Question 4 of 5: The Multibeam Patch Test

Question 4: The Multibeam Patch Test (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.

The patch test determines the angular boresight misalignments between the multibeam transducer and the motion/heading reference (roll, pitch, yaw) plus the positioning latency. Each bias is isolated by running a dedicated line pattern over chosen bottom relief and adjusting the corresponding offset until the two swaths agree. The tests are solved in dependency order: latency first (its along-track shift would otherwise be absorbed into the pitch estimate), then roll and pitch (roll, measured on a flat bottom, is decoupled from the along-track pair, so many procedures take pitch before roll and others roll before pitch), and yaw last, because outer-beam feature positions depend on the roll and pitch corrections. Latency → roll → pitch → yaw is used below. The four sub-parts below are given in the question's order.

(a) Pitch bias. Pitch misalignment tilts the swath fore-and-aft, so a feature is placed too far ahead of or behind its true position along-track. Method: run the same line in opposite directions (reciprocal) at the same speed over a distinct slope or an isolated feature (a ridge, a wreck, a seabed step). A pitch bias shifts the imaged slope/feature along-track in opposite directions on the two runs; the pitch offset is adjusted until the feature falls at the same along-track position (the two profiles coincide). Pitch bias mainly affects the nadir/central beams, so a slope viewed near nadir is the sensitive geometry.

(b) Time offset (latency). Positioning latency is a time lag between the GNSS position and the sounding, so the whole swath is displaced along-track by an amount proportional to speed. Method: run the same line, same direction, over a slope or feature, at two different speeds (e.g. a slow and a fast pass). A latency error shifts the feature along-track by a distance that scales with speed, so the two passes disagree; the time offset is adjusted until the feature coincides on both the slow and fast lines. (Running reciprocal lines at one speed is avoided for latency because it is then confounded with pitch.)

(c) Roll bias. A roll misalignment rotates the whole swath about the fore-aft axis, tipping the seafloor athwartships: a flat bottom appears to slope across-track, and the apparent slope reverses sign when the vessel runs the line the other way. Method: run reciprocal lines over a flat, featureless bottom. Overlay the two athwartships profiles; a roll bias makes them "rock" — cross like a shallow X — and the roll offset is adjusted until the flat bottom reads flat and the two profiles are horizontal and coincident. Roll bias is the largest error at the swath outer beams, so a wide flat swath is the sensitive geometry.

(d) Heading (yaw) bias. A yaw misalignment rotates the swath in plan about the vertical axis, so a sounding at across-track distance $y$ is displaced along-track by about $y\,\delta\psi$ — an error that grows toward the swath ends and is zero at nadir. Method: run two adjacent, overlapping lines in the same direction (offset so a distinct feature — a wreck, a small mound — is seen on the outer beams of each swath). Because the feature lies on the starboard side of one swath and the port side of the other, a yaw bias displaces it along-track in opposite directions on the two lines; the heading offset is adjusted until the feature's position agrees between the two swaths. The outer-beam, adjacent-line geometry maximises sensitivity to yaw.