Bathyswath accuracy (error budget)

Context

When planning a survey, consideration must be given to the accuracy required. Bathyswath is essentially an angle-measuring instrument, so that depth accuracy reduces with horizontal range. The angular accuracy of both the Bathyswath sonar and commonly available MRUs is better than 0.05 degrees. The accuracy of the combined system is thus better than 0.1 degrees. The maximum range required for a given depth accuracy can easily be calculated. One accuracy specification is that of the International Hydrographic Organisation (IHO) S44 specification. Bathyswath has been used, and quality checked, in surveys at all IHO S44 accuracy orders, including Special Order. This section considers the accuracy and resolution of Bathyswath; these two parameters are closely related, and can be selected for, against each other, using statistical methods in data processing. It is derived from a model of the accuracy of Bathyswath, related to resolution. This model has been validated using data collected and published for the 2008 Shallow Survey conference. Bathyswath can output pulses down to 2 cycles (A single-wavelength pulse will not have sufficient transfer efficiency into the water), so the physical limit of measurement resolution is as per the following table.

 

117 kHz

234 kHz

468 kHz

Actual Frequency(1)

117.1875 kHz

234.3750 kHz

468.7500 kHz

Divisor (1) – f

512 (or 29)

256 (or 28)

128 (or 27)

Period

T=1.f-1

8.55 μs

4.27 μs

2.14 μs

Wavelength

λ=c.T

12 mm

6 mm

3 mm

Resolution detection limit(2)

½.λ – Half wavelength

6 mm

3 mm

1.5 mm

Min. pulse time

2 cycles = 2.T

17.09 μs

8.55 μs

4.27 μs

Max. pulse time

1000 cycles = 1000.T

8.55 ms

4.27 ms

2.14 ms

Pulse length

2. λ

2.5 cm

1.2 cm

0.6 cm

Measurement resolution limit(3)

½ pulse length

1.2 cm

0.6 cm

0.3 cm

Resolution Across Track

7.5 cm

5cm

3cm

Beam Width, Azimuth

1.7°

1.1°

1.1°

Beam Width, Azimuth (2-way)

0.85°

0.55°

0.55°

Transmit Pulse Length

17µs to 1 ms

8.5µs to 500µs

4.3µs to 250µs

Source level

1μPa @ 1m

224 dB

220 dB

222 dB

(1)    Bathyswath is a single frequency (also known as Continuous Wave – CW) system; the sonar frequency is built into the electronics systems. The frequencies are derived by dividing a 60 MHz base frequency in powers of two (i.e. 60000 kHz / 29 = 117.1875 kHz)

(2)    Any sonar system can detect objects that are larger than half of its wavelength. The limit to measurement resolution is determined by the sonar pulse:

Where

c              is the speed of sound

τ              is the pulse time

c.τ           is the pulse length in meters

β             is the grazing angle. In the best case, cosβ is 1

 

(3)    These are theoretical values, but practically there is no way any sonar could tell the difference between a seabed at 20.000 metres and another one at 20.003m.

Sampling

The software allows the user to select between 28 to (215 + 214) samples

For a 234 kHz system, at 50m with 4096 samples, we get 12 mm sample interval (so 6 mm at 8192, 3mm at 16384 and 2mm at 24576; halve these values for a 468 kHz system).

However, getting a very low interval by collecting huge amounts of data is meaningless and would in some cases reach USB buffer limits

Filtering, Accuracy and Resolution

Interferometric swath bathymetry systems give many data points per side, typically 2000 to 8000. However, the spread (standard deviation) of raw data points is usually greater than that of beam-forming multibeams, which typically produce 100 – 200 points per side.

Software filtering can be used to reduce this standard deviation to internationally acceptable survey limits. However, this filtering also reduces the resolution of the filtered data.

The International Hydrographic Organisation (IHO) Special Publication number 44 sets out standards for both accuracy (termed “uncertainty”) and resolution. These are defined in a set of “Orders”, of which “Special Order” is the most stringent, followed by Order 1.

Accuracy is specified in terms of the depth uncertainty to 95% confidence.

Resolution is specified in terms of the size of objects that must be detected, and the number of acceptable data points per square meter.

Beam Width, Azimuth

The beam width of the transmit and receive elements of Bathyswath, for the three sonar frequencies available, is given in "Beam Width, Azimuth" in the table below. These figures are for both the transmit and receive elements. The effective width of the sonar “footprint” on the seabed is found by combining the “footprint” of both the transmit and receive staves, which is done by halving the beam width of the separate staves, to get a “two-way” azimuth angle.

 

117 kHz

234 kHz

468 kHz

Beam Width, Azimuth

1.7°

1.1°

1.1°

Beam Width, Azimuth (2-way)

0.85°

0.55°

0.55°

Azimuth Angle (Stave and 2-way Footprint)