1x x R sin sin
1 1z z R cos cos
1
1
cR
g cos
1
1
cos cos
c c
1
1
c c cg
z z z
Example 1
• Given: c1 = 964 m/s, c2 = 1299 m/s, 2 = 30o
z(between 1 and 0) = 3000m
• Find: 1, co, g (between pt 1 and 0), R
c0
1
2 0c1
c2
Example 2
• Find gradient, g• Find Radius of Curvature, R, for each ray.• Skip distance – i.e. the distance until the ray hits
the surface again• Max depth reached by each ray
I=20
II=30
csurface=1500 m/s
c100 m=1510 m/s
Backups
1
1
1
1 1
cos cos
c c
cos cos
c c gz
1z R cos cos
1 1 1 1c cos gz cos c cos
11
1
cz cos cos
g cos
1
1
cR
g cos
Slope = tan
x1
z1
z2
x2
2 1
2 1
z z z dztan
x x x dx