Day 49: Speed of Sound & Refraction – Masterpiece Edition | River Warrior

🔊 DAY 49: SPEED OF SOUND & REFRACTION

⏱️ Estimated Reading Time: 15 Minutes | 🎓 Level: Professional Hydrographer / Acoustic Specialist

Why Sound Bends – The Physics Behind Ray‑Bending and SVP Corrections

Instructor: Engr. Rokib Hossain | River Warrior Academy

🏠 Course Homepage

📖 Table of Contents (Serialised)

Why Speed of Sound Is Not Constant
Physics of Sound Velocity (Chen‑Millero)
Sound Velocity Profile (SVP) and Its Measurement
Refraction and Ray‑Bending (Snell’s Law)
Interactive Ray‑Bending Simulator
Consequences of Ignoring Refraction
Applying SVP Correction in MBES
Case Study: Jamuna River Thermocline
SVP & Refraction Correction Checklist
Resources & References
Frequently Asked Questions
Action Items & Next Steps

1. Why Speed of Sound Is Not Constant

Echosounders calculate depth using the travel time of an acoustic pulse and an assumed sound velocity (often 1500 m/s). However, the actual speed of sound in water varies with temperature, salinity, and pressure (depth). Using a wrong velocity leads to depth errors and, for multibeam, refraction artefacts (“smile” or “frown”).

🧠 Golden Rule: A 1% error in sound velocity = 1% error in depth. For 20 m depth, that’s 0.2 m – enough to fail IHO Order 1a in shallow water.

🌊 River Warrior Pro-Tip: Jamuna SVP Lesson

During a monsoon survey, the surface water was warm (30°C) and bottom water cold (24°C). Without a correct SVP, our MBES outer beams showed a 0.35 m “smile”. A fresh SVP cast fixed the error instantly. Rule: cast SVP every 2‑4 hours in stratified waters.

2. Physics of Sound Velocity (Chen‑Millero)

The accurate formula for sound speed in seawater is complex, but the simplified Chen‑Millero equation (UNESCO) is:

c = 1449.2 + 4.6T – 0.055T² + 0.00029T³ + (1.34 – 0.01T)(S – 35) + 0.016D

Where:

T = temperature (°C)
S = salinity (PSU; typically 30‑35 for oceans, 0‑5 for rivers)
D = depth (m) – pressure effect

In fresh water (salinity ≈ 0), the equation reduces to a temperature‑dependent approximation. For most rivers, ignoring salinity gives a small error (<0.5 m/s).

Linear increase of sound velocity with temperature (approx).

3. Sound Velocity Profile (SVP) and Its Measurement

An SVP records sound velocity vs depth. It is measured with a dedicated profiler (e.g., AML, Valeport) or a CTD (Conductivity, Temperature, Depth). Casting procedures:

Deploy probe at slow, constant rate (0.5‑1 m/s).
Record from surface to near bottom (or max survey depth).
For shallow rivers (<10 m), a single mid‑depth measurement may suffice, but full profile is better.

📌 In tidal rivers, cast SVP at every tide change (approx every 3 hours) because salinity and temperature vary.

4. Refraction and Ray‑Bending (Snell’s Law)

As sound passes through layers of different velocity, the ray bends according to Snell’s Law:

sin θ₁ / c₁ = sin θ₂ / c₂ = constant

For multibeam, the outer beams are most affected – without correction, the seabed appears “smeared” or distorted (smile/frown). Modern MBES software applies ray‑bending using the SVP.

📐 Interactive Ray‑Bending Simulator

Simulate the effect of a thermocline on an outer beam (30° from nadir).

Surface sound velocity (m/s): Bottom sound velocity (m/s): Water depth (m):

Horizontal error without correction: 0.00 m

For a beam at 30° from vertical, with linear velocity gradient. Actual error depends on profile.

5. Consequences of Ignoring Refraction

Smile/frown artefacts: Outer beams show incorrect depths, creating false ridges or troughs.
Horizontal misposition: Features (wrecks, rocks) are shifted laterally by metres.
Cross‑line mismatch: Differences between lines run in opposite directions.
Non‑IHO compliance: Depth errors exceed tolerance.

💡 In a 30 m depth with a 1% gradient error, the outer beam (60° from vertical) can be mispositioned by >5 m.

6. Applying SVP Correction in MBES

Acquisition software (Hypack, QINSy, PDS) imports the SVP file and applies ray‑bending in real time (or during post‑processing). Steps:

Cast SVP and save as .svp, .asvp, or .csv.
Load SVP into software.
Enable “Ray‑bending” or “Refraction correction”.
Set number of layers (use 1 m vertical resolution).
Verify corrected depth on a test line.

✅ Always check that the SVP covers the full depth range of your survey. Extrapolation beyond the measured depth is unsafe.

7. Case Study: Jamuna River Thermocline Effect

Situation: Post‑monsoon survey, strong vertical temperature gradient: 28°C at surface, 22°C at 10 m depth. SVP not cast for 6 hours.

MBES recorded a 0.4 m “smile” in outer beams.
Cross‑line standard deviation = 0.28 m (Order 1a requires <0.15 m).
Fix: Fresh SVP cast (using Valeport MiniSVP). Refraction correction applied in Qimera.
After correction: smile disappeared, cross‑line std = 0.09 m → compliant.

🌊 Lesson: In rivers with thermal stratification, cast SVP at least every 2 hours. A 1°C change over 5 m depth can cause noticeable refraction.

8. SVP & Refraction Correction Checklist

SVP cast performed at start of survey (and every 2‑4 hours).
SVP covers full depth range (extend 10% beyond max depth).
SVP file loaded into acquisition software.
Ray‑bending / refraction correction enabled.
Test line run over flat area – check for smile/frown.
Surface sound velocity sensor (SVS) also calibrated.
If using CTD, compute SVP from T,S,P using UNESCO formula.
Cross‑line differences re‑checked after SVP application.
SVP file name and cast time logged in survey metadata.

Click items to track progress (saved in browser).

9. Resources & References

.htmlValeport SVP Guide那样Instrument operation那样Valeport.htmlNOAA SVP Best Practices那样Field procedures那样NOAA PDF.htmlQPS Qimera SVP Manager那样Import and apply SVP那样qps.nl/qimera

Resource	Purpose	Link
UNESCO Sound Speed Calculator那样Online c(T,S,D) calculator那样Visit

10. Frequently Asked Questions

How often should I cast an SVP in a tidal estuary?

Every 2‑3 hours, because salinity and temperature change with tide. Cast more often during flood/ebb transitions.

What is the difference between SVP and CTD?

SVP measures sound velocity directly (time‑of‑flight). CTD measures conductivity, temperature, depth, then calculates sound velocity. Both are acceptable; CTD also provides salinity.

Can I use a single surface sound velocity (SVS) for shallow water?

For depths <5 m and uniform temperature, a surface SVS may suffice. For deeper or stratified waters, a full SVP is essential.

Why does my MBES show smile/frown even after applying SVP?

Possible causes: incorrect SVP (outdated or wrong location), improper patch test, or motion sensor misalignment. Re‑cast SVP and check roll calibration.

What is the typical sound velocity in fresh river water?

At 25°C, fresh water c ≈ 1497 m/s; at 15°C, c ≈ 1473 m/s. Salinity adds ~1.4 m/s per PSU.

11. Action Items & Next Steps

📌 Use the UNESCO online calculator to compute c for T=20°C, S=0, Depth=10 m.
📌 Play with the ray‑bending simulator: change surface and bottom velocities and observe the horizontal error.
📌 If you have an SVP file, import it into your processing software and verify the correction.
📌 Proceed to Day 50: Midway Milestone & Review.

🌊 Day 49: Speed of Sound and Refraction Error Management