Transmission loss and SNR — reading reach

TL is the sum of spreading and absorption

Underwater sound weakens with range in two ways: a geometric spreading loss that thins the wavefront, and absorption as some energy is converted into heat and other forms. As a rule of thumb at this level, spherical spreading gives about 20 log10(R), and cylindrical spreading gives about 10 log10(R). Add absorption on top to obtain an estimate of TL.

Absorption tends to grow with frequency, so higher frequencies give finer detail but suffer more at long range — a classic tradeoff.

When to use spherical vs. cylindrical spreading

The spreading loss model depends on the geometry in which the wavefront expands.

• Spherical spreading (20 log10 R): applies when sound from the source spreads equally in all directions. Valid in deep water, or where propagation is not constrained by the surface or the sea floor.
• Cylindrical spreading (10 log10 R): applies when the horizontal range is much larger than the water depth, so the sound becomes trapped between the surface and the sea floor and spreads in a 2-D cylindrical fashion.

As a guide, with water depth H and horizontal range R: R ≪ H is closer to spherical, while R ≫ H with repeated surface/bottom reflections approaches cylindrical. In intermediate regimes, an empirical coefficient like 15 log10 R is sometimes used. The simulator in this course exposes this coefficient as a selectable parameter.

Building the passive SNR equation

Start with passive. The sound radiated by the target propagates one way to the receiver. With the source level (target's radiated source level) as SL, the one-way transmission loss as TL, the noise level as NL, and the receiver-side array gain as DI, the signal level at the receiver is SL − TL and the effective noise level is NL − DI. The difference between the two is the SNR.

SNR_passive = SL − TL − (NL − DI)

The key point is that in dB, these are additions and subtractions, not multiplications. Larger TL drops the signal further; larger DI pushes the noise side down.

Building the active SNR equation

Active uses a round-trip path: the sonar transmits a ping, it reflects from the target, and returns to the receiver. The transmitted sound is attenuated by TL on the outbound leg, the target reflects with strength TS, and the return leg attenuates by another TL. Highlighting the difference from the passive equation:

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

Compared to the passive equation, the only changes are that −TL becomes −2TL, and a new term TS for the target's reflective characteristics is added. Since 2TL dominates as range grows, the differential reading shows directly why active SNR drops sharply at long range.

Typical SL value ranges

SL (Source Level) varies widely with the device or target. As a guide for the values used in the exercises:

• Passive SL (target's radiated source level): small craft 140–160 dB re 1 µPa @ 1 m; merchant or large naval vessels 170–190 dB re 1 µPa @ 1 m. The SL = 165 dB used in passive exercises corresponds to a representative merchant ship.
• Active SL (transmitted source level): portable echo sounders 180–200 dB re 1 µPa @ 1 m; large hull-mounted sonars or low-frequency ASW sonars can exceed 220 dB re 1 µPa @ 1 m. The SL = 210 dB used in active exercises corresponds to a mid-to-large sonar.

All dB values are referenced to re 1 µPa @ 1 m (reference pressure 1 µPa, reference distance 1 m).

The role of TS

Target Strength (TS) measures how strongly a target backscatters sound. A large, flat metal surface reflects very differently from a slender, compliant structure. For an introductory picture, "bigger TS means the echo is easier to pick up" is enough.

We only use the simplified equations here, and we set aside multipath, reverberation, refraction, and boundary scattering that matter in real environments. The goal is to build a first-order dB intuition.

Takeaways from this chapter

• Read TL as the approximate sum of spreading and absorption.
• Higher frequencies absorb more and tend to be at a disadvantage at long range.
• Passive and active SNR can both be read as addition and subtraction in dB.