Marine Survey & Sonar Physics

The Acoustic Channel: Why Sound Over Light?

Electromagnetic signals in water — including light and radio waves — attenuate exponentially with depth. A blue-green laser (the optimal frequency for seawater) loses 90% of its power within approximately 100 meters. Sound, by contrast, can travel thousands of kilometers through the ocean due to the high acoustic impedance and low absorption of water at sonar frequencies.

Sound Propagation in Seawater

The speed of sound in seawater is not constant; it is a function of temperature, salinity, and depth. The empirical Medwin equation provides a practical approximation:

c = 1449.2 + 4.6T - 0.055T^2 + 0.00029T^3 + (1.34 - 0.01T)(S-35) + 0.016D

Where $T$ is temperature (┬░C), $S$ is salinity (PSU), and $D$ is depth (m). Typical shallow water values are approximately 1500 m/s; deep ocean varies from 1450•ô1550 m/s across depth layers.

The variation in sound speed with depth creates a phenomenon called acoustic refraction — sound rays bend toward regions of lower velocity. This forms the SOFAR Channel (Sound Fixing and Ranging) at approximately 700•ô1200m depth, where sound is naturally trapped and can propagate thousands of kilometers with minimal loss. The exact depth changes with ocean conditions.

Multibeam Echosounder (MBES) Geometry

A single-beam sonar measures depth at one point directly below the vessel. A multibeam echosounder transmits a fan of acoustic beams simultaneously, covering a swath width typically 3•ô7 times the water depth. This allows a vessel to map large areas efficiently in a single pass.

Sonar Pulse Mechanics

Acoustic transit time to depth conversion (c ≈ 1500 m/s)

Approx. 150m

Transit Time (\u0394t)

---ms

Calculated Depth (D)

---m

D = (c × \u0394t) / 2 where c ≈ 1500 m/s

Sound Velocity Profile (SVP) Corrections

Because the speed of sound changes with depth (and thus with the acoustic path), accurate bathymetry requires a real-time Sound Velocity Profile (SVP). Without SVP correction, the beamformer uses an incorrect velocity, causing the outer beams to be mapped at the wrong position and depth — a systematic error called refraction smiling (the outer-swath bathymetry curves upward like a smile).

SVPs are measured using a Conductivity-Temperature-Depth (CTD) sensor cast to the seabed before each survey line, or at regular intervals when conditions are dynamic. The water column model is then loaded into the MBES processing software for real-time ray-bending correction.

Sub-Bottom Profiling (SBP)

Multibeam sonar maps the surface of the seabed. Sub-bottom profilers penetrate below the seabed to image geological layering — sediment thickness, buried features, and geohazards. They operate at lower frequencies (typically 2•ô15 kHz compared to multibeam at 200•ô400 kHz) to achieve greater penetration.

Underwater Positioning: USBL vs. LBL

GPS signals do not penetrate water. Positioning ROVs, AUVs, and seabed equipment requires acoustic positioning systems:

USBL (Ultra-Short Baseline)

A single transducer head with multiple elements measures the angle and range to a subsea transponder. Accuracy is typically 0.5•ô1% of slant range. Simple to deploy but position error grows with depth and range.

LBL (Long Baseline)

Multiple seabed transponders form a calibrated acoustic baseline array. Position is computed by trilateration. Achieves 0.1•ô0.3m accuracy independent of water depth. Used for deep-water pipeline and well head work.

Vessel Data Network Architecture

A modern survey vessel is a floating data center. The MBES alone can generate 50•ô200 MB/s of raw backscatter data. Combined with SBP, USBL, motion reference units (MRUs), and GNSS systems, the total data throughput requires a dedicated vessel LAN architecture with timestamping accuracy in the microsecond range.

Conclusion

Marine surveying is the engineering discipline at the intersection of acoustics, oceanography, hydrodynamics, and geomatics. Every depth measurement is a calculation — sound travel time multiplied by sound speed, corrected for water column variability, vessel motion, and timing precision. The ocean is not a passive medium; it is a dynamic, refracting, absorbing channel that must be actively characterized to produce data that meets the centimetric accuracy standards of modern hydrographic survey.

Engineering Knowledge Expansion

Optical

Side-Scan Sonar and Synthetic Aperture Sonar

While multibeam echosounders measure bathymetry (depth), side-scan sonar produces acoustic imagery of the seabed. A side-scan towfish (or hull-mounted transducer) emits a narrow fan-shaped pulse to either side of the vessel's track. The intensity of the backscattered return is recorded as a function of time (range), producing a two-dimensional "acoustic photograph" of the seafloor. Hard, rough surfaces like rock or shipwrecks produce strong returns (high backscatter, appearing as bright areas), while soft, smooth surfaces like mud or sand produce weak returns (dark areas). The shadows behind elevated objects are diagnostically critical — they reveal object height and shape through the geometry of the acoustic shadow zone.

The resolution of a side-scan system is fundamentally limited by the acoustic footprint of the transducer. For a given pulse length $\tau$ and range $R$ , the along-track resolution degrades as the beam spreads with range. At near range, resolution may be centimeter-scale; at the maximum range of 500 meters, it may degrade to several meters. This is where Synthetic Aperture Sonar (SAS) provides a revolutionary improvement.

Motion compensation is the most challenging aspect of SAS processing. The towfish position must be known with sub-wavelength accuracy (better than $\lambda/4$ , or approximately 1.25 mm at 300 kHz) for coherent summation to work. This requires a tightly coupled inertial navigation system (INS) with Doppler velocity log (DVL) aiding, updated at 200 Hz or higher. Any uncompensated yaw or heave motion introduces phase errors that defocus the SAS image, creating the characteristic "smearing" artifact that SAS processors must detect and correct through contrast-optimization autofocus techniques.

\delta_{along} = \frac{\lambda R}{2L_{synthetic}} = \frac{\lambda}{2\theta_{synthetic}}

The along-track resolution of a SAS system, where $L_{synthetic}$ is the length of the synthesized aperture and $\theta_{synthetic}$ is the synthetic beamwidth.

Acoustic Noise Budgeting and Signal Processing

The performance of any sonar system is fundamentally limited by the acoustic noise budget. The sonar equation, which relates the source level (SL), transmission loss (TL), target strength (TS), and noise level (NL), determines whether a signal is detectable above the ambient acoustic background:

SL - 2TL + TS - (NL - DI) = SNR_{detection}

The active sonar equation. The detection SNR must exceed the receiver's detection threshold (typically 6–12 dB depending on the required probability of detection and false alarm rate).

Ambient noise in the ocean has multiple components. At sonar frequencies (1–500 kHz), the dominant noise sources are wind and wave action (Knudsen spectra), biological sources (snapping shrimp, which can produce broadband pulses exceeding 180 dB re 1 μPa at 1 meter), and vessel self-noise from propulsion and auxiliary machinery. A survey vessel must characterize its own noise signature through a self-noise survey before commencing operations, identifying frequency bands where propeller cavitation, thruster noise, or generator harmonics contaminate the sonar bandwidth.

In the digital signal processing chain, the raw acoustic data flows through several stages: (1) beamforming — applying time delays to each transducer element to steer and focus the receive beams; (2) match filter correlation — pulse compression using fast convolution in the frequency domain; (3) envelope detection — extracting the magnitude of the analytic signal via Hilbert transform; and (4) time-varying gain (TVG) — applying a range- dependent gain ramp to compensate for spherical spreading and absorption losses. The TVG law typically follows a $20\log_{10}(R) + 2\alpha R$ curve, where $\alpha$ is the absorption coefficient in dB/km. At 200 kHz, $\alpha$ is approximately $50\,\text{dB/km}$ , making TVG correction a dominant factor in the dynamic range of the receiver.

The ultimate limiting factor in sonar signal processing is often not the noise floor, but the reverberation level. Reverberation is the cumulative backscatter from the water column (volume reverberation from suspended particles and biologics) and from the sea surface and seabed (boundary reverberation). Unlike ambient noise, reverberation is directly proportional to the source level — increasing transmit power cannot improve the signal-to-reverberation ratio. This is the acoustic analogue of the nonlinear Shannon limit in optical fiber, and it sets the fundamental ceiling on sonar detection range.