Question 3 of 5: Single-Beam Echo-Sounding in Suspended Sediment

Question 3: Single-Beam Echo-Sounding in Suspended Sediment (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Frequency choice and instruments. In water carrying suspended sediment (fluid mud / fluff) the problem is that a single high frequency stops at the top of the suspended layer, while navigation needs the true consolidated bottom — so you choose a dual-frequency sounder and operate a high and a low channel together: a high frequency (~200 kHz, range ~100–210 kHz) that reflects off the top of the suspended-sediment / fluff layer, and a low frequency (~24 kHz, range ~12–50 kHz) that penetrates the fluid mud and returns from the hard, navigable bottom. The difference between the two traces maps the suspended layer thickness. Low frequency is chosen for penetration because acoustic absorption in water and sediment rises steeply with frequency; high frequency is kept for a sharp, well-defined top-of-layer and a narrow beam.

Three single-beam echo-sounders suitable for this dual-frequency work: Odom Echotrac CV100 / MkIII (dual-frequency), Kongsberg (Simrad) EA400/EA440 dual-frequency survey sounder, and Knudsen 320M dual-frequency sounder (the Teledyne Reson NaviSound 210 dual-frequency is an equally acceptable fourth example; a single-frequency unit such as the Odom Hydrotrac II is not suitable here, because it cannot record the high and low returns together).

(b) Calibrating the echo-sounder — the bar-check. The classic field calibration is the bar-check (and, complementarily, a sound-velocity profile). A metal plate or bar is lowered beneath the transducer on graduated lines to a sequence of known depths (e.g. 2, 5, 10, 15 m). At each depth the operator adjusts the sounder's assumed sound speed and the transducer-draft index so the displayed depth equals the true lowered depth. This ties the instrument to the actual mean sound speed of the water column and fixes the draft/index constant in one operation.

Given. An assumed sound speed $v=1500\ \text{m/s}$, a measured round-trip time $t=0.0200\ \text{s}$, and a sound-speed uncertainty $\Delta v=30\ \text{m/s}$. Find. the indicated depth and, in part (c), the depth error the sound-speed uncertainty produces. The physical basis is the two-way travel-time relation:

1. Depth from travel time. $$d=\tfrac{1}{2}\,v\,t$$ With an assumed $v=1500\ \text{m/s}$ and a measured round-trip $t=0.0200\ \text{s}$, $$d=\tfrac12(1500)(0.0200)=\boxed{15.0\ \text{m}}$$ The bar-check forces this computed $d$ to match the true 15.0 m by tuning $v$, thereby absorbing the real column sound speed. A CTD / sound-velocity probe (a Valeport or similar cast) gives the same information as a measured profile for beam ray-tracing.

(c) Error sources, limitations, and remedies.

• Sound-speed error — the dominant systematic error. Because $d=\tfrac12 v t$, a fractional sound-speed error maps one-for-one into depth: $\dfrac{\Delta d}{d}=\dfrac{\Delta v}{v}$. A $\Delta v=30\ \text{m/s}$ mis-assumption gives $\tfrac{30}{1500}=2.0\%$, i.e. $\boxed{0.30\ \text{m}}$ at 15 m. Remedy: bar-check and/or measure a sound-velocity profile and re-reduce.
• Ambiguous bottom in suspended sediment — a single frequency picks the wrong interface (fluff vs. hard bottom). Remedy: dual frequency (above), and where the "nautical bottom" must be defined in fluid mud, a tuning-fork/rheology density criterion (e.g. the 1200 kg/m³ isopycnal) is surveyed instead.
• Transducer draft, squat and settlement, and heave — change the true transducer depth. Remedy: measure static draft, apply a squat/settlement correction (or GNSS height as in Q2), and use a heave compensator/filter.
• Beam width and slope — a finite beam on a slope returns the shoalest point in the footprint, biasing depth shallow. Remedy: narrow beam, run lines along-slope, and correct for slope.
• Tide reduction error, aeration/entrained air, and vegetation — wrong water-level model, or bubble/weed false echoes. Remedies: proper tide zoning or GNSS-tide; avoid aerated wakes; gain/threshold tuning and manual editing.

Most of these are correctable in the field (bar-check, SVP, dual frequency, heave/draft/tide corrections) or in post-processing; the irreducible limitation is defining "the bottom" itself where the sediment is a continuous density gradient rather than a sharp interface.