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