Mapping the seabed

A simulated study: an image of the seabed, from a single beam of sound.

  • Acoustics

2020, finished in 2026

How to draw from a single-beam sonar the most faithful image of a seabed, and read its relief and its nature? Another TIPE subject, considered in the preparatory classes in 2020, on the same “Ocean” theme: little explored then, with a few devices drawn to aim the transducer.

In 2026 I decided to see it through, as a study and a simulation: a transducer fixed in a sealed sphere turned by three wheels, an inertial unit to know where the beam points, a line-by-line sweep, and the image rebuilt sharper than the beam, by deconvolution. The piloting program is written, the code of the two boards too; the whole drives a simulated rig, over a simulated 50 × 50 cm bed. A 58-page report accounts for it, to read from this page.

Nothing is built yet: every result on this page is a simulation, and the report says so.

Read the report

Isometric drawing of a tank whose floor reproduces a relief. Above it, an immersed sphere held by a cradle with three wheels, with a beam leaving it towards the floor. By step: the relief to map; the pulse and the echo; the sphere in section, with the transducer and the wheels set 35° from the pole; the same section, with the inertial unit at the centre and the beam’s direction; the sweep line by line; the lateral and axial resolution; the floor divided into cells of four types, and the sphere’s five positions.
Thousands of thin orange lines leave a small circle, the sphere, and fan down to a cloud of black dots that draws a seabed in relief, in perspective.
A contour map in black ink, one contour in four in orange, over a fine grid: a mound, rocks, a diagonal channel, a pipe and a wreck show where the contours crowd.
The same seabed drawn as stacked black profiles, like ridge lines, two of them in orange: the mound, the wreck and the channel show in the shapes of the lines.
Two bands side by side, in shades of orange on paper: on the left, broad blurred patches in the shape of an arch; on the right, the same arch made of thin, sharp strokes.
A wide orange band streaked with thin vertical teeth, drawing an arch: each column is the echo of one pulse.
Section of the tank to scale: the 10 cm sphere in its cradle, 40 cm above a seabed in relief, its beam reaching the bed, and the cable linking the cradle to a computer.

What was done

  1. 01

    The simulation of the bed and the echoes

    A relief on a 2 mm grid with four bed types, and for each pulse the synthesised echo: the transducer’s directivity, the sonar equation, backscatter against the angle, speckle noise.

    Python · NumPy · SciPy

  2. 02

    The sphere and its cradle

    The device’s geometry: the three wheels 35.26° from the pole for perpendicular axles, the buoyancy that presses the sphere against them, the transmissible torques, the magnetic couplings.

  3. 03

    The piloting

    The line-by-line sweep, the 100 Hz control and the orientation estimate from the inertial unit, with the reset at every stop; one program for the simulated rig and the real one.

    Python

  4. 04

    Electronics and firmware

    The transmit and receive chain, and the code of two boards: one in the sphere, for the pulse, the echo’s digitisation, the inertial unit and the optical link; the other on the cradle, for the motors. Never compiled for the boards: only the shared part is tested on a computer.

    C++ · Raspberry Pi Pico

  5. 05

    Imaging and classification

    The relief from the echoes’ barycentre, then by deconvolution over angles and range; the bed’s nature cell by cell, from five positions.

    Python · Richardson–Lucy

  6. 06

    The report

    Fifty-eight pages, begun in 2020 and finished in 2026, with the programs in the appendix and twenty-one tests that check the physics and the system.

    LaTeX · unittest

Isometric drawing of a tank whose floor reproduces a relief. Above it, an immersed sphere held by a cradle with three wheels, with a beam leaving it towards the floor. By step: the relief to map; the pulse and the echo; the sphere in section, with the transducer and the wheels set 35° from the pole; the same section, with the inertial unit at the centre and the beam’s direction; the sweep line by line; the lateral and axial resolution; the floor divided into cells of four types, and the sphere’s five positions.

How it works

  1. Scroll: the drawing follows.

  2. 01 / 07

    Mapping a seabed with a single beam

    Draw from a single-beam sonar the most faithful image of a seabed, and read its relief and its nature. The bed is simulated, 50 × 50 cm: a mound, a hollow, sand ripples, a silted channel, five rocks, a buried pipe, a wreck, over four bed types, sand, gravel, mud and rock. Nothing is built: everything here is simulated.

  3. 02 / 07

    Send a pulse, wait for the echo

    A 12.7 mm piezoelectric disc emits five periods near 1 MHz, then listens. The time the echo takes to come back gives the distance, in the beam’s direction, seven degrees wide: at 35 cm it lights a spot of four centimetres. The shape and strength of the echo also tell what the bed is made of: seen obliquely, mud returns twenty to thirty decibels less than rock.

  4. 03 / 07

    A sphere turned by three wheels

    The transducer is glued at the south pole of a sealed 10 cm sphere, immersed. Its buoyancy presses it against three omnidirectional wheels, set 35° from the pole so that their axles are perpendicular, like the three edges of a cube’s corner; each motor, in its sealed box, drives it through a magnetic coupling. Every beam leaves from its centre, which never moves.

  5. 04 / 07

    Know where the beam points

    An inertial unit at the sphere’s centre gives its orientation, two hundred times a second. Every time the three motors stop, the drift of its gyros is measured again. A board inside the sphere times the pulse, digitises the echo and talks to the cradle through an optical link across the wall; a second one, on the cradle, drives the motors. In simulation, the aim is off by 0.22° on average.

  6. 05 / 07

    Sweep the bed, line by line

    The sphere sweeps a ±38° square, line by line, back and forth, one pulse per degree: 8,333 pulses in 166 seconds. The piloting program is the real one; here it drives a simulated rig, with its slips, its delays and its lost messages.

  7. 06 / 07

    Rebuild the relief, sharper than the beam

    The beam blurs the bed, like a photograph out of focus: each point is seen by about twenty pulses. The classical method places the barycentre of each echo on the beam’s axis and strays from the true relief by 9.8 mm; by treating all the pulses together, through deconvolution over angles and range, the error drops to 7.5 mm, in simulation.

  8. 07 / 07

    Recognise the bed’s nature

    The echo’s strength against the viewing angle betrays the bed. From five positions of the sphere, each three-centimetre cell is compared with the curves of the four types, and gets the nearest: 64 % of cells right on average, against 25 % by chance. Reliable at the scale of zones, not of the spot.

Specifications

Date
2020, finished in 2026
Context
A personal scientific project, begun in preparatory classes as a TIPE research project, that I wanted to carry on and finish.
Built with
Python (NumPy, SciPy, Matplotlib) · C++ for Raspberry Pi Pico · LaTeX