Transmission Loss and SNR — Can the Signal Arrive and Be Detected?

One-way transmission loss (TL) comes from spreading and absorption

Sound becomes weaker as it travels through water. The main reasons are spreading, which distributes acoustic energy over a wider area, and absorption, which converts some of that energy into heat and other forms. In this chapter, TL means the loss accumulated while sound travels one way along a path.

As introductory approximations, use 20 log10(R) for spherical spreading and 10 log10(R) for cylindrical spreading, then add the absorption loss to estimate TL. Absorption generally rises with frequency, so higher frequencies can resolve finer detail but tend to be less effective at long range.

Choose the spreading model that matches how the sound expands

Spherical and cylindrical spreading are simplified models of the space into which the sound energy spreads.

• Spherical spreading (20 log10 R): models sound expanding in three dimensions from the source. It is useful in deep water or over ranges where the surface and seafloor do not yet strongly constrain propagation.
• Cylindrical spreading (10 log10 R): approximates long horizontal propagation in shallow water. The surface and seafloor constrain the sound, so its energy spreads mainly horizontally.

Let H be water depth and R horizontal range. Conditions with R ≪ H are closer to spherical spreading, while long-range propagation with repeated surface and bottom reflections and R ≫ H approaches cylindrical spreading. An intermediate case is sometimes approximated with 15 log10 R. The Chapter 6 simulator lets you switch this coefficient and compare the results.

Build the passive-sonar SNR equation

In passive sonar, sound radiated by the target travels one way to the receiver. Let SL be the target's radiated source level and TL the one-way transmission loss. The received signal level is then SL − TL. Let NL be the noise level and DI the receiving array's directivity index. In this simplified model, the effective noise level in the look direction is NL − DI. Signal-to-noise ratio (SNR) is the signal level minus that effective noise level.

SNR_passive = SL − TL − (NL − DI)

Because all terms are expressed in dB, they combine through addition and subtraction. Larger TL weakens the received signal; larger DI makes it easier to suppress noise outside the look direction.

Build the active-sonar SNR equation

In active sonar, the transmitted sound travels to the target and the echo returns to the receiver. The sound experiences one one-way transmission loss TL outbound, reflects according to target strength TS, and experiences another TL on return. Written in that order:

SNR_active = SL − TL − TL + TS − (NL − DI)
           = SL − 2TL + TS − (NL − DI)

Compared with the passive equation, the one-way −TL becomes the round-trip −2TL, and TS is added to describe the target's reflectivity. As range increases, the round-trip loss grows, so active-sonar SNR tends to fall rapidly at long range.

Put the SL values in the exercises into perspective

Source level (SL) varies widely with the target or transmitting equipment. The following representative ranges provide context for the exercise values.

• Passive SL (the target's radiated source level): 140–160 dB re 1 µPa @ 1 m for small craft, and about 170–190 dB re 1 µPa @ 1 m for merchant ships or large naval vessels. The passive exercise uses SL = 165 dB as a representative example.
• Active SL (transmitted source level): 180–200 dB re 1 µPa @ 1 m for portable echo sounders; large hull-mounted sonar and low-frequency ASW sonar can exceed 220 dB re 1 µPa @ 1 m. The active exercise uses SL = 210 dB as an example of a medium-to-large sonar.

All source levels shown here use the reference re 1 µPa @ 1 m (reference pressure 1 µPa, reference distance 1 m).

TS describes how readily the target returns sound

Target strength (TS) describes how strongly a target backscatters incident sound toward the sonar. A large, flat metal surface and a slender, flexible structure can return very different echo levels. At this stage, it is enough to remember that a larger TS generally makes the echo easier to receive.

Real oceans also introduce multipath, reverberation, refraction, and scattering from the surface and seafloor. We set those effects aside here and use simplified equations to build a working understanding of dB arithmetic and SNR.

Takeaways from this chapter

• Estimate one-way transmission loss (TL) by combining spreading loss and absorption loss.
• Absorption generally rises with frequency, so the signal tends to weaken more at long range.
• Find passive- and active-sonar SNR by adding and subtracting SL, TL, NL, DI, and TS in dB.