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| Miniature Time of Flight Sound Velocimeter Offers Increased Accuracy over Sing-Around Technology and CTD Instrumentation
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ABSTRACT
Increasing demands for high accuracy sound speed data has prompted the development of a next generation sound velocimeter, which overcomes some of the inherent problems associated with the sing-around technique in use since the early 1950's. The authors show short path length sing-around techniques cannot achieve accuracies better than 0.25 m/s due in part to phase errors introduced from multiple reflections and by thickness / radial mode ringing of the transducer element(s). Overall, accuracies reported thus far on the new velocimeter are better than 0.06 m/s r.m.s. with respect to Del Grosso and Mader's pure water equation. Comparisons between sound speed equations incorporating pressure and salinity terms show significant deviations in excess of the accuracy capabilities of the new technology. This accuracy level places considerable constraints on calibration technique and highlights the requirement for a universally accepted sound speed standard.
BACKGROUND
Sound speed data can be collected in the field by any one of the following techniques:
1) Calculated from expendable bathythermograph (XBT) data using one of the sound speed equations and a single salinity estimate
2) Sound speed calculated from CTD data using one of several sound speed equations
3) Direct sound speed measurement using the sing-around approach
All three of these techniques exhibit errors preventing accuracies better than 0.25 m/s. The first two techniques suffer from errors in pressure, salinity and temperature measurement in addition to the errors associated with the equations used to convert these parameters to sound speed. Errors in collecting the data include the accuracy of each of the pressure, temperature, and conductivity sensors; differences in sensor response times; sensor hysteresis; inadequate flow through the sensors, and the thermal mass of the sensors and surrounding hardware. Errors associated with the sound speed equation(s) used can be significant, even if care is exercised in choosing the most applicable equation for the water being sampled.1 Differences between calculated sound velocities using the two most widely accepted sound speed equations (Chen and Millero, Del Grosso and Mader) can be as high as 0.3 m/s. Without due care in the design, calibration, and deployment of the CTD and improper choice of equation, sound speed errors in excess of 2 m/s can be realised. With proper care, the errors can be reduced to about 0.25 m/s.
The direct measurement sing-around (hereby referred to as SA) sound velocimeters also have a significant number of inherent errors. These include, transducer ringing (both radial and thickness mode) summing with the echo, multi-path reflections summing with the echo, inadequate or turbulent flow through the sensor, and temperature effects on the path length and electronics.
Proper design of the instrument can reduce many of these errors, however the ringing and multi-path problems associated with the SA technique limit the accuracy.
EVOLUTION OF THE NEW TECHNOLOGY
The project began by trying to improve the accuracy of an existing SA velocimeter from 0.25 m/s to 0.1 m/s or better. The first step in the design process was to improve the resolution of the SA sensor. Digitising errors were determined to be the most significant limitation on resolution and had to be reduced to less than 2 nanoseconds to meet the 0.02 m/s resolution objective for a 0.2 m path length SA sensor. (Sound speed resolution = PL/t1 - PL/t2, where PL = path length, t1 = transit time for an echo, and t2 = t1 + counter resolution). However, a 500 MHz or higher clock frequency has several significant disadvantages, namely, high power consumption, circuit complexity (ECL logic required), and EMF radiation. The digitising errors can be eliminated with the use of asynchronous circuits in both the SA sensor excitation loop and the pulse repetition rate timing circuit.
Several prototype SA sensors were constructed utilising conventional transducers and asynchronous circuitry. Lab testing of these prototypes showed that the 0.02 m/s resolution objective could be achieved, however accuracies better than 0.25 m/s could not be obtained. The 0.25 m/s error was a result of a step like function which showed up in all SA tests done. An error analysis revealed significant sources of error stemming from complex constructive and destructive interference patterns from repetitive echoes of both the transmitted pulses and the transducer ringing causing cyclic phase shifts to the primary echo. This is an important aspect to consider when dealing with SA sensors.
The level of interference is highly dependent on the transducer Q factor, pulse frequency, ringing frequencies, path length and acoustic attenuation within the water sample. In our tests (11 < Q < 80, path lengths of 0.1, 0.2 and 0.254 m, pulse frequency of 1.25 MHz, ringing frequencies of 1.25 MHz, 330 KHz and 210 KHz) this interference caused errors from 0.25 m/s to 1.6 m/s depending on the transducer assembly used. While the interference pattern varies with sound speed (and slightly with salinity, pressure and temperature due to attenuation effects) it is unique and fairly stable for each instrument. Unfortunately, the pattern is so complex that it is difficult to compensate for the pattern without using very high order calibration equations.
The order of the curve fit required is dependent on the ringing frequencies and the dynamic range of the velocimeter. If any of the ringing frequencies are less than 1 MHz, then ringing echo amplitude will vary with salinity and the sensor accuracy will therefore degrade as the instrument is used in water with salinity versus sound speed profiles differing from that used in the calibration.(2)
The 0.2 m/s limit is primarily due to the inability of the calibration to track the interference pattern. Since the interference patter is mainly a combination of the mechanical ringing of the transducer, the desired acoustic pulse, undesired multi-path echoes, and multiple reflections of these three acoustic waves, the interference pattern varies in both amplitude and phase with the sound speed of the water.
When profiling, SA sensors with long integration times will smooth out the step function so that it is not as apparent. However the errors are only masked and the long integration time has its own disadvantages, such as low pass filtering of the sound speed data and introducing a lag between the sound speed and depth data.
The second disadvantage the SA technique has is each new transmission lags the previous echo by an electronic time delay. This delay varies with circuit temperature (Dte) and not sound speed. For the 0.2 m path length SA sensor tests performed, this variation in electronic delay (Dte) resulted in sound speed errors of up to .07 m/s for a Dte of 10 ns and up to 0.34 m/s for a Dte of 50 ns. The magnitude of the phase shift due to Dte is a function of the te and echo frequency.
The two problems listed above can be reduced significantly be reducing the pulse repetition frequency allowing the ringing to subside and decreasing the ratio of time delay to acoustic transit time when dealing with SA technology. This can be accomplished in SA systems by increasing the path length. To avoid using a long path length, other techniques of measuring the sound speed were examined.
The second technique examined was a continuous wave, constant wavelength, variable frequency system based on phase locked loop technology. While this approach eliminated the electronic delay time as described in the SA approach, the phase errors associated with the phase detector and loop filter stability resulted in errors in excess of 1 m/s. This approach was therefore abandoned without extensive investigation.(3)
TIME OF FLIGHT APPROACH
A back to basics philosophy was taken for the third approach based on the simple c=PL/t relationship. A technique was developed to measure the transit time (t) of a single acoustic pulse traversing a path length (PL) of stable dimensions with respect to temperature and pressure. The major advantages of this approach are the elimination of the multiple echo errors, ringing echo errors and electronic time delay associated with the sing-around technique as well as improving sensor response time to <150 ms.
A 0.2 m path length was chosen for the prototypes to allow the transducer ringing to subside and the path was folded to reduce flow-induced errors. The stable path length was attained with a combination of Invar36Ô and T-316 stainless steel configured to provide opposing expansion characteristics in both length and rate of change. This resulted in a path length stable to within + 5.5 nm/oC. Over the temperature range of -2oC to 32oC the resulting maximum deviation in sound speed is + 0.0014 m/s.
The timing circuits were temperature compensated and capable of a 1.2 nanosecond resolution over the range of 129 ms giving the sensor 0.015 m/s resolution. Precision is + 2.4 ns (+ 0.027 m/s) over the temperature range of -2oC to 32oC.
LAB TESTING RESULTS
Calibration and testing of the prototype time of flight (hereby referred to as ToF) velocimeters was performed using a Hewlett Packard 2804A quartz thermometer, a Guildline 8400B laboratory salinometer, a Neslab PBC-2 heat exchanger, a Budenberg dead-weight tester, and a custom designed calibration bath.
Initial lab testing was performed using Chen and Millero's salt-water equation as the sound speed standard since this is the equation which has been accepted by UNESCO.(4) It was possible to fit the data at one salinity quite well however errors in excess of 0.25 m/s occurred at other salinities during the post calibrations. Examination of the Chen and Millero equation and several other salt-water equations show discrepancies between the estimations of sound speed for a given water sample. The two most accepted salt-water equations (Chen and Millero, Del Grosso(5) and Mader) show relative deviations up to 0.3 m/s. It quickly became apparent that the salt-water equations were unacceptable for calibrating the new velocimeter.
What is required is a universally accepted sound speed reference which is accurate to, 0.01 m/s. Since a practical sound speed standard which met our calibration criteria could not be found, we examined all the aqueous sound speed equations published for use as a reference. The only equation which had multiple independent validations of an accuracy, 0.05 m/s was Del Grosso and Mader's pure water equation.6,7,8 Del Grosso and Mader's work was also the only work in which the authors found no significant errors or omissions in the technique for gathering the raw data upon which the equation was based.
Since distilled water was to be used to calibrate the new velocimeters, it had to be determined if the calibration would still be valid when the velocimeters were used in salt-water. Waveform attenuation changes with variations in salinity and temperature. The salinity attenuation effects can be reduced by choosing a frequency of operation above 1 MHz.2 The temperature attenuation effect introduces a 1% change in the echo amplitude which resulted in a triggering error of 1.5 ns or the equivalent of a 0.017 m/s sound speed error. In addition, varying the salinity means a given sound speed can occur over a range of temperatures. This has two effects on the velocimeter, the path length must be stabilised over the temperature range, and the electronic circuitry requires stable time measurement characteristics throughout the temperature range.
The calibration technique is also quite involved to ensure that the 0.05 m/s accuracy of Del Grosso's equation is attained. The water sample must be maintained to <5 ppm total dissolved solids. In order to attain a sound speed range of 1400 to 1550 m/s the distilled water sample must be varied through a temperature range of 0oC to 59oC. The water in the bath must be well mixed and the velocimeter path length must be perpendicular to the water flow to prevent flow-induced noise. To ensure a homogeneous water sample three high-speed temperature sensors (+0.005oC accuracy, 10 ms response time) in addition to the HP 2804A temperature sensor, are spaced alongside the velocimeter path. Over the course of an eight-hour cycle, 750 to 1000 data points are collected for post processing. Care must be exercised to ensure dissolved gases do not form bubbles on the reflector plate and transducer assembly.(9)
Using Del Grosso and Mader's pure water equation limits the useful range of the sensor to 1400-1550 m/s. To extend the range to 1600 m/s or better, without the use of a sound speed standard, the sensor must be calibrated using one of the salt-water equations. As previously stated, the accuracy of these equations are suspect and therefore the accuracy of the calibration would degrade.
Mechanical ringing is still a problem with the new technique though not as significant as seen with the SA approach. Since the repetition rate with the ToF approach is very low there is no significant variation in the interference pattern with respect to the water sample before the arrival of the primary echo. In addition, the signal to noise ratio of the ToF approach is significantly higher than that seen in the SA approach. Initial errors due to ringing interference with the ToF approach were about +0.15 m/s. This was reduced to <+0.03 m/s by: changing the transducer design to a lower Q factor, increasing the resonant frequencies, and matching the order of the calibration curve fit to the ringing cycles within the operating range of the velocimeter timing window.
Figure 7 shows a typical calibration and post calibration verification. Calibrations typically track Del Grosso and Mader's pure water equation to within 0.06 m/s and typically to 0.04 m/s r.m.s.
FIELD TESTING
Several trials were conducted in the Saanich Inlet aboard the University of Victoria's research vessel, John Strickland. The trials consisted of numerous profiles with the following instruments: two ToF sensors, a SA sensor, an Applied Microsystems CTD-12 Plus, and another manufacturer's CTD based sound velocity profiler. These instruments were mounted together for each profile.
All field profiles of the ToF sensors displayed excellent correlation from down cast to up cast. The CTD data did not show the same correlation as expected due to thermal shedding and flushing characteristics.
Figure 9 shows a profile with a ToF sensor and an STD-12 Plus. The ToF sensor shows a faster response to changes in sound speed, whereas the CTD data displays a smoothing of the data as well as a lag with respect to pressure (depth).
CONCLUSIONS
Efforts to upgrade the existing sing-around technology revealed significant obstacles to achieve accuracy's better than 0.25 m/s without the use of long path lengths. CTD based sound velocimeters are limited to about 0.25 m/s due to the inaccuracies of the sound speed equations.
The new ToF sensor is capable of tracking Del Gross and Mader's pure water equation to better than 0.06 m/s r.m.s. over the range of 1400 - 1550 m/s. Since Neptunian waters can attain sound speeds in excess of 1550 m/s, a universally accepted sound speed standard is required to realise the full potential of the time of flight sensor.
By Greg Eaton and D. Tom Dakin, Applied Microsystems Ltd.
First published in Oceanology International 96 Proceedings.
ACKNOWLEDGEMENTS
The following people and organisations assisted Applied Microsystems Ltd. in the development of this instrument:
Mr. William Beall, AUTEC Range Services, Florida, U.S.A.
Mr. Richard Dunn, Naval Undersea Warfare Center (NUWC), Florida, U.S.A.
Mr. Erik Hammerstad, Simrad, Norge AS
Capt. Don Horn, Research Vessel John Strickland, University of Victoria, Canada
REFERENCES
(1) Pike J. M. and Beiboer F. L., "A Comparison Between Algorithms For the Speed of Sound
in Seawater". The Hydrographic Society, v.34. (1993)
(2) Coates R. F. W., "Underwater Acoustic Systems". Wiley, New York, (1989)
(3) Yost W. T. and Cantrell J. H., "Fundamental Aspects of Pulse Phase-Locked Loop
Technology-Based Methods for Measurement of Ultrasonic Velocity". The Journal of
the Acoustical Society of America, v.91, pp 1456-1468. (1992)
(4) Chen C. T. and Millero F. J., "Sound Speed in Seawater at high Pressures". The Journal of
the Acoustical Society of America, v.62, pp 1129-1135. (1977)
(5) Del Grosso V. A., "New Equations for the Speed of Sound in Natural Waters (with
Comparisons to other Equations)". The Journal of the Acoustical Society of America, v.
56, pp 1084-1091. (1974)
(6) Del Grosso V. A. and Mader C. W., "Speed of Sound in Pure Water". The Journal of the
Acoustical Society of America, v.52, pp 1442-1446. (1972)
(7) Kroebel W. and Mahrt K. H., "Recent Results of Absolute Sound Velocity Measurements in
Pure Water and Sea Water at Atmospheric Pressure". Acustica, v.35, pp 154-164. (1976)
(8) Fujii K. and Masui R., "Accurate Measurements of the Sound Velocity in Pure Water by
Combining a Coherent Phase-Detection Technique and a Variable Path-Length
Interferometer". The Journal of the Acoustical Society of America, v.93, pp 276-282.
(1993)
(9) MacKenzie K. V., "Calibrations of Oceanographic Research Velocimeters". The Journal of
the Acoustical Society of America, v.53, pp 869-875. (1973)
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