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After completing the module, the learner should be able to do the following:

Physics of sound propagation

  • Explain why sound is a pressure wave
  • List and describe the important characteristics of sound waves
  • Describe the relationship between sound pressure and sound intensity

Sound Speed

  • List the factors that affect underwater sound speed (temperature, salinity, pressure)
  • Describe how sound speed changes with changes in temperature, salinity, and pressure
  • Describe typical sound speed profiles in the world’s oceans and major marginal seas

Refraction and Reflection

  • Given a sound speed profile, describe how sound will refract
  • Describe the relationship between refraction and frequency
  • Describe the factors that affect sound reflection off of the seafloor or sea surface

Propagation Paths

  • Describe the surface duct, mixed layer, and sonic layer depth and their interrelationship.
  • Describe sound propagation in the surface duct
  • Describe the conditions that lead to sound channels
  • Describe the deep and secondary sound channels
  • Describe the convergence zone
  • Describe factors that lead to bottom bounce

Ocean Structures

  • Describe how sound propagation is affected by oceanic fronts and eddies

Sources of Change in Ocean Acoustic Features

  • Describe seasonal and diurnal effects on ocean sound speed profiles
  • Describe the effect of large storms on ocean sound speed profiles
  • Describe the effect of internal waves and tides on sound propagation

Scattering and Absorption

  • Describe the factors that affect scattering and absorption of sound at the seafloor
  • Describe how bathymetry affects scattering and sound propagation
  • Describe how seawater absorbs sound energy
  • Describe how air bubbles affect sound propagation

Factors Affecting Detection of Sound

  • List the factors that affect the detection of sounds under water
  • List sources of ambient noise in the ocean
  • Describe the difference between spherical and cylindrical spreading of sound waves
  • Describe how sound propagation paths affect the detection of sound sources


  • Explain the difference between active and passive sonar systems
  • Describe the strengths and weaknesses of active and passive sonar systems
  • Describe the factors that determine target strength

SONAR Equation (Advanced Topic)

  • List the variables in the sonar equation
  • Recall the difference in the sonar equation for active and passive systems
  • Describe the Figure of Merit (FOM)

History of Ocean Acoustics

The First Measurement of Sound Speed

In 1490 Leonardo da Vinci first proposed detecting ships by listening to the noise they radiate into water. He demonstrated that sound propagating through the ocean could be used for detection or tracking of objects in the water.

Later, in 1826 Colladon and Sturm recorded the underwater speed of sound in Lake Geneva, Switzerland. In their experiment, a bell was struck underwater simultaneously with a gunpowder flash. By timing the interval between the flash and the arrival of the sound, they calculated the speed of sound. The value they determined was remarkably accurate.

Drawing of Titanic hitting an iceberg

Interest in using sound to detect objects in the water was aroused following the Titanic accident. Could the iceberg have been detected and the subsequent accident avoided?

Photo of submarine (USS Grayling) in 1909

However, it was the advent of the submarine that drove the development of sonar and the science of ocean acoustic/acoustical oceanography. The submarine shown here predates World War I.

3-dimensional distribution of widow rockfish schools overlayed on bathymetry (blue surface) off the coast of Oregon, as observed using scientific echosounders. The green lines represent the vessel track and the acoustic energy is represented on a color scale with grey denoting low fish density to red denoting high fish density.

Today, acoustic waves are used under water to detect and locate objects and targets; to measure the characteristics of the environment or the velocity and location of moving underwater objects; and to transmit signals.

Physics of Sound Propagation

Sound as a Pressure Wave

conceptual animation of a pressure (sound) wave
Click image to view animation.

Although sound is often illustrated with a sine wave, sound is actually a pressure wave, with the peak in the sine wave indicating compaction of the medium and the trough indicating rarefaction (spreading out—thinning) of the medium.

The speed of sound depends on the distance between molecules and the strength of the intermolecular interactions. Consequently sound speed increases with density and temperature.

conceptual animation of a slow pressure (sound) wave
Click image to view animation.

In a gas, the molecules are widely spaced with very low intermolecular forces. As a result, the speed of sound tends to be slower in gasses than liquids or solids. The speed of sound tends to be highest in solids: the molecules are relatively close together and the bonds and structure between them are stable.

Characteristics of Sound Waves

Sound waves are characterized by their amplitude, intensity, frequency, speed, wavelength, and phase.

Amplitude and Intensity

Plot showing sine waves with 3 different amplitudes

The amplitude is proportional to the maximum displacement of the particles in the medium. An increase in amplitude is perceived as a louder sound.

Plot of Underwater Sound Pressure versus Sound Intensity

We measure loudness in terms of the sound intensity, generally given in terms of decibels (dB). The intensity of a sound is the power per unit area in the direction of propagation. The decibel is a logarithmic pressure scale. This is because human perception of sound is on a logarithmic scale – every increase of 10dB is perceived as being twice as loud, but has 10 times the sound pressure. For example, a sound pressure of 100 µPa has a sound intensity of 20 dB, while a sound pressure of 1000 µPa has a sound intensity of 30 dB. 30 dB is perceived by humans as being twice as loud as 20dB.

Frequency, Speed, and Wavelength

Plot of Underwater Sound Pressure versus Sound Intensity

The frequency is the rate of oscillation of the wave particles. To the human ear, an increase in frequency is perceived as a higher pitched sound. The speed of a wave is the rate at which it passes through the medium and depends on the properties of the medium. The wavelength is the length peak-to-peak of a sound wave.

Frequency, speed, and wavelength are all related as:

Frequency x Wavelength = Speed

For example, if the Frequency = 100 Hz (cycles per second) and the wavelength = 15 m, then the Speed = 1500 m/s.

100 Hz x 15 m = 1500 m/s = Speed


The Effect of Phase Interaction Between 2 Sound Waves
Click image to view interaction.

The phase of a sound wave refers to whether we are in the compression or rarefaction portion of the wave (increased or decreased pressure). The phase of the sound has its primary importance in how sound waves interact. Two waves with the same phase (and similar frequency) will interact constructively. The amplitude of the resulting wave will equal the sum of the two. Two waves with opposite phase, off by 1/2 wavelength, will interact destructively. The amplitude of the resulting wave will equal the difference between the two. If the amplitudes of both waves are the same, two will completely cancel each other out.

Use this interactive tool to examine how varying the phase and amplitude of two interacting sound waves changes the resulting sound wave.

Note that as the relative phases of the waves change with respect to each other, the resultant wave will alternately grow to its maximum amplitude then shrink back to its minimum.


Question 1

As sound waves propagate through a medium, in what direction do the molecules move? (Choose the best answer.)

The correct answer is (a) back and forth, parallel to the direction of propagation. Sound is a pressure wave. The back and forth motion parallel to the propagation direction results in compaction and rarefaction of the medium through which the sound propagates.

Question 2

A sound that is 10 times higher in pressure is perceived as being _____ as loud. (Choose the best answer.)

The correct answer is (b) twice as loud. This is because human perception of sound is on a logarithmic scale.

Question 3

How is an increase in sound frequency perceived by the human ear? (Choose the best answer.)

The correct answer is (a) As a higher pitched sound.

Question 4

How are frequency, speed, and wavelength related? (Choose the best answer.)

The correct answer is (b) Frequency x Wavelength = Speed. Here’s an example: 150 cycles/second x 100meters/cycle = 1500 meter/second.

Question 5

When two sound waves with similar frequency interact, the sound intensity (loudness) always increases. (Choose the best answer.)

The correct answer is (b) False. The result of the interaction depends on the phase of the waves. Waves with the same phase will interact constructively, resulting in higher amplitude than the two separately. However, waves with opposite phase will interact destructively and cancel each other out.

Sound Speed

Sound speed variations in seawater typically are relatively small, with the sound speed between 1450 and 1540 m/s. However, even small changes in sound speed can significantly affect the propagation of sound in the ocean.

Factors Affecting Sound Speed Variations

Three ocean properties determine underwater sound speed: temperature, salinity, and pressure. Sound speed increases with increasing temperature, salinity, and pressure.

This calculator uses a simple equation for the speed of sound from Medwin, 1975:

Sound speed (m/s) = 1449.2 + 4.6T - 0.055T2 + 0.00029T3 + (1.34 - 0.010T)(S - 35) + 0.016z

T is the temperature (°C),
S is the salinity (parts per thousand), and
z is the depth (m).

Let’s use the calculator to see how much of an effect these three factors have on sound speed. Ocean salinity typically varies from about 32 to 37 parts per thousand (ppt) and averages 35 ppt. Using default values for depth and temperature of 0 meters and 15°C, how much does increasing salinity from 32 ppt to 37 ppt change the sound speed? (Choose the best answer.)

The correct answer is (a) 6 m/s. The sound speed ranges from 1503 m/s at 32 ppt to 1509 m/s at 37 ppt. Clearly, in the open ocean, salinity has little effect on sound speed.

Now suppose that you are on a ship that enters Chesapeake Bay, where the water is much less salty, and you find a salinity of 10 ppt at the surface in the middle of the bay. How much does decreasing salinity from 35 ppt to 10 ppt change the sound speed? (Choose the best answer.)

The correct answer is (b) 29 m/s. The sound speed drops from 1506 to 1477 m/s, or about 29 m/s. If you continued all the way to Baltimore, where the water is nearly fresh (just a few ppt), the sound speed drops to about 1465 m/s, about 40 m/s slower than typical ocean conditions. So we see that salinity can be a significant factor in estuarine environments.

Operationally, we usually treat salinity as a constant over a region. However, there are places in the ocean that salinity plays a significant role in the sound velocity structure:

  • Near the outlets of major fresh water rivers or
  • Where very salty Mediterranean Sea water intrudes into the Atlantic Ocean

Temperature and Sound Speed

Now let’s look at temperature. In the open ocean, significant temperature gradients occur in the vicinity of warm currents like the Gulf Stream. Across the north side of the Gulf Stream near Cape Hatteras, NC, temperature drops 10°C, from 25°C to 15°C, over a very short distance. How does the sound speed change in response? (Choose the best answer.)

The correct answer is (a) It drops about 30 m/s. Sound speed drops from 1534 to 1506 m/s, about 30 m/s, when temperature drops 10°C, a significant change with important operational implications.

Pressure and Sound Speed

Suppose now that you’re lucky enough to cruise to the North Pole on an Icebreaker. Under the sea ice, the temperature and salinity is nearly constant from the surface to the seafloor: 2°C and 35 ppt. How does the sound speed change from the surface to the seafloor at 4000 meters? (Choose the best answer.)

The correct answer is (c) It increases about 60 m/s. Sound speed increases from 1458 to 1522 m/s, about 64 m/s, when pressure increases with a depth increase of 4000m.

The Interplay Between Pressure and Temperature

Temperature Profile in the Western North Atlantic. GDEM February Climatology at 22.8N, 307.3E

This plot shows a vertical profile of soundspeed from the Western North Atlantic taken from the Generalized Digital Environmental Model (GDEM), a climatology compiled by the U.S. Navy. In most of the world’s oceans, a relatively warm mixed surface layer is underlain by a sharp thermocline with temperatures dropping to about 4°C at 1500m depth. Assuming 15°C at the surface and 4°C at 1500 meters depth, use the sound speed calculator to determine whether the sound speed increases or decreases through the thermocline. In other words, which has a greater effect, the decrease in sound speed due to the drop in temperature or the increase in sound speed due to the rise in pressure? (Choose the best answer.)

The correct answer is (b) Sound speed will decrease through the thermocline from 1506 to 1490 m/s. Due to temperature alone, the sound speed would drop 40 m/s, but this is partially offset by an increase in pressure. Overall, in the upper 1500 m (5000 ft)—above the base of the thermocline—temperature generally drives the sound speed variations.

Profile of Temperature, Salinity, and Sound Speed in the Western North Atlantic.

This plot shows representative temperature, salinity, and sound speed profiles. Sound speed drops through the thermocline. From the base of the thermocline at 1200m down to the seafloor at 5000 m, temperature and salinity change very little, while pressure increases with increasing depth. The slow rise in sound speed below the thermocline results in a sound speed minimum near the base of the thermocline.

Sound Speed Profiles

Vertical Profiles of Temperature, Salinity, and Sound Speed from Around the World.
Click image to view animation.

Compare the sound speed profile for the Arctic with other regions. What is unique about this profile? (Type your response in the box below.)

The Arctic Ocean is unique in that the sound speed, temperature, and salinity are all lowest at the surface. This has interesting consequences for sound propagation, as we shall see later in the module.

The Mediterranean and Sea of Japan share some interesting characteristics, much different than the midlatitude open oceans. What are they? (Type your response in the box below.)

In both the Mediterranean and Sea of Japan, the temperature profile is nearly isothermal from a very shallow depth to the seafloor. This results in a very shallow sound speed minimum in both seas.

Compare the Eastern Atlantic to the Western Atlantic. How do they differ? (Type your response in the box below.)

The Eastern Atlantic has local maximum in the profile centered at about 1200 meters depth. This bump is caused by warmer, saltier water, which causes a bump in the sound speed. The source of the warm, salty water is outflow from the Mediterranean Sea. After exiting the Mediterranean, this water settles to a level centered about 1200 meters deep. A similar bump can be found in the Indian Ocean near the outflow of the Red Sea.

Refraction and Reflection

Transmission loss diagram for sound propagation near a shallow sound channel, also showing surface reflections.

As sound waves pass through the ocean, they refract as they speed up and slow down, and reflect off of interfaces at the sea surface and seafloor. In this section we examine how this refraction and reflection affect sound propagation, like that shown in this graphic.

Sound Rays

conceptual animation of wave propagation with rays. Includes reflection off the seafloor and sea surface, but no refraction
Click image to view animation.

So far in our discussion of sound waves, we have viewed them as wave fronts moving away from some source. We can also visualize sound as a series of rays emanating from that source. These rays are lines that always stay oriented perpendicular to the wave front. These rays make it easier to see wave propagation paths.


conceptual animation of wave refraction
Click image to view animation.

In an ocean with a uniform sound speed, sound rays would always travel straight paths. However, when sound waves encounter a change in speed, they refract and bend. Analogous to surface waves at the ocean surface, sound wave bend toward the slower speed. This animation illustrates how that occurs. In the ocean, the amount that sound refracts is determined by its frequency and speed. The ocean is a complex medium where the sound speed changes with position, both horizontally and vertically, and with time. Consequently, sound continually bends as it passes through seawater.

Sound Velocity Gradients

Vertical Profiles of Temperature, Salinity, and Sound Speed from the Western Atlantic.

We start by looking at vertical changes in sound speed. We can characterize sound velocity profiles as having a positive, negative, or neutral gradient. With a positive gradient, the sound velocity increases with depth, with a negative gradient, sound velocity decreases with depth, and with a neutral gradient, the sound velocity is constant.

Schematic diagram showing the effect of sound speed gradient on wave refraction

Note that the amount of refraction experienced by a sound wave is not constant . As this schematic diagram shows, the greater the sound speed gradient, the more sound waves curve.

Refraction and Frequency

As the previous sections have illustrated, sound refracts as it passes through water due to changes in sound speed. The refraction may be described using Snell’s Law, where the amount of refraction varies with the index of refraction (which is the ratio of the sound speed in the medium to a reference sound speed). However, it is not simply a matter of applying Snell’s law. The index of refraction in the water is actually frequency dependent, and increases with increasing frequency. The rate of change in the index of refraction is proportional to the wavelength of the sound, consequently it changes more rapidly at low frequencies than at higher frequencies.


Sound propagating through water encounters a variety of interfaces, the most obvious being the sea surface and the seafloor. According to Haines (1974), "…the interface between sea and air acts as a virtually complete barrier to sound." However, neither the sea surface nor the seafloor can be considered a 100% hard surface where the sound is guaranteed to reflect.

Schematic animation showing how ocean waves scatter sound waves
Click image to view animation.

At the surface, waves and ripples scatter incoming waves.

Schematic animation showing how the seafloor absorbs sound waves
Click image to view animation.

At the seafloor, sediments can absorb much of the sound without reflection and a rough bottom can scatter much of the energy.

Regardless of the details, a great deal of sound energy is typically reflected at these surfaces. And generally, the angle between the surface and the incoming wave equals the angle between the surface and the outgoing wave.

Propagation Paths

Photo of whale breaching

To badly paraphrase an old question: If a whale falls in the ocean, will anyone hear it? In other words, if we make a noise in the ocean, where does the sound go? The answer is complicated and depends on several factors.

Profile of Temperature, Salinity, and Sound Speed in the Western North Atlantic.

In our discussion we start with a relatively common and simple situation: a sound source at the surface with a simple, common sound velocity profile: a positive sound velocity gradient in an isothermal mixed layer near the surface, a negative sound velocity gradient in the thermocline down to about 1000 meters, then back to a positive sound velocity gradient in the deep, cold isothermal layer that extends to the seafloor.

With these conditions, we’ll see what happens as sound waves propagate progressively deeper into the ocean.

The Surface Duct, Mixed Layer, and Sonic Layer Depth

Temperature and Sound Speed Profiles showing Mixed Layer, Surface Duct, and Sonic Layer Depth. GDEM climatology for February at 36.1 N, 314.4 E

The terms surface duct, mixed layer, and sonic layer depth are often used interchangeably; however they are not the same thing.

Surface Duct

Temperature and Sound Speed Profiles showing Mixed Layer, Surface Duct, and Sonic Layer Depth. GDEM climatology for February at 36.1 N, 314.4 E

A surface duct exists any time the surface sound speed is less than the sound speed at the top of the thermocline, resulting in a positive sound speed gradient.

Sound Propagation and Bottom Bounce
Click image to view animation.

If the sound speed gradient is steep or the surface duct is sufficiently deep (which depends on the frequency of the sound), the sound will be refracted upward. Once the sound reaches the surface, it is reflected, only to be refracted upward again by the gradient. This effectively "traps" the sound in the surface duct. A surface duct of 50 ft is sufficiently deep to trap sound at frequencies above around 3000 Hz. However, a duct 300 ft deep or more is needed to duct frequencies 300 Hz or lower. Thus, higher frequencies may duct while lower frequencies do not.

Mixed Layer

Temperature and Sound Speed Profiles showing Mixed Layer, Surface Duct, and Sonic Layer Depth. GDEM climatology for February at 36.1 N, 314.4 E

The mixed layer is defined as a layer of surface water that has a nearly constant temperature.

Schematic diagram showing origin of the mixed layer

The mixed layer arises from mixing in response to wind and waves. As you might imagine, stronger winds and larger waves result in a deeper mixed layer. At times the mixed layer and the surface duct coincide. However, it is possible to have a surface duct without a mixed layer.

Sonic Layer Depth

Temperature and Sound Speed Profiles showing Mixed Layer, Surface Duct, and Sonic Layer Depth. GDEM climatology for February at 36.1 N, 314.4 E

The bottom of the surface duct is located where the sound velocity gradient changes from positive in the mixed layer to negative in the thermocline. The sonic layer depth (SLD) is the maximum depth of the surface duct.

Schematic diagram showing sound ray propagation and sonic layer depth.
Click image to view animation.

The ray path that leaves the sound source with the steepest angle and still refracts back up to the surface at the SLD is called the limiting ray. Shallower ray paths stay in the surface duct, steeper ray paths refract downward as they enter the negative sound speed gradient in the thermocline.


Temperature, Salinity, and Sound Speed Profiles from Indian Ocean near Antarctica.

This graphic shows profiles of temperature, salinity, and sound speed profiles from near Antarctica in February and August.

Which month exhibits a surface duct? (Choose the best answer.)

The correct answer is (b) August. A surface duct requires that sound speed increase with depth from the surface downward. The August profile shows this.

What is the sonic layer depth in August? (Choose the best answer.)

The correct answer is (a) 30 m. The sonic layer depth marks the sound speed maximum immediately below the surface, typically at the top of the thermocline. However, near Antarctica, ocean temperatures at the surface are colder than those at depth.

Convergence Zone Paths

Limiting Rays

Schematic diagram showing sound ray propagation and convergence zone

In the deep ocean, sound paths that leave a surface source at an angle just steep enough to escape the mixed layer refract downward through the thermocline, and then back upward in the deep isothermal layer.

Several factors promote sound propagation through the mixed layer to the thermocline below:

  1. A low sound frequency that doesn’t refract as much.
  2. A negative or only weakly positive sound velocity gradient.
  3. A shallow sonic layer depth that limits the depth through which the sound can refract.

The shallowest ray to turn back toward the surface is called the limiting ray. The limiting ray becomes horizontal at the conjugate depth, as shown here. This same ray is essentially the same as the limiting ray in the surface duct, but ever so slightly steeper so that it refracts downward at the sonic layer depth. Thus, the limiting ray is horizontal at both the sonic layer depth and the conjugate depth, where the sound speed is the same.

Sound rays that leave the source at steeper angles than the limiting ray dive progressively deeper. Eventually, one of those rays will just graze the bottom. This is our bottom limiting ray. Any steeper and it runs into the seafloor.

Note that, technically speaking, the conjugate depth occurs where the sound speed equals that at the source. However, in the case of a source at the surface, the conjugate depth is taken as the depth where the sound speed equals that at the sonic layer depth.

Convergence Zones

Schematic diagram showing sound ray propagation and convergence zone

As we can see here, all of the sound rays bracketed by the upper and lower limiting rays tend to come together near the surface in what we call a Convergence Zone (CZ). This concentrates the sound in a small area and can have important operational implications. How much sound gets concentrated depends on the distance from the conjugate depth to the seafloor, labeled as the depth excess. The greater the depth excess, the greater the window for sound energy to pass through and refract back to the surface.

Note that for very deep water and relatively high frequency, very little sound energy comes anywhere close to the seafloor. When this happens, the depth excess can actually be far less than the depth below the conjugate depth.

Multiple Convergence Zones

Schematic diagram showing sound ray propagation and multiple convergence zones

As you might expect, when the sound waves return to the surface in a convergence zone, they reflect back down, and refract back up in a second convergence zone further away. In fact, under the right circumstances, this occurs several times, resulting in several convergence zones at regular intervals.

Bottom Bounce

Schematic animation showing sound ray propagation and bottom bounce
Click image to view animation.

Bottom bounce is the term used to describe rays that leave the sound source, run into the bottom and reflect off it. When these rays return to the surface, they reflect again and head back to the bottom. In theory, these sound waves could travel a long way, alternately reflecting off the seafloor and sea surface. In practice the sound energy usually diminishes rapidly as the seafloor, sea surface, and water column absorb and scatter energy.

There are two situations where bottom bounce occurs. The first are rays that leave the source at angles steeper than the bottom limiting ray. The second is where the water is so shallow that there is no conjugate depth. In this last situation, all rays will bounce off the bottom at some point.

Frequency Dependence

It bears repeating that the propagation paths discussed previously depend on frequency, sound velocity profile, and water depth. The interplay of these three factors determines whether sound rays are trapped in a surface duct, form a convergence zone, or bounce off the bottom. Higher frequency waves refract the most and are most likely to trap in the surface duct. Lower frequency waves do not refract as much and thus are more likely to bounce off the seafloor.


Which of the following factors promote trapping of sound waves in a surface duct? (Choose all that apply.)

The correct answers are (a) and (c).

Higher frequencies refract more, thus are more likely to curve back to the surface and become trapped than low frequencies. A deeper sonic layer depth also promotes trapping because it allows more room for sound to refract back to the surface. However, a negative sound speed gradient hinders trapping of waves because it means that sound speed decreases with depth. Since sound refracts toward lower sound speed, sound will refract away from the surface, rather return to it.

Sound Channels

Schematic animation showing sound ray propagation in the deep sound channel
Click image to view animation.

Sound channels are defined as regions in the water column where sound speed decreases from above and below to some minimum. The depth of the minimum defines the sound channel axis. The boundaries of the sound channel are sound speed maxima immediately above and below the sound channel axis. Within the sound channel waves refract toward lower sound speeds, so sound rays above the minimum bend downward and sound rays below the minimum bend upward. The likelihood of a sound ray remaining trapped depends on several factors:

  1. the thickness of the sound channel (distance between the upper and lower boundaries),
  2. strength of the sound channel (the difference between the sound speeds at the axis and the boundary),
  3. the sound frequency, and
  4. the propagation angle.

Deep Sound Channel

Profile of Temperature, Salinity, and Sound Speed in the Western North Atlantic. GDEM February Climatology

The deep sound channel (DSC), sometimes called the primary sound channel, occurs where the water is deeper than the thermocline. A temperature profile shows temperature decreasing with depth to a minimum value and then remaining nearly isothermal to the seafloor. The deep sound channel axis (DSCA) is located where water becomes isothermal, at the base of the thermocline.

Above the deep sound channel axis, sound speed variations are primarily driven by temperature. The sound speed decreases with depth due to the decrease in temperature through the thermocline. Below the DSCA, the temperature is practically constant and the sound speed increases with depth due to increasing pressure. Thus, sound waves above the DSCA refract downward while those below the DSCA refract upwards.

At mid -latitudes the DSCA is typically around 3000 ft; it is deeper near the equator and shallower at extreme latitudes or in confined seas such as the Mediterranean Sea.

Secondary Sound Channels

A secondary sound channel is any sound channel that occurs in the water column above the DSCA—above the point where the water becomes isothermal. Secondary sound channels may form within or below the surface layer. To be exploited, a secondary sound channel must be thick enough and strong enough to trap the frequency of interest and it must be shallow enough for the sensor to operate.

Schematic animation showing sound ray propagation in the surface sound channel
Click image to view animation.

Secondary sound channels come in two general types. The first is caused by heating at the sea surface in the presence of a surface duct or mixed layer. As the surface heats, the surface sound speed may increase until it is greater than the sound speed at the top of the thermocline. However, a minimum sound speed remains between the surface and the top of the thermocline, resulting in a sound channel that acts like a surface duct. Such a sound channel is sometimes called a surface sound channel. These may be transient, appearing during heating of day and disappearing over night to reappear the following day. As a result, this has been called the "afternoon effect."

Vertical Profile of Sound Speed, Temperature, and Salinity in the Eastern Atlantic. GDEM February Average

The second type of secondary sound channel is longer lived and more widespread with the axis generally deeper than a surface sound channel. These may be formed due to intrusions of cold, low salinity water into warmer more saline water (or the reverse). This can occur along fronts and eddies or result from outflow from marginal seas. The depth of the intrusion is determined by its density. For example, this profile from the Eastern Atlantic shows the intrusion of warm, salty outflow from the Mediterranean Sea centered about 1000m. This produces a sound speed maximum resulting in a secondary sound channel above and a deep sound channel below.

Half-Channel and Near-Bottom Sound Channels

There are two conditions that result in acoustic propagation similar to that of a sound channel, but fail the condition of a sound channel of being bound at the top and the bottom by the same maximum sound velocity. These are half-channel and near-bottom sound channel conditions.

Sound propagation path in a half channel

If a positive sound velocity gradient extends from the surface to the seafloor, the result is a surface duct that extends all the way to the bottom. This type of propagation path is called a half-channel. This condition occurs in shallow water, under ice, during seasonal transitions, and in the winter in parts of the Mediterranean Sea. In these cases, the greatest sound speed is at the bottom (due to the effects of pressure), and the sound energy is refracted upward with increasing depth and then reflected back downward at the surface. Sound can propagate great distances under half-channel conditions.

Near-Bottom Sound Channel

Sound propagation path in a near bottom channel

A uniquely shallow water sound speed feature is a near-bottom sound channel. This occurs when the thermocline either reaches the seafloor or the deep sound channel axis is very close to the seafloor. In this case the negative sound speed gradient of the thermocline bends the sound toward the bottom. Sound waves reflect off of the bottom, then refract back down. At times the gradient is sufficient to keep sound emitted within the channel from reaching the sea surface, and may even trap sound originally emitted above the near-bottom channel. Unlike half-channel conditions which tend to extend propagation, near–bottom sound channel conditions usually result in increased bottom interactions and reduced propagation ranges.


Question 1

Question 2

Ocean Structures

So far, we have only discussed vertical variations in sound speed. But what happens when there are horizontal variations? This section looks at several types of ocean structures with horizontal variations in sound speed.

Ocean Fronts

Vertical cross section of temperature across the north wall of the gulf stream

Oceanic fronts are boundaries between water masses with different temperatures and/or salinities. Oceanic fronts can extend from the surface to very deep. Some fronts are current driven; others are weather driven.

Oceanic fronts may be either permanent or transient features, depending on the source. Permanent oceanic fronts are generally associated with strong ocean currents, such as the Gulf Stream, off the east coast of North America, and the Kuroshio Current, located off the east coast of Asia. This cross section shows the front on the north side of the Gulf Stream northeast of Cape Hatteras, NC. These frontal boundaries always exhibit a pronounced horizontal temperature gradient and can be thousands of meters deep. Transient oceanic fronts usually occur seasonally and are generally weaker, with more diffuse boundaries. Transient fronts may occur only a few weeks a year.

Cross Section of Acoustic Energy Crossing an Ocean Front Showing Duct Leakage

Acoustically speaking, fronts act as a barrier to acoustic energy, though not all fronts are significant. Strong fronts having a large density gradient can act as a wall, with no acoustic energy crossing the front. In areas such as this, energy trapped in a surface duct will be dumped below the layer in a process called duct leakage. In this example, nearly all of the acoustic energy from a source in the upper left escapes the surface duct into deeper water.

The effect of a front will be more pronounced as the frequency increases and refraction becomes more pronounced.


Eddies, in the oceanographic sense, are large rotating masses of water. They can be treated as circular fronts with the water trapped inside having different physical characteristics than the water outside.

Typically eddies are classified as one of two types—warm core or cold core.

Warm Core Eddies

Vertical Cross Section of Temperature Across a Warm Eddy NCOM Analysis valid 00 UTC 23 Jan 2009

As the name implies, the water inside warm core eddies is warmer than the water outside the circulation. This leads to an elevated sea surface height, resulting in anti-cyclonic circulation (clockwise in the Northern Hemisphere, counterclockwise in the Southern Hemisphere). Also, the mixed layer tends to be deeper inside than outside the eddy, increasing the sonic layer depth. The increased surface duct depth allows lower-frequency sound to propagate across the eddy.

Map of sonic layer depth (SLD) in the vicinity of Taiwan for an unspecified time/date

However, the improved acoustic propagation inside the eddy is often less significant than the boundary effects. This graphic shows sonic layer depth (SLD) in the vicinity of Taiwan. Warmer colors indicate a deeper SLD. Near the center of the plot we see a warm core eddy with deep SLD. However the north and east sides of this eddy are bounded by a very shallow SLD. This is caused by the entrainment of cooler water from the north around the edges of the eddy.

Eddies of any type can entrain water in their circulation from a water mass of very different characteristics than the eddy. Thus the boundary of the eddy can be far more significant acoustically than the body of the eddy itself.

Cold Core Eddies

Vertical Cross Sections of Temperature Across Warm- and Cold-Core Eddies NCOM Analysis valid 00 UTC 23 Jan 2009

Cold core eddies typically have a cyclonic circulation with cold, deep water upwelling in the center. As this graphic shows, upwelling decreases the depth of the mixed layer and results in a significant slope to the isotherms.

Map of sonic layer depth (SLD) in the vicinity of Taiwan for an unspecified time/date with cold core eddy annotated

In our plot of SLD, we see a cold core eddy with a resulting shallow SLD.

Sources of Change in Ocean Acoustic Features

Several processes in the ocean result in short-term changes to sound propagation, particularly in shallow water. This section examines some of those processes and their effects.

Seasonal Effects – Winter

Photo of a ship in rough seas

During winter months, strong, cold midlatitude cyclones frequently sweep across oceans.

What effect would you anticipate after passage of such a storm? (Choose the best answer.)

The correct answer is (a). During the winter, cold air cools the surface and severe storms mix the surface water, potentially hundreds of feet deep. This leads to a deep surface duct that effectively traps mid to high-frequency energy near the surface. At times, the surface duct can be deep enough to trap lower-frequency energy as well.

Seasonal Effects - Summer

Photo of a ship in rough seas

During summer months, fewer storms and warmer temperatures occur.

What effect would you anticipate after a long warm, calm spell? (Choose the best answer.)

In the summer , solar heating of the sea surface can reduce the efficiency of the duct or eliminate it completely. However, a surface sound channel may develop that behaves much like a surface duct.

Depth Profile of Temperature in the Afternoon (solid, 1840 LST) and Nighttime (dashed, 2125 LST) 28 May 1973 in the Western Atlantic

While this effect tends to be seasonal, it can occur on a daily basis with afternoon heating and disappearance of the surface duct. This graphic shows one example from a summer day in the western Atlantic.

Weather Effects – Tropical Cyclones

SST in the Philippine and East China Seas before and after typhoon passage in Sept 2007

Deep mixing from storm generated waves doesn’t just occur in the winter months. Tropical cyclones, in particular, can mix the water tens to hundreds of feet deep, cooling the surface water by bringing cold water from below to the surface. These images show sea surface temperatures before and after the passage of Typhoons Nari and Wipha. Note the significant cooling to the east of Taiwan. The dots on the maps mark the location of vertical profiles we will examine next.

Vertical Profiles of Salinity, Temperature, and Sound Speed Before (top) and After (bottom) Typhoon Passage
Modeled Signal Excess (dB) Showing Surface Duct Before (top) and After (bottom) Typhoon Passage

This graphic shows a vertical cross section of the modeled signal excess (signal minus noise and transmission loss) for a source within the area. Before , the surface duct is confined to a small area on the left side of the cross section. After typhoon passage, the surface duct spreads across the area.

Seasonal Effects – Fall and Spring Transitions

Fall and spring are transitional periods. The sea surface tends to be hottest in the early fall, after a summer of heating, while the surface duct will be deepest in the early spring when winter storms have mixed the layer to great depths and summer heating has not yet started.

Internal Waves/Internal Tides

Time depth cross-sections of temperature in the East China Sea from 21 Sep to 15 Oct 2007 from glider observations and East China Sea NCOM

Internal waves are wavelike motions that propagate below the surface through the ocean. Instead of traveling along the sea surface, they travel along surfaces where there is a strong vertical change in density, such as occurs at the base of the mixed layer or along some ocean fronts.

Internal waves generated by tides are called internal tides . They form when tidally driven currents in the deep ocean slosh on and off the edge of the continental shelf or ridges associated with island chains. The resulting internal tidal waves tend to have diurnal (24 hour) or semidiurnal (12 hour) periods.

These graphics show time versus depth cross sections of water temperature for a location in the western Pacific during a 24-day period. Contours on the plot are isotherms, or surfaces of constant temperature. The squiggles in the isotherms represent internal tides. The heavy purple line near the surface indicates the depth of the mixed layer.

The primary oceanographic effect of internal tides is the fluctuation of the sonic layer depth. These fluctuations can lead to duct leakage, which causes sound propagation into random places across an area and can lead to detections where we wouldn’t expect any. Unless the SLD is very deep, these variations primarily affect higher frequency sound that has been trapped in the surface duct.

Scattering and Absorption

Sound propagating through water encounters a variety of interfaces, some obvious some not so obvious. Additionally, there are impurities and suspended objects that can scatter or absorb sound. In this section, we examine common cases of scattering and absorption.

Side-by-side animations of coherent and scattered reflections
Click image to view animation.

Scattering occurs when sound waves run into something that alters their propagation path. In the absence of scattering, the incoming and reflected sound waves have the same angle to the reflective surface. With scattering, the reflected sound waves come off the surface at various angles, and the reflection is diffuse, not coherent.

Animation illustrating reflected versus absorbed sound energy at the seafloor
Click image to view animation.

Generally, when we are talking about ocean acoustics, absorption is the difference between the incoming sound energy and the reflected sound energy for some surface.

Reflectivity of Sediments

Schematic illustration of the effect of sediment grain size on reflectivity /absorption

Seafloor material can have a significant effect on sound propagation. For example, fine-grained silt and clay absorb sound efficiently, while sand, gravel, and bedrock are more reflective.

Schematic illustration of the effect of sound frequency on reflectivity /absorption

Reflectivity is also frequency dependent, with the higher-frequency sound reflecting more efficiently than lower-frequency sound.

Schematic illustration of the effect of shells embedded in mud on  reflectivity /absorption

Because lower-frequency sound penetrates further into seafloor sediments, layering in those sediments becomes an important consideration when evaluating seafloor reflectivity.

A reflective layer below the surface may become the dominant influence on the reflected sound. For example, in a study in the Mediterranean Sea, an area of mud with embedded shells reflected a higher proportion of sound energy than did a sandy region. Based on the surface sediment types, we would have expected the opposite.

Distribution of Sediments

Distribution of Surficial Sediment in Long Island Sound

The distribution of sediment types can be highly variable, particularly near the coast. For example, this map shows sediment distribution in Long Island Sound, near New York City. Seafloor sediments range from silty clay to gravel and bedrock. This will have a tremendous effect on any propagation path that involves bottom bounce.

Maps similar to this one exist for other coastal regions, as well as the deep ocean basins.


Photo of Diver over Sandy Bottom
Shaded relief image of submarine volcanoes
Shaded relief image of Astoria Submarine Canyon

Not just the material, but the shape of the seafloor can have a tremendous effect on reflecting sound waves. The seafloor is covered with ripples, plains, ridges, seamounts, and canyons on scales from a few centimeters to hundreds of kilometers across.

Deep sound channel propagation blocked by a seamount
Click image to view animation.

Large seamounts and ridges can play an important role in deep water acoustic propagation; these features can block a signal, reflect or channel it into the deep sound channel where it is not detectable, or scatter it so much that it becomes undetectable.

Modeled Transmission Loss for Sound Striking Sand Waves at Different Angles and Frequencies showing lower transmission loss with ripples.

In shallow water at high frequencies, small sand ripples can have a significant effect on the intensity of scattered and reflected sound. In fact, it has been observed that reverberation off the small-scale ripples can introduce so much noise that it becomes impossible to locate or identify a target.

These graphics show modeled transmission loss for sound striking sand waves at different angles to the wave crests over a range of frequencies. In the plot on the left, the sand wave is smooth. As the angle of the transmitted sound increases, less sound is reflected back, so the transmission loss increases. Higher frequencies reflect more efficiently, so they also show higher transmission loss.

In the plot on the right, random ripples cover the sand wave. We can see that there is less transmission loss with the rippled surface, meaning that the scattered sound energy is much stronger. This is true across all frequencies and angles.

Thus, for active sonar systems operating in shallow water with small random ripples, it will be much more difficult to discern a target from the noise caused by reverberation off the seafloor. For passive systems, more of the signal from the source will be scattered rather than propagated forward, reducing the potential for detection.

Absorption by Seawater

Because sound is a pressure wave, its propagation requires some motion of molecules. Any time motion is involved, friction acts to dissipate, and sound propagation is no different. In seawater, friction between and within molecules converts sound energy to heat, and absorbs sound in the process. Absorption varies directly with frequency. Low frequency sound will propagate through the water with very little loss for very long distances; low frequency whale songs can be heard across ocean basins. In contrast, high frequency attenuates very quickly; high frequency sound such as an aircraft pinger may propagate only a few nautical miles from the source, even at very high source levels.

Absorption of sound by seawater decreases with depth by about 2% for every 1000 ft of depth. By 15,000 ft depth, the absorption coefficient is around 71% of its value at the surface.

Bubbles and Swim Bladders

Bubbles in seawater and gas-filled swim bladders in fish have very similar acoustic responses. For that reason, we combine the topics here.

Photo of waves in the deep ocean

Gas bubbles have two origins: air bubbles resulting from breaking waves and whitecaps and methane bubbles resulting from the decay of organic material. Bubbles in the sea are very small because large bubbles tend to rise quickly to the surface. They are a very small percentage of the sea in which they occur, but their effects on underwater sound are significant due to the differences in density and compressibility and because of the resonant characteristics of suspended bubbles.

Diagram of a Swim Bladder in a Fish

Most species of fish have gas-filled swim bladders. Swim bladders provide buoyancy and enhance hearing. Experiments have shown that fish swim bladders can have a large effect on acoustic transmission loss. Fish swim bladders may be thought of as suspended, oblong bubbles.

Animation showing reverberation of a bubble
Click image to view animation.

So what do swim bladders and bubbles do to sound waves? If the sound waves are the right frequency and wavelength for the size of the bubbles, the bubble will oscillate in harmony with the sound waves. This resonance absorbs sound energy and re-radiates it as the bubble reverberates. Thus, clouds of bubbles or schools of fish between you and some sound source may effectively block sound propagation from that source.

Reverberation in Active Sonar Systems

Diagram showing reverberation from surface, bottom, and water column.

As sound propagates through seawater, it encounters inhomogeneities ranging in size from very tiny particles of dust that make the sea blue to schools of fish to large seamounts and pinnacles on the seafloor. All of these serve to absorb and reradiate a portion of the acoustic energy. Reverberation is the sum of all the contributions from the various scatterers. Reverberation is often a primary limiting factor on active sonar performance, particularly if the system is high power or low directivity.

There are three types of reverberation: volume reverberation produced by scatterers in the water column, sea surface reverberation, and bottom reverberation. Reverberation is difficult to separate from the received signal because the spectral characteristics are very similar, except for the Doppler effect of a moving target [Lurton, 2002].


Which of the following properties promotes reflection of sound off the seafloor? (Choose the best answer.)

The correct answer is (b) Larger sediment grain size. Fine sediments, like mud, tend to absorb more sound than coarser sediments, like sand and gravel. More sound energy from low-frequency sound tends to penetrate sediments, than from higher-frequency sounds, which tend to reflect off of sediments.

Which of the following features tend to cause scattering and reverberation? (Choose all that apply.)

The correct answers are (a), (c), (d), and (e). All of these features, except (b) dissolved salts, tend to cause reverberation of sound waves. Certain dissolved salts do, however, tend to cause the absorption of sound waves by seawater.

Factors Affecting Detection of Sound

Up to this point we have examined how sound travels through water and the various factors that affect that propagation. Now, let’s turn our attention to what we actually hear underwater and how this affects our ability to detect noise from a particular source.

Most areas of the world can be categorized into one of three detection zones: 

  1. Noise limited, where the ambient noise is the primary predictor of detection potential;
  2. Range limited, where detection potential is determined primarily by range and the reduction of signal to noise through losses due to scattering and absorption in the water.
  3. Bottom limited, where detection probability and ranges are governed primarily by bottom interactions, in other words, how does the bottom absorb/reflect/scatter the sound, how many times does the sound hit bottom?

Ambient Noise

Schematic diagram showing some sources of ambient noise in the ocean

One common perception of the open ocean is that when you get below the surface layer, where waves and light don’t penetrate, the ocean is still, dark, and silent. As ocean measurements and modeling advance, it becomes more and more apparent that while the depths of the ocean may be dark, they are hardly still and far from silent, even far from any human activity.

Ambient noise is any sound in the water that is not emitted by the source of interest. There are many sources of sound in the water, but they all can be generally classified under the headings of either natural sources or man-made sources. The frequency range of ambient noise is as great as the number of sources of sound.

Natural Sources of Noise

Natural sources of ambient noise run the spectrum from geological processes, to weather phenomena, to biological sources.

Whenever sources of marine biologic sound in the water are discussed, the most people think of aquatic mammals, in particular whales and dolphins. While these are sources of sound in the ocean, they are far from the only biological sources of acoustic noise. Several species of fish raise a racket under water. Among invertebrates, Snapping Shrimp are quite noisy.

Underwater sound spectra for different weather events

Not all sounds underwater come from animals. Breaking waves and rainfall can also be heard. Geologic processes like volcanic eruptions, earthquakes, and landslides add to the noise.

The table below lists the sound characteristics of animals and phenomena. Click the link to hear the sound they make.

Source Link
Dolphin clicks
Humpback whales
Snapping shrimp
Volcanic Eruption

Human Sources of Ambient Noise

Photo of cargo ship

Shipping traffic is a significant source of ambient noise at lower frequencies. The noise peaks around 60 Hz, the maximum in the cavitation spectrum of typical merchant ships.

Click to hear the sound of the Ron Brown, a NOAA oceanographic research vessel:

Click to hear a large cargo ship:

Global shipping activity

The contribution to ambient noise depends on the distance from the shipping lane. This map shows global shipping lanes. Clearly, most of the traffic is in the Northern Hemisphere.

Self Noise

Self noise is exactly what it says—it is the noise related to the vessel or apparatus of the listener. It can be due to machine operations, motion through the water, and even the hum of electronic equipment.

Self noise can present a problem if you are listening for a sound with a frequency close to the self noise. This may make it hard to detect the noise even if it would be loud enough to hear otherwise.

Source Level

Source level is how loud the noise emitted by the object is. For example, a whisper has a much lower source level than a shout. And just as you may need to shout to be heard in a crowded room, the level of the sound you’re interested in needs to exceed the ambient noise level to be detected.

Although source level is usually reported as a single value for a given frequency, it may have a directional component dependent on the relative orientations of the source and receiver. The frequency and source level of emitted sound may also vary with time.

Transmission Loss (TL)

animation showing spherical spreading
Click image to view animation.

When sound waves leave a source they typically start uniformly spreading out. As the sound wave expands, the energy is essentially spread over a larger surface. This decreases the intensity of the sound at any one location. Even focused beams of acoustic energy will spread as they propagate through the water.

Most of the time spreading near the source can be approximated by spherical spreading. In spherical spreading, the intensity decreases as the square of the distance from the source, called the range.

animation showing cylindrical spreading
Click image to view animation.

If the sound becomes trapped in a surface duct or sound channel, its spreading becomes cylindrical, with the height of the cylinder equal to the depth of the surface duct or thickness of the sound channel. In cylindrical spreading, the intensity decreases linearly with increasing range. Cylindrical spreading of the sound will predict a reduction of 3 dB in intensity every time the range is doubled. Cylindrical spreading occurs in the sound duct and in sound channels.


Which of the following are sources of noise in the ocean? (Choose all that apply.)

The correct answer is all of the above, though some are certainly more common than others.

Propagation Paths

The last factor we will consider regarding sound detection is the propagation path. Once sound leaves a source, if it can’t follow a propagation path to your receiver, you’ll never hear it. Sometimes, as they say, "You can’t get there from here." This section looks at propagation paths as they affect sound detection.

Direct Path

Direct path propagation

The simplest propagation path is direct path. This means that the sound travels through the water directly from the source to sensor. Only effects related to the water column between the source and sensor affect the propagation and detection potential is determined by the ratio of the signal strength to the noise at the sensor location. The frequency dependence of the sound path is generally not significant. While higher frequencies are attenuated at a greater rate than lower frequencies, ambient noise may mask low frequencies, but not high ones.

In certain areas, only direct path energy is detectable. This may be due to a seafloor that absorbs so much sound that any reflected energy is not detectable. In other areas, the sound has such a low source level or the ambient noise is sufficiently high that its strength falls below detectable levels before it travels very far.

Sound Channels

Sound Channel Propagation

Sound channel propagation paths include surface duct, half-channel, and shallow sound channel. From a detection standpoint, if your detector is in the sound channel, you have a good chance of detecting a source that is also in the sound channel. Conversely, if your source is in the sound channel, but your detector is not, your chances of detection are slim.

Convergent Zones

Convergence Zone

Sound following a convergent zone propagation path comes to the surface at regular intervals measured in kilometers. If you are in the convergent zone, constructive interference of multiple rays results in a strong sound signal. Sometimes a target within the propagation path of the refracted rays may be detected, other times there is insufficient energy for detection anywhere except in the convergent zone. However, outside the convergence zone, the sound signal vanishes.

Duct Leakage

Duct Leakage

Duct leakage occurs when energy trapped in the surface duct or shallow sound channel is released or "leaks" into deep water as a result of variations in the SLD. Because these variations are difficult to know or predict, so are the propagation paths. Thus, detection of sound along a duct leakage path is erratic and somewhat random.

Bottom Bounce

Bottom Bounce

Bottom bounce and near-bottom sound channels have in common that both propagation paths require reflection off of the seafloor. In some shallow water areas, sound tends to fill the water column for long ranges due to multiple bottom bounces. This obviously helps sound detection.

Down-Slope Propagation

Down-Slope Propagation Path

Down-slope propagation includes elements of both bottom bounce and sound channel propagation. In this case, a sound source is located in shallow water near a drop-off in bathymetry. The acoustic energy initially strikes the seafloor in shallow water and bounces back. However, as the sound follows the slope downward, it will eventually bounce off the slope at a point below the top of the thermocline. Once this happens, the sound becomes entrained or trapped in the deep sound channel, typically at depths below the maximum depth of most sensors.

Shadow Zones

Shadow Zone

Shadow zones are areas where sound from a source at a given location cannot go due to the sound speed structure. This example shows a shadow zone below the surface duct, where sound is refracted upward, and near the top of the thermocline, where the sound is refracted downward. In practice, a shadow zone is never truly free of radiated sound because of scattered sound from the sea surface and by diffusion of sound from the sound channel. However, the sound leaked into the shadow zone is usually too weak to reveal a target.

Multipath Detection

Multipath Propagation: multiple paths between source and receiver

Multi-path detection is when sound emitted by or reflected off the target reaches the sensor via two or more propagation paths. In the graphic, sound from the whale is reaching the sensor via direct path and bottom bounce pathways. For an active system, multi-path detection would be heard as two or more returns for every ping, with each return representing the two-way travel time from the source/sensor to the target via one of the propagation pathways.


Question 1

Will the ship hear the whale? (Choose the best answer.)

Propagation path

The best answer is (b) No. The whale lies in a sound channel from which its call is unlikely to escape. Of course, this depends on several factors, most importantly the frequency of the whale song and the depth of the sound channel.

Question 2


All sonar can be classified as one of two types: active or passive, though some can do both.

Passive sonar/sensors

Ship Towing Passive Sonar Array

Passive sonar operates by listening for sound in a specified, typically low-frequency, bandwidth. Some passive sonars can hear sound emitted over a wide band of frequencies, others are more limited in bandwidth; these often have a much higher receiver gain so they can hear sound from greater distances.

Passive sensors are typically long arrays of hydrophones towed behind a ship or submarine. The frequencies typically detected by passive sensors generally will not trap in the surface duct, unless it is very deep.

Reciprocity in Propagation Paths

Vertical Cross Section of Transmission Loss Modeled from Both the Source and Sensor Showing a Failure of Reciprocity

Sonar modeling for passive acoustic propagation often assumes reciprocity of propagation paths. Reciprocity states that for a source that radiates equally well in all directions and a receiver that receives equally well from all directions, the source and receiver can be interchanged without affecting the answer, regardless of how complicated the propagation paths. Thus, passive acoustic modeling for sonar performance predictions often models transmission loss relative to the location/depth of the sensor (sensor centric). In other words, the assumption is made that by modeling the sensor as a source, the propagation paths emanating out from that location will show where a target could be detected.

In some cases, this is a reasonable approximation. Reciprocity can be shown to hold point-to-point: sound radiated from either point will have (approximately) the same intensity regardless of which direction it follows along the propagation path.

The problem with this is that reciprocity holds ONLY point-to-point. The transmission loss values are reciprocal only at the specified source and sensor points. However, the actual detection potential depends on the entire sound field. The fields are rarely reciprocal and in some cases are not even close to reciprocal.

This example shows two cross sections extending from sensor (left) to source (right). The top one shows transmission loss modeled from the sensor location (sensor-centric). The bottom one shows the same thing modeled from the source location (source-centric). From the sensor-centric model, there is little transmission loss between sensor and source so one would expect to detect the source. However, source-centric modeling shows much greater transmission loss. Not enough sound energy reaches the sensor for detection.

When the acoustic environments of the source and sensor are very different, sensor centric modeling may be at best misleading and at worst completely wrong. "Different" can mean different water depths, in and out of a sound channel or duct, or very different depths relative to the deep sound channel.

Active Sonar/Sensors

Conceptual animation showing active sonar
Click image to view animation.

Active sonar operates by sending out a pulse of sound at a specified frequency, then listening for the reflection from the target. Most of the time, frequencies used by active sensors are 2000 Hz and above. Although the higher frequency sound experiences greater attenuation, it facilitates localization of the reflector. The catch is that not only does the sound reflect off any target in the area, it also reflects off the seafloor, the sea surface, and even "stuff" in the water. As a result, the return signal is a jumble of the reflections off many reflectors. Plus, it may also contain ambient noise components due to weather and biological sources.

Active systems are often attached to the hull of a ship. Consequently, ocean features near the surface of the water have a significant effect on the propagation and detection of sound. Furthermore, higher frequencies are more likely to trap in the surface duct. Therefore, active sonar may have very long detection ranges against any reflector in the surface duct, but a low probability of detecting a deep target.

Target Strength

Conceptual animation showing strong and weak target strength
Click image to view animation.

The probability of detection for an active sonar system depends in part on target strength. Target strength is a measure of how efficiently an object reflects sound of a certain frequency. It depends on the reflectivity of the object (at the specific frequency) and its size. A small object that reflects sound efficiently might have a higher target strength than a larger object that tends to absorb or scatter sound rather than reflecting it.

Conceptual animation showing importance of target aspect ratio to active sonar source level
Click image to view animation.

For most objects, target strength is also aspect dependent. That is, for a very flattened or elongate target, the strength of the reflection will depend on the orientation of the target relative to the sound waves.

SONAR Equation (Advanced Topic)


Note: This section has no audio.

Sonar performance is predicted based on the interplay between several parameters that depend on the equipment, environment, and target. Very simply detection is possible if

Signal – noise + gain > detection threshold

Each of the variables on the left-hand side of the equation is a combination of several parameters. The units of each term in the sonar equation are decibels (dB. The use of the decibel as the "unit" for terms in the sonar equation makes it possible to combine unlike physical parameters to obtain a usable result.

The Variables

Before detailing the breakdown of the variables, a few definitions are in order.

  Active Passive
Parameters depending on the equipment:
Projector Source Level (SL) X  
Self-noise level (NL) X X
Receiving directivity index (DI) X X
Detection Threshold (DT)/ Recognition Differential (RD) X X
Parameters depending on the environment:
Transmission Loss (TL) X X
Reverberation Level (RL) X  
Ambient Noise Level (AN, sometimes referred to as NLAN) X X
Parameters depending on the target:
Target Strength (TS) X  
Target Source Level (SL)   X

Sonar Equation: Passive Systems

Now, back to the basic form of the Sonar equation:

Signal – noise + gain > detection threshold

Let’s expand this equation for the simpler passive systems.

The signal is the signal level received by the system. For passive systems it is the sound source level minus the one-way transmission loss:

Signal = SL – TL

The noise affecting reception is the power sum of the ambient noise and the self-noise of the system (which includes both noise in the processors, etc. and noise due to own-ship):

Noise = AN ⊕ NLs

The power sum just means that we sum the pressure intensities of the noise sources, rather than the decibel levels. Because the decibel is a logarithmic measure, this has a significant effect on the calculation.

The gain is the array directivity index, which includes the receiver processing gain. This number varies with target location relative to the receiver array orientation.

Gain = DI

The detection threshold (DT) is the minimum value of receiver output that leads to detection of a target. Detection threshold is also known as the recognition threshold or sensor recognition differential (RD). Thus, a target can be detected if

[signal – noise + gain] > DT

Or in a more expanded form:

[SL – TL – (AN ⊕ NLs) + DI] > DT

Usually the sonar equation is given in terms of signal excess (SE), which is the amount by which the received signal exceeds the detection threshold. When this is done, the DI and DT, both of which depend on the sensor, are often combined.

SE = SL – TL – AN + (DI – DT )

SE = SL – TL – NL + (DI – DT )

Note that we assume that either the ambient noise (AN) or the self noise (NL) dominates, so that we neglect the other noise term.


Given a case with the values in this table. Can the source be detected by our sensor? (Choose the best answer.)

(Remember from the previous page that SE = SL – TL – AN + (DI – DT ))

Source SL = 130 dB
Sensor DI – DT =   18 dB
Environment AN =   65 dB
TL =   83 dB 

The answer is (a) Yes, the signal can be detected.

Substituting the values from the table into the passive sonar equation we find

SE = SL – TL – AN + (DI – DT)

SE = 130 dB – 83 dB – 65 dB + 18 dB

SE = 0 dB

Or, the signal is just strong enough to meet the detection threshold.

Note that if we tried to do this same calculation using the intensities and power rather than the dB ratios, the simple equation above would not yield the correct result.

Sonar Equation: Active Systems

The signal term for active systems differs from that for passive systems. For active systems we must consider the two-way transmission loss (to target and back) plus the target backscattering strength.

Signal = SL – 2TL + TS

For the noise, we add a term for the reverberation level. The total noise affecting reception is the power sum of the ambient noise, the reverberation level, and the self-noise of the system (all at the frequency of interest).

Noise = AN ⊕ RL ⊕ NLs

The total noise is given in terms of dB, which means for an active system there is interplay between the ambient noise, the reverberation level, and the self-noise as to which is the dominant factor in determining the total noise level.

The gain term remains unchanged:

Gain = DI

Now, we can expand the sonar equation for an active system in two forms:

(1) the noise limited form

Signal Excess (SE) = SL – 2TL + TS – NL + DI – DT

(2) the reverberation limited form:

Signal Excess (SE) = SL – 2TL + TS – RL – DT

where RL is the equivalent plane-wave reverberation level and includes the ambient noise and DI terms.

DT vs RD vs RT

One of the most confusing terms used with the sonar equation is detection threshold (DT). This factor may be called detection threshold, as it is here, recognition differential (RD), used in many standard Navy publications and sensor databases, or even recognition threshold (RT).

To make matters worse, the same terminology might mean slightly different things depending on the technical background of the author and/or the context.  For example, recognition differential or detection threshold may refer each of the following:

  • The level at which a signal will appear on the screen, an intrinsic property of the sensor,
  • The level at which a trained, alerted operator will call a detection 50%  of the time, or
  • The difference in the ability of a trained versus untrained operator to detect a signal.

For active sensors, there is a minimum signal level for a signal to show up on the sonar screen.  Now suppose a particular sensor requires 10 dB of signal for something to show on the screen.  If the signal is less than 10 dB, the probability of detection is zero; the signal that is not on the screen cannot be seen by even the best operator.  However, appearing on the screen is not sufficient criteria for detection.  Often the required signal level for a trained operator to call a detection is greater than the signal required for it to appear on the screen.  Furthermore, usually a trace must be present for some number of pings and exhibit behavior consistent with that expected from the target before a contact is called.

Passive sensors do not have minimum signal at the sensor required for the signal to show on the screen.  However, as with active sensors, it is usually necessary for a signal to persist long enough at some minimum signal level and display behavior consistent with that of the target for a contact to be called.

Figure of Merit (FOM)

The sonar equations are often rearranged and stated in terms of a "figure of merit" (FOM). The FOM represents the maximum allowable one-way transmission loss for passive sensors and the maximum allowable two-way transmission loss for active sensors. The FOM is usually considered dimensionless, values included in the calculation are in dB.

The passive FOM is given by:

FOM = SL – NL + DI – DT

The FOM for active sensors verses a target with target strength TS is given by:

FOM = SL + TS – NL + DI – DT

The utility of the FOM is it can be used to give "rule-of-thumb" detection ranges. For example, an FOM of 76 for a passive sensor is generally assumed to translate to a detection range of approximately 20 kyds. Of course, the actual detection range varies with propagation pathway, condition of the equipment, and the environment, both water and sediment.


Sound is a pressure wave.Sound waves are characterized by their amplitude, frequency, speed, wavelength, and phase. Waves with the same phase interact constructively, resulting in higher amplitude. Waves with opposite phase interact destructively.

Sound speed variations in seawater typically are relatively small. 

Sound speed increases with increasing temperature, salinity, and pressure.

In most of the world’s oceans, a relatively warm, well-mixed surface layer is underlain by a sharp thermocline with temperatures dropping to about 4°C at 1500m depth.  Sound speed increases slightly through the mixed layer, drops through the thermocline, and increases slowly below that.

As sound waves pass through the ocean, they refract as they speed up and slow down, bending toward the slower speeds. Higher frequencies refract more than lower frequencies.

A surface duct that can trap sound exists any time the sound speed increases with depth in the mixed layer.  The sonic layer depth (SLD) is the maximum depth of the surface duct. 

Sound paths that escape the mixed layer refract downward through the thermocline, and then back upward in the deep isothermal layer. All of the sound rays passing below the conjugate depth and above the seafloor tend to come together near the surface in the convergence zone.

Sound channels are levels in the ocean that trap sound waves. A sound channel can occur anytime there is a minimum in a vertical sound speed profile. The deep sound channel occurs deep in the ocean, typically at depths around 3000 ft. Secondary sound channels also occur, typically at shallower depths.

A half-channel occurs when a positive sound velocity gradient extends all the way from the surface to the seafloor. Sound continually refracts upward toward the surface throughout the water column.

A near-bottom sound channel occurs when the there is a negative sound speed gradient from the surface to the seafloor, usually in shallow water. Sound continually refracts downward toward the seafloor throughout the water column.

Ocean fronts act as a barrier to acoustic energy. Energy trapped in a surface duct will be dumped below the layer in a process called duct leakage.

Eddies can be treated as circular fronts. In warm core eddies, the mixed layer tends to be deeper inside the eddy, increasing the sonic layer depth.  In cold core eddies the sonic layer depth tends to be shallow.

Severe storms mix the surface water, leading to a deep surface duct. At times, the surface duct can be deep enough to trap even lower-frequency energy. 

In the summer, solar heating can reduce the surface duct or eliminate it completely.  A surface sound channel may develop. This effect can occur on either a seasonal or a daily basis.

The primary oceanographic effect of internal tides is the fluctuation of the sonic layer depth.

Sound reflects off the seafloor and the sea surface. Reflectivity depends on several factors, including sediment type, shape of the seafloor, and sound frequency. Seafloor sediments can absorb much of the sound without reflection and a rough bottom can scatter much of the energy.

Scattering and reverberation also occur at the sea surface and in the water column. Fish swim bladders and air bubbles both reverberate and scatter sound energy. Absorption also occurs in seawater by the presence of some impurities that convert sound energy to heat.

Detecting sound underwater depends on whether the sound we would like to hear is stronger than the background ambient noise. Ambient noise has many sources, including marine fauna, ships, and weather.

As sound travels through water it weakens due to spreading of the sound waves. This can occur as either spherical spreading or cylindrical spreading. The propagation path sound takes will also determine whether you can hear it.

Sonars that detect targets underwater can be either passive or active. Passive sonars just listen for sound from a source. Active sonars emit a sound and listen for the reflection off of a target. Target strength and target aspect are important properties in determining whether a reflected sound is strong enough to be detected.