Final Report

Development of acoustic methods to measure oil droplet size 

and slick thickness on ROV and AUV platforms

Paul D. Panetta1,2, Ted Argo1, Hualong Du1,2, Donglai Gong2, 

L. N. Ferris2

, and Jeanna Kidwell2

1

Applied Research Associates, Inc.

2 The College of William & Mary, Virginia Institute of Marine 

Science

Report For

U.S. Department of the Interior

Bureau of Safety and Environmental Enforcement (BSEE)

Sterling, VA 

May 31, 2017

This study was funded by the U.S. Department of the Interior, Bureau of Safety and 

Environmental Enforcement (BSEE), Oil Spill Preparedness Division (OSPD), 

Washington, DC under Contract Number E15PC00009.
2

ACKNOWLEDGMENTS 

The authors wish to thank the Ohmsett staff for their assistance with this work.

DISCLAIMER

This final report has been reviewed by the Bureau of Safety and Environmental 

Enforcement (BSEE). Approval does not signify that the contents necessarily reflect the 

views and policies of the BSEE, nor does mention of the trade names or commercial 

products constitute endorsement or recommendation for use.
3

Table of Contents

Acknowledgments _________________________________________________________ 2

Disclaimer ________________________________________________________________ 2

Executive Summary ________________________________________________________ 5

1. Overview and Objective ________________________________________________ 6

2. Slick thickness measurements from ROV and AUV platforms __________________ 7

2.1. Ohmsett tank setup________________________________________________________ 7

2.2. Oil configuration __________________________________________________________ 7

2.3. Acoustic measurement of slick thickness______________________________________ 16

2.4. Speed of sound of oil as a function of temperature _____________________________ 17

2.5. ROV measurement of slick thickness _________________________________________ 19

2.5.1. ROV acoustic sensor set up, and deployment ___________________________________ 19

2.5.2. Slick thickness results from ROV platform ______________________________________ 22

2.6. Glider measurement of slick thickness________________________________________ 28

2.6.1. Glider Acoustic Sensor Mount setup and deployment_____________________________ 28

2.6.2. Slick thickness results from glider platform _____________________________________ 32

3. Acoustic measurement of subsurface releases of oil and gas from an ROV platform

36

3.1. Acoustic measurement of gas bubble size distribution___________________________ 39

3.1.1. Measurement Apparatus ___________________________________________________ 39

3.1.2. Analysis _________________________________________________________________ 42

3.1.3. Bubble Size Distribution ____________________________________________________ 50

3.1.4. Comparison between static and free swimming platform__________________________ 52

3.2. Acoustic measurement of dispersant effectiveness from ROV platform_____________ 54

4. Deployment platforms for oil spill response _______________________________ 56

5. Summary and Conclusions _____________________________________________ 56

6. References _________________________________________________________ 57

Appendix: Inertial Positioning Measurements of Unmanned Underwater Vehicle (UUV) 

Dynamics __________________________________________________________________ 58

Introduction __________________________________________________________________ 58

Background ___________________________________________________________________ 58

Data Processing________________________________________________________________ 59

Coordinate Transformations____________________________________________________________ 59

Posterior Approximation of Euler Angles __________________________________________________ 61

Filtering ____________________________________________________________________________ 63

Cross-Correlation ____________________________________________________________________ 64

Metrics of Angular Position ____________________________________________________________ 65
4

Results _______________________________________________________________________ 68

Dynamics of Subsurface Release ROV Configuration __________________________________ 75

References____________________________________________________________________ 80
5

EXECUTIVE SUMMARY

In this project we have begun the transition of acoustic measurements of slick 

thickness, gas bubble size distribution, and oil dispersant effectiveness to free 

swimming ROV and glider platforms. Using a SeaBotix LBV150 ROV vehicle, we have 

demonstrated the ability to effectively measure both oil slick thickness as well as gas 

bubble/oil droplet size distribution while operating the ROV in free swimming mode in 

our labs and at Ohmsett. We also demonstrated the ability to measure the slick 

thickness using acoustic sensors mounted on a Slocum glider. The oil slick thickness 

measurements were performed both in the absence of waves as well as the presence of 

waves. Acoustic transducers were mounted externally on the frame of the ROV and the 

glider and tethered via cables to data collection and processing hardware.

While the extra sensors and cabling associated with oil slick thickness 

measurements do impact the performance and flight dynamics of the ROV, proper 

ballasting and mounting of the sensors allowed the vehicle to remain controllable and 

flyable. The existing setup could be deployable in an open water setting if the currents 

and waves are within specific limits.

The measurement of bubble size and oil droplet size distribution required the 

mounting of a relatively large and heavy low-frequency transducer and receiver on top 

of the ROV. This sensor configuration severely affected the stability, controllability and 

flight dynamics of the vehicle. While extensive ballasting measures allow the vehicle to 

become stable, it was still difficult to control and move. A larger ROV would be able to 

deal with the size and mass of the low frequency sensor much more effectively. For the 

purposes of research deployment at Ohmsett, the setup was functional but unlike the 

measurement of oil slick thickness, it would be too difficult to use in an open water 

deployment scenario.

To better understand the influence of sea state on vehicle motion and thus 

measurement precision, the team designed and built a custom inertial motion sensor 

package to quantify the motion of the vehicle while making oil slick thickness 

measurements as well as subsurface measurements of gas bubble distribution 

measurement and dispersant effectiveness. 

The technical progress made to measure the gas bubble size distribution using 

acoustic backscattering is significant and opens the opportunity to provide gas bubble 

size measurements as well as oil dispersant effectiveness from a single set of acoustic 

sensors on a single platform. The measurements of oil droplet scattering related to 

dispersant efficiency show the proof of concept from ROV platforms and produced 

results similar to static platforms from previous work. We advanced these capabilities to 

TRL 6 through multiple measurements at Ohmsett in many spill scenarios including 

surface slicks in various sea states and subsurface releases of methane and dispersed 

oil.
6

1. OVERVIEW AND OBJECTIVE

Combatting oil spills requires an array of instruments and methods to improve 

collection and physical removal of oil from the environment, burning the oil, or 

dispersing the oil into the water column. Ensuring that instrumentation exists to 

characterize the oil is crucial for responding to both surface spills as well as subsurface 

releases of oil and gas. To help improve oil spill response, we are developing acoustic 

measurements of the thickness of an oil slick the droplet size distributions of oil and 

gas. Mapping the slick thickness will help direct spill responders to the thickest areas of 

the slick and can be used to measure the burn rate and efficiency during In-Situ Burning 

(ISB), measuring the oil droplet size distribution and gas bubble size distribution at the 

source of a subsurface release, throughout the water column, and just below a slick to 

monitor the effect of aerial or surface applications of dispersant will help determine 

dispersant efficiency and provide input into fate and transport models. The goal of this 

project is to begin the transfer of acoustic methods for measurement of slick thickness 

and oil droplet and bubble size distributions from static platforms to free swimming ROV 

and AUV platforms. The technical objectives of this program are to optimize the 

measurement electronics and begin compensating for the relative motion of the freeswimming platforms and the slick surface. 

To address this goal, measurement methods previously developed for slick 

thickness, oil droplet sizing, and bubble size distribution measurement were integrated 

onto an ROV platform. Three weeks of testing in the simulated spill environment at

Ohmsett provided an opportunity to test, evaluate, and improve all three of these 

measurement methods while for various aspects of the potential operational 

environments including sea states, slick thicknesses, and slick configuration. In addition, 

measurements of the temperature-dependent speed of sound in various oils was 

measured to aid in determining the slick thickness in various environments. In the 

following sections, a description of the slick thickness measurements using Alaska 

North Slope (ANS) crude oil and subsurface release measurements of ANS dispersed 

with Corexit 9500, air bubbles, and methane bubbles, will be presented. Results of 

these measurements and implications for future implementation of this technology will 

be discussed.
7

2. SLICK THICKNESS MEASUREMENTS FROM ROV AND AUV 

PLATFORMS

2.1. OHMSETT TANK SETUP

We accomplished this goal through several measurements of surface slicks and 

subsurface releases at our lab and during three trips to Ohmsett. For our work at 

Ohmsett the oil in the tank was arranged as shown in Figure 1. 

Figure 1. The tank at Ohmsett was configured with various surface slicks and subsurface releases during 

each of the three weeks the ARA team was performing measurements.

2.2. OIL CONFIGURATION 

We performed measurements with two different boom configurations in sea states 0 

to 3. In one configuration the boom was placed along the side of the tank and corralled 

with ice eaters as shown in Figure 2. The oil did not form a uniform slick on the surface 

as it spread out and moved around the boomed area due to wind and wave action. 

Typically, between 70 L to 132 L of oil was placed in the boomed region resulting in 

slick thicknesses of approximately 3 mm and 5 mm, respectively. The setup showing 

the arbitrary shaped boomed region are in Figure 3 and Figure 4.

 

Slicks

1. Boomed against wall– straight edge

2. Contained with Ice Eaters

2. Two 4 foot x 4 foot PVC squares

Oil: ANS

Subsurface releases

• Oils: ANS ~ 1+ L/min

• Dispersant: Corexit 9500

• Methane

• Nozzle in vertical position ~ 3 feet 

from vertical mast

• Bubbler beneath nozzle

~2 mm ~5 mm to 

~1 cm

Ice eater

~2 mm – ~3 mm

~ 20 feet

~ 15 feet

North
8

Figure 2. A linear boomed area was filled with 70 L to 132 L of ANS oil and contained with ice eaters at 

either end to prevent oil loss during testing.

Figure 3. The arbitrary shaped boom configuration tested at Ohmsett more closely simulated an 

operational environment by allowing for more maneuverability under the slick, less control over 

the surface area and slick thickness.
9

Figure 4. Upon collapsing to its minimum surface area, the arbitrary boom slick allowed measurements of 

a thicker slick.

Multiple acoustic transducers were mounted to the ROV and glider platforms as 

shown in Figure 5. The sensors were mounted at various angles to accommodate for 

the pitch and roll of the ROV and the motion of the glider as it yos through the water 

column and the motion of the surface of the slick due to the waves. A more detailed 

description of the angles will be given in a latter section. A schematic of the acoustic 

beams propagating through the water column under the waves is shown in Figure 9 for 

the ROV and glider platforms.
10

Figure 5. Configurations of the acoustic sensors on the ROV and glider platforms

Figure 6. Waves varied in height throughout the experiments at Ohmsett; the waves made during Test 14 

had a mean height of 15.9 Inches and wavelength of 39.8 Feet.
11

Figure 7. Waves varied in height throughout the experiments at Ohmsett; the waves made during Test 17 

had a mean height of 21.4 Inches and wavelength of 39.3 Feet.

Figure 8. Waves varied in height throughout the experiments at Ohmsett; the harbor chop made during 

Test 20C had a mean height of 6.0 Inches and wavelength of 11.6 Feet
12

Figure 9. Slick thickness was measured from ROV and AUV platforms in sea states with the following 

extremes (from top to bottom): Sea State 3 at 0.56 meter wave height, Sea State 1 Harbor 

Chop, Sea State 2 at 10.3 meter wavelength, and Sea State 1 at 16.4 meter wavelength.
13

To successfully transition these measurements to the open water to help with a real 

spill requires operation in multiple sea states. Sample sea states are shown in Figure 6

through Figure 8. The extremes of the sea states experienced throughout this testing 

are depicted, to scale, in Figure 9 for the highest sea state, shortest wavelength, and 

longest wavelength tested with the ROV, and a representative sea state tested with the 

glider.

Figure 10 and Figure 11 show the sea states where the acoustic measurements 

measured the slick thickness at Ohmsett. Figure 10 shows the average wave height vs 

wavelength for a given measurement period and Figure 11 shows the highest 1/3 of the 

waves. The sea states included no waves, harbor chop with small heights and short 

wavelengths and traveling waves with amplitudes as over 0.5 meters and wavelengths 

over 20 meters. The World Meteorological Organization Sea State ranged from 0 where 

no waves were present to a Sea State 3. 

Figure 10. Slick thickness measurements were performed in a variety of sea states for a variety of 

wavelengths. The sea state, based on mean wave height, is presented here for each collection 

of tests. Circles and triangles represent separate days of testing within each test paradigm 

denoted by different colors.
14

Figure 11. Slick thickness measurements were performed in a variety of sea states for a variety of 

wavelengths. The sea state, based on the highest one third of waves, is presented here for 

each collection of tests. Circles and triangles represent separate days of testing within each 

test paradigm denoted by different colors.

The detailed specifications of these sea states along with the dates of our 

measurements are shown in Table 1.
15

Table 1. All wave states studied under this program includes data from February 2016 and March 2017.

*Based on Significant Wave Height (top 1/3) as defined by the World Meteorological Organization sea state 

code, https://en.wikipedia.org/wiki/Sea_state

2016 1.1 5.6 7.7 66.4 2 (Smooth)

2016 1.2 5.4 7.7 66.4 2 (Smooth)

2016 2.1 5.8 10.2 23.8 2 (Smooth)

2016 2.2 6.8 10.2 23.8 2 (Smooth)

2016 2.3 5.4 10.2 23.8 2 (Smooth)

2016 2.4 5.5 10.2 23.8 2 (Smooth)

2016 2.5 6.2 10.2 23.8 2 (Smooth)

2016 2.6 6.3 10.2 23.8 2 (Smooth)

2016 2.7 6.3 10.2 23.8 2 (Smooth)

2016 2.9 6.2 10.2 23.8 2 (Smooth)

2016 2.10 6.4 10.2 23.8 2 (Smooth)

2016 2.11 6.7 10.2 23.8 2 (Smooth)

2016 3.1 6.9 12.2 16.6 2 (Smooth)

2016 3.2 6.2 12.2 16.6 2 (Smooth)

2016 1 1.6 0.0 0.0 0 (Calm)

2016 2 1.5 8.5 51.0 2 (Smooth)

2016 2A 1.9 11.0 51.0 2 (Smooth)

2016 2B 2.1 11.0 51.0 2 (Smooth)

2016 3 1.9 15.6 40.3 2 (Smooth)

2016 3A.1 2.2 15.6 40.3 2 (Smooth)

2016 3A.2 2.2 15.6 40.3 2 (Smooth)

2016 3A.3 2.2 15.6 40.3 2 (Smooth)

2016 5.2 5.5 15.9 34.5 2 (Smooth)

2016 5.3 5.4 15.9 34.5 2 (Smooth)

2016 5.4 5.8 15.9 34.5 2 (Smooth)

2016 6.1 5.1 17.4 34.3 2 (Smooth)

2016 6.2 5.2 17.4 34.3 2 (Smooth)

2016 6.3 4.0 17.4 34.3 2 (Smooth)

2017 4 70 10.1 13.2 38.4 2 (Smooth)

2017 5 70 10.2 12.1 40.8 2 (Smooth)

2017 6 70 12.3 14.3 42.7 2 (Smooth)

2017 7 70 7.3 10.9 54.5 2 (Smooth)

2017 8 70 14.6 20.8 40.7 3 (Slight)

2017 9 70 15.6 22.6 39.4 3 (Slight)

2017 10 70 4.1 7.6 31.7 1 (Calm)

2017 11 132 0 (Calm)

2017 12 132 19.1 23.1 40.5 3 (Slight)

2017 13 132 13.0 14.9 39.9 2 (Smooth)

2017 14 132 15.9 16.8 39.8 2 (Smooth)

2017 15 132 4.8 8.8 36.7 2 (Smooth)

2017 16 132 19.8 22.5 39.3 3 (Slight)

2017 17 132 21.4 23.3 39.3 3 (Slight)

2017 18 132 6.6 11.2 38.0 2 (Smooth)

2017 19A 132 3.9 4.8 21.2 2 (Smooth)

2017 19B 132 2.1 3.5 10.5 1 (Calm)

2017 19C 132 2.5 4.0 15.5 2 (Smooth)

2017 19D 132 4.3 7.1 19.4 2 (Smooth)

2017 20A 132 6.7 9.0 9.6 2 (Smooth)

2017 20B 132 6.1 9.4 12.1 2 (Smooth)

2017 20C 132 6.0 9.2 11.6 2 (Smooth)

2017 20D 132 3.6 5.7 12.1 2 (Smooth)

2017 20E 132 0 (Calm)

2017 29 132 1.6 2.8 53.6 1 (Calm)

2017 30 132 1.7 3.3 49.7 1 (Calm)

No Waves

No Waves

Harbor Chop State 1

Harbor Chop State 2

Sine waves

Sine waves

Sine Waves

ANS, Arbitrary Boom, Sine Waves

ANS, Parallel Boom, Sine Waves

Year

 Oil 

Volume 

(L) 

Mean Wave 

Height 

(inches)

Significant 

Wave Height 

(top 1/3) 

(inches)

Average 

Wavelength 

(feet)

World 

Meteorological 

Organization Sea 

State*

Test #
16

2.3. ACOUSTIC MEASUREMENT OF SLICK THICKNESS

Data was collected by flying the platforms under the slick at various heights similar 

to previous work for BSEE [Panetta et al.] where we developed an ROV which rolled 

along the bottom of the tank. The free swimming platforms offered a more realistic 

deployment scenario and thus provided the opportunity to study the effects of the

motion of the platforms and the surface of the slick. Figure 12 shows a “sonar-like” 

image of the reflection from the water surface and the slick surfaces. The slick is most 

visible as multiple reflections around 10 seconds and in the 30 to 70 second range. A 

closer look at the raw ultrasonic time-domain signal in Figure 13 shows the reflection 

from the bottom of the slick arriving first followed by the reflection from the top of the 

slick. The third signal is a reverberation inside the slick. To calculate the thickness we 

calculated the difference in the arrivals of the bottom and top of the slick. 

Figure 12. The acoustic signals from the surface and the slick in the sonar-like image of the slick from the 

glider platform shows the motion of the glider platform as it is tilted up and down independent 

of waves. 

 

Figure 13: Schematic of measurement, zoomed in region of reflections from slick in the 40 to 60 second 

region and a typical acoustic “ping” from the glider platform showing a slick approximately

7.5mm thick.

Bottom 

of slick

Top of 

slick

Reverberations 

inside slick

See Figure 13 for 

zoomed in view

of this region
17

2.4. SPEED OF SOUND OF OIL AS A FUNCTION OF TEMPERATURE

The acoustic wave speed in oil is significantly affected by the temperature. Thus 

knowing speed of sound is necessary to accurately determine the thickness of the slick.

Figure 14 shows the experimental set up for measuring the speed of sound as a 

function of temperature. The oil chamber was fabricated from stainless steel and 

surrounded with insulation. Thermal insulation fibers were used to wrap the 3.5’’ 

diameter cylindrical stainless tube to keep the temperature of the oil constant. The 

stainless tube was welded onto a 7.0’’ diameter steel plate and placed on a hot plate to 

heat the oil. An acoustic transducer mounted on a 5-axis positioning system was 

lowered through a central hole in the top thermal insulation cap and transmitted the 

acoustic signal into the oil and received the reflection from the bottom of the oil filled 

container. Three thermocouples were mounted in the insulated cap to measure 

temperatures at different depths in oil. The temperature was collected by the National 

Instruments data collection device and acquired simultaneously with the acoustic data. 

Figure 15 shows a closer view of the inside of the oil chamber. Figure 16 shows three 

thermocouples mounted through the insulated cap for measuring the temperature in the 

oil at different depths.

Figure 14. The experimental setup for measuring compression wave speed in oil at high temperature was 

maintained using an insulated vessel on a hot plate.

High 

Temperature 

Chamber

Hot plate

Thermally 

insulated cap

Acoustic 

Transducer

Thermocouples

NI Data Collection 
18

Figure 15. The cylindrical oil container was wrapped with insulation fiber to maintain temperature.

Figure 16. The thermal insulation cap for the oil container supported three protruding thermocouples.
19

Figure 17 shows the dependence of the measured speed of sound on temperature 

from 30°C to 180°C in ANS, Dorado and Rock crude oils. 

Figure 17. Wave speed Vs. Temperature in various crude oils demonstrate a change of nearly 40% over 

the 25 to 180 degree temperature range.

2.5. ROV MEASUREMENT OF SLICK THICKNESS

2.5.1. ROV acoustic sensor set up, and deployment

Multiple acoustic transducers were mounted on the ROV to account for the relative 

motion of ROV and the slick. Figure 18 shows our final configuration of six acoustic 

transducers with a center frequency of 2.25 MHz mounted to the ROV. Three were 

attached on the left side with angles (-15°, 0, 15°) to accommodate the pitch of the ROV 

and three were attached to the back of the ROV with angles (-10°, 0, 10°) to 

accommodate the roll of the ROV. These angles were chosen based on the results from 

our measurements in waves at Ohmsett and at our facility at VIMS in Gloucester Point, 

VA.
20

Figure 18. Side, top, and back views of the ROV showing the placement of the acoustic transducers 

mounted at various angles to account for the pitch and roll of the ROV platform.
21

Images of the ROV are shown in Figure 19 at two different depths. As the acoustic 

beam propagates through the water from the small transducer, it diverges causing the 

acoustic “spot size” on the surface of the slick to increase with increasing distance. To 

determine if the spot size affects the ability of the acoustics to measure the slick 

thickness for various sea states we performed measurements at two different depths, 

1.2 m and 1.8 m as shown in Figure 19. 

Figure 19. The ROV performed acoustic measurements of oil slick thickness at two depths – 1.2 meters 

(top) and 1.8 meters (bottom).

At these depths, the spot size on the surface of the slick is 10.7 cm (4.1 inches) and 

15.7 cm (6.2 inches), respectively. Figure 20 shows a schematic of these depths along 
22

with the theoretical prediction of the beam diameter as a function of distance assuming 

the beam has a Gaussian shape. The pictures are not to scale. Details of these 

calculations are in previous reports. We found no significant effect on the resultant slick 

thickness from performing measurements at these two depths for the sea states we 

studied. For transition to open water, the beam diameter and the interaction with real 

waves will be an important topic to study.

Figure 20. The spot size of the acoustic beam on the surface increases as depth increases, though 

measurements were successfully made using the spot sizes experienced in this program with 

the sea states studied.

2.5.2. Slick thickness results from ROV platform

The slick thickness was measured using the ROV in the sea states described in

Table 2 along with the thicknesses obtained.
23

Table 2. The table of all surface slick measurements performed under this program including slick 

thickness data from February 2016 and March 2017.

*Based on Significant Wave Height (top 1/3) as defined by the World Meteorological Organization sea state 

code, https://en.wikipedia.org/wiki/Sea_state

Average 

(mm)

Range 

(mm)

Standard 

Deviation 

(mm)

2016 1.1 5.6 7.7 66.4 2 (Smooth) 5.6 1.3 0.3

2016 1.2 5.4 7.7 66.4 2 (Smooth) 5.4 1.8 0.3

2016 2.1 5.8 10.2 23.8 2 (Smooth) 5.8 1.5 0.2

2016 2.2 6.8 10.2 23.8 2 (Smooth) 6.8 1.8 0.3

2016 2.3 5.4 10.2 23.8 2 (Smooth) 5.4 3.6 0.8

2016 2.4 5.5 10.2 23.8 2 (Smooth) 5.5 3.1 0.4

2016 2.5 6.2 10.2 23.8 2 (Smooth) 6.2 2.9 0.4

2016 2.6 6.3 10.2 23.8 2 (Smooth) 6.3 1.1 0.2

2016 2.7 6.3 10.2 23.8 2 (Smooth) 6.3 1.6 0.4

2016 2.9 6.2 10.2 23.8 2 (Smooth) 6.2 1.0 0.3

2016 2.10 6.4 10.2 23.8 2 (Smooth) 6.4 1.1 0.2

2016 2.11 6.7 10.2 23.8 2 (Smooth) 6.7 1.4 0.4

2016 3.1 6.9 12.2 16.6 2 (Smooth) 6.9 1.5 0.4

2016 3.2 6.2 12.2 16.6 2 (Smooth) 6.2 2.1 0.6

2016 1 1.6 0.0 0.0 0 (Calm) 1.6 1.1 0.1

2016 2 1.5 8.5 51.0 2 (Smooth) 1.5 2.7 0.6

2016 2A 1.9 11.0 51.0 2 (Smooth) 1.9 1.5 0.4

2016 2B 2.1 11.0 51.0 2 (Smooth) 2.1 1.7 0.5

2016 3 1.9 15.6 40.3 2 (Smooth) 1.9 1.8 0.5

2016 3A.1 2.2 15.6 40.3 2 (Smooth) 2.2 1.8 0.5

2016 3A.2 2.2 15.6 40.3 2 (Smooth) 2.2 1.8 0.6

2016 3A.3 2.2 15.6 40.3 2 (Smooth) 2.2 2.0 0.5

2016 5.2 5.5 15.9 34.5 2 (Smooth) 5.5 4.4 1.4

2016 5.3 5.4 15.9 34.5 2 (Smooth) 5.4 4.7 1.4

2016 5.4 5.8 15.9 34.5 2 (Smooth) 5.8 4.1 1.0

2016 6.1 5.1 17.4 34.3 2 (Smooth) 5.1 3.5 1.2

2016 6.2 5.2 17.4 34.3 2 (Smooth) 5.2 3.2 0.9

2016 6.3 4.0 17.4 34.3 2 (Smooth) 4.0 3.4 0.8

2017 4 70 10.1 13.2 38.4 2 (Smooth) 2.8 1.8 0.3

2017 5 70 10.2 12.1 40.8 2 (Smooth) 3.4 3.0 0.5

2017 6 70 12.3 14.3 42.7 2 (Smooth) 3.3 3.8 1.2

2017 7 70 7.3 10.9 54.5 2 (Smooth) 3.0 4.3 1.0

2017 8 70 14.6 20.8 40.7 3 (Slight) 3.3 3.7 1.0

2017 9 70 15.6 22.6 39.4 3 (Slight) 2.9 3.7 1.0

2017 10 70 4.1 7.6 31.7 1 (Calm) 3.1 3.4 1.0

2017 11 132 0 (Calm)

2017 12 132 19.1 23.1 40.5 3 (Slight) 4.2 3.6 1.0

2017 13 132 13.0 14.9 39.9 2 (Smooth) 4.0 2.6 0.8

2017 14 132 15.9 16.8 39.8 2 (Smooth) 5.0 3.1 0.7

2017 15 132 4.8 8.8 36.7 2 (Smooth) 4.7 4.2 0.9

2017 16 132 19.8 22.5 39.3 3 (Slight) 4.5 3.3 0.9

2017 17 132 21.4 23.3 39.3 3 (Slight) 5.4 3.8 1.1

2017 18 132 6.6 11.2 38.0 2 (Smooth) 4.8 4.2 1.0

2017 19A 132 3.9 4.8 21.2 2 (Smooth) 3.8 3.5 0.8

2017 19B 132 2.1 3.5 10.5 1 (Calm) 4.2 3.5 1.0

2017 19C 132 2.5 4.0 15.5 2 (Smooth) 3.8 3.5 0.9

2017 19D 132 4.3 7.1 19.4 2 (Smooth) 4.1 3.5 0.9

2017 20A 132 6.7 9.0 9.6 2 (Smooth) 4.0 3.2 0.8

2017 20B 132 6.1 9.4 12.1 2 (Smooth) 3.2 3.4 0.9

2017 20C 132 6.0 9.2 11.6 2 (Smooth) 3.6 3.5 1.0

2017 20D 132 3.6 5.7 12.1 2 (Smooth) 3.2 6.4 1.2

2017 20E 132 0 (Calm) 6.9 2.7 0.8

2017 29 132 1.6 2.8 53.6 1 (Calm) 3.8 3.7 1.1

2017 30 132 1.7 3.3 49.7 1 (Calm) 4.3 3.8 1.2

No Waves

No Waves

Harbor Chop State 1

Harbor Chop State 2

Sine waves

no data

Sine waves

Sine Waves

ANS, Arbitrary Boom, Sine Waves

ANS, Parallel Boom, Sine Waves

Thickness

Year

 Oil 

Volume 

(L) 

Mean Wave 

Height 

(inches)

Significant Wave 

Height (top 1/3) 

(inches)

Average 

Wavelength 

(feet)

World 

Meteorological 

Organization Sea 

State*

Test #
24

For brevity we will present the detailed results of the acoustic measurements of slick 

thickness in calm water and for Tests 6, 11, 15, 16, 17, 18 which covers the range of 

wave heights from 0 inches to 23.5 inches. An example of the measurements for calm 

water are shown in Figure 21 for the transducer mounted in the center of the back of the 

ROV. The reflection from the surface was measurable throughout the data collection 

time and the slick was measureable for most of that time. The top pane of Figure 21

shows the time of arrival of the acoustic reflections versus measurement time and the 

bottom pane shows a single acoustic signal depicting (1) the reflection from bottom of 

the slick, (2) the reflection from the top of the slick, and (3) the reverberation inside the 

slick. Two regions labeled “Gate 2” and “Gate 3” highlight the reflection from the bottom 

of the slick and the reverberation inside the slick, respectively. The large signal in the 

center is the reflection for the top of the slick at the oil-air interface.

The reflection from the oil slick surface was dynamically changing throughout the 

measurement due to surface and ROV motion, especially when waves were applied, 

resulting in reflections from the bottom of the slick which were not always clearly 

separated from the reflection from the surface or the electronic noise. Therefore, we 

selected signals with visible and clear separation between these returns for processing 

and optimized the analysis algorithm to calculate the slick thickness using the time 

difference between the reflections of the top and bottom of the slick. The following 

figures show the measurements of oil slick thickness as a function of measurement time 

using the zero degree roll transducer mounted in the back of the ROV for each test.

For Test 15 through 20E, the ROV was moved closer to the water surface to 

decrease the spot sizes of acoustic transducers at the water surface. The goal was to 

diminish the negative effects of dynamic wave surfaces on the reflection from the oil 

slick so that more usable signals were collected in the following tests. Based on this 

limited data set no effect due to depth was observed.
25

Figure 21 Acoustic measurements of oil slick thickness from the zero degree roll transducer for calm 

water show the arrival of the individual acoustic signals versus time (top) and a single acoustic 

return (bottom).

Figure 22. The measured oil slick thickness without waves in Test 3 was approximately 3.5 mm. 
26

Figure 23. The measured oil slick thickness without waves in Test 11 was approximately 5 mm.

Figure 24. The measured oil slick thickness for waves as high as 14 inches in Test 6 was approximately 

4.5 mm.

Figure 25. The measured oil slick thickness for waves as high as 8.8 inches in Test 15 was approximately 

5 mm.
27

Figure 26. The measured oil slick thickness for the Test 18 where the waves where as high as 11 inches.

Figure 27. The measured oil slick thickness for the Test 16 where the wave as high as 22 inches. 

Figure 28. The measured oil slick thickness for the Test 17 where the waves where as high as 23 inches.
28

2.6. GLIDER MEASUREMENT OF SLICK THICKNESS

2.6.1. Glider Acoustic Sensor Mount setup and deployment

The glider was prepared by Professor Donglai Gong and Lauren Ferris from VIMS 

for oil slick thickness measurements. The glider was ballasted for coastal seawater 

densities of 1020 kg/m3 to 1026 kg/m3. During an open water deployment, the glider 

would operate untethered at water depths from the surface down to 30 to 1000 meters. 

The maximum depth for each vehicle depends on the vehicle’s buoyancy pump 

configuration. The glider has a buoyancy pump that can move roughly 460 cc of 

seawater into and out of the glider’s forward wet section. The glider can also move its 

forward battery fore and aft by roughly 1-2 inches. Both the buoyancy pump and the 

battery can be used to control the glider’s pitch. For directional control, the glider has a 

rudder in the tail section. Under normal flight conditions, the glider would glide with a 

pitch angle of 26 degrees and a forward speed of 25-35 cm/s. The gliders inflect near 

the surface at an average depth of 3-5 meters. 

Figure 29: ARA’s VIMS partners prepared this Slocum Glider for testing acoustic transducers at Ohmsett 

during February 2017.

The acoustic sensors were mounted onto the glider at two pitch angles (-26°, +26°) 

as shown in Figure 30; the angles were chosen to study the effects of the glider 

inflection motion near the surface on the acoustic measurements of surface slick 

thickness. The sensor mount was custom designed at VIMS and was rapid-prototyped 

using one of ARA’s 3D printers from our Littleton, CO office. The acoustic transducers 

were powered and controlled from the surface for this study using the same acoustic 

equipment used on the ROV. The Raspberry Pi inertial motion sensors were also 

installed on the glider and ROV to record the pitch, roll, and yaw of the glider as shown 

in Figure 31. The results from this motion sensor are described in the appendix.
29

Figure 30. The acoustic transducers were mounted on the glider at +/- 26 degrees from vertical to match 

the dive and surface angles during the glider flight path.
30

Figure 31. Inertial motion sensors and transducers were mounted on the glider to obtain slick thickness 

measurements for measured glider orientations.

The glider was deployed and manually placed in the boomed area before being 

moved underneath the oil slicks as shown in Figure 32 and Figure 33. The glider was 

near perfectly ballasted for the experiment which allowed the team the maximum 

flexibility in maneuvering the platform. The glider was programed to automatically 

maneuver the tilt and depth of the glider for series of yos to enable slick thickness 

measurements as shown in Figure 34.

Figure 32. The glider was deployed into the tank from the side using deployment techniques similar to 

techniques used in the open water.

Motion 
31

Figure 33. Additional adjustments were made to the glider’s tethering and operational profile before flying 

under the oil slick.
32

Figure 34. The glider was programmed to perform a standard yo profile (+/- 26 degrees) spanning the 8 

foot depth of the water column.

2.6.2. Slick thickness results from glider platform

The thickness of oil slicks was measured from the glider in sea states ranging from 

no waves to small amplitude long wavelength waves as shown in Table 2. Figure 35

shows results for the acoustic transducer at tilted 26° towards the front of the glider. The 

top pane shows the time of the acoustic arrival with respect to measurement time. The 

bottom pane shows the acoustic arrival at the cursor location shown in the top pane. 

The acoustic arrival shows multiple reflections: (1) the reflection from bottom of the slick 
33

arriving first, (2) the reflection from the top of the slick arriving second, and (3) a 

reverberation inside the slick arriving third. The two regions labeled “Gate 2” and “Gate 

3” show the bottom of the slick and the reverberation. The time differences between the 

reflection from the top and the bottom of the slick and the time difference between the 

reflection from the top of the slick and reverberation were obtained for each A-scan. The 

oil slick thickness was calculated by multiplying the wave speed of sound in the oil by 

the measured one way acoustic travel time. Figure 36 and Figure 37 show thickness of 

the ANS oil slick measured from the glider platform without waves over two different 

time periods as it ascended and descended through the water column.

Figure 35. The acoustic return versus time (top) and the single acoustic return at the vertical cursor 

(bottom) as measured from the transducer at 26° angled towards toward the front of the glider 

was measured without waves during Run 1 without waves.
34

Figure 36. The oil slick thickness in the absence of waves measured by the transducer angled 26° toward 

the front of the glider was approximately 4 mm during Run 1 without waves.

Figure 37. The oil slick thickness in the absence of waves measured by the transducer angled 26° toward 

the front of the glider was approximately 4 mm during Run 2 without waves.

The oil slick thickness was also measured from the glider platform when the sine 

waves were produced during Test 29 and Test 30. Figure 38 shows the acoustic arrival 

versus time and a single acoustic signal measured by the transducer angled 26° toward 

the front of the glider. Thus the data was collected while the glider was pointed up 

moving vertically through the water column towards the surface. Figure 39 shows the 

calculated thickness of the oil slick measured from the transducer angled 26° toward the 

front of the glider during Tests 29 and 30 where the height of the waves was at most 3.3 

inches (Sea State 1).
35

Figure 38. The acoustic return versus time (top) and the single acoustic return at the vertical cursor 

(bottom) as measured from the transducer at 26° toward the front of the glider (Run 3).

Figure 39. The oil slick thickness in the absence of waves measured by the transducer angled at 26° 

toward the front of the glider was approximately 3.5 mm (Run 3)
36

3. ACOUSTIC MEASUREMENT OF SUBSURFACE RELEASES OF OIL 

AND GAS FROM AN ROV PLATFORM

Measurements of the gas bubble size distribution and the scattering from the oil 

droplets were performed from the ROV platform. The gas bubble size distribution was 

measured with low frequency acoustic waves using a transducer that was mounted to a 

custom-designed rapid-prototyped bracket as shown in Figure 40. The transducer was 

bolted into the bracket and the bracket subsequently attached to the frame of the ROV 

using cable ties. The scattering from the oil droplets were measured using high 

frequency acoustic waves above 2 MHz using two ultrasonic transducers mounted to 

the underside of the bracket. 

Figure 40. The large low frequency AirMar transducer was mounted on the ROV and floatation was 

added to ensure the ROV was neutrally buoyant. The high frequency acoustic measurements 

were performed using the two transducers mounted beneath the large AirMar low frequency 

transducer.
37

Once the transducers were mounted, the ROV was lowered into the water from the 

side of the tank at Ohmsett. Careful ballasting of the ROV with the large transducer 

attached was performed to ensure both the ROV and trailing cable were neutrally 

buoyant to ensure maneuvering was possible. Once buoyancy was achieved, the freefloating ROV was maneuvered to face the target bubble column and was held at station

keeping while each dataset was collected (Figure 41). During tests where oil was 

present, the ROV maintained a distance of approximately 1 to 2 meters from the 

releases as shown in Figure 42.

Figure 41. The ROV was deployed in the tank by carefully lowering over the side (Left) before 

maneuvering near the bubble generator (Right).

Figure 42. Left – The top view of ROV measuring the scattering from the air bubble and dispersed oil with 

the low and high frequency transducers. Right – The top view of the ROV with the low and high 

frequency transducers measuring the scattering from the crude oil droplets and air bubble.

We performed measurements multiple subsurface releases of methane, ANS and 

methane, and dispersed ANS and methane using Corexit 9500 at a dispersant to oil

ration (DOR) of 1:20 as shown in Figure 43.
38

Figure 43. ROV performing measurements in three scenarios, methane (top), ANS and methane 

(middle), and dispersed ANS and Methane (bottom).

In the remainder of this section we will describe the measurements of the gas bubble 

size distribution followed by the oil droplet measurements.
39

3.1. ACOUSTIC MEASUREMENT OF GAS BUBBLE SIZE DISTRIBUTION

In this program, measurements of the bubble size distribution of a bubble plume 

during a subsurface release of oil and gas were performed. Acoustic transducers were 

mounted to an ROV which aimed them at a bubble plume with and without oil droplets 

present; the measurement paradigm is shown in Figure 44. A single acoustic pulse is

transmitted toward the bubble cloud and the reflected signal is received by the same 

transducer. Based on the known properties of the water, distance to target, and 

transducer properties, the bubble size distribution can be inferred from the received 

signal. In this section, the experimental, theoretical, and data processing development 

necessary to capture this bubble size distribution is presented.

Figure 44. Measurement processes for acoustic scattering from a bubble cloud. A single transducer 

transmits (1), bubbles scatter sound in all directions (2), and the backscattered signal is 

received using the same transducer (3).

3.1.1. Measurement Apparatus

3.1.1.1. Bubble Generation

Bubbles for this program were generated using bubblers developed and proven on 

previous research and development programs. The bubbler consisted of a porous 

ceramic disc sealed into a cylindrical aluminum plenum, as shown in Figure 45. Each 

porous disc is designed to be used with a given pressure differential; in these 

experiments a 2 Bar disc was used for air bubbles and a 1 Bar disc was used for 

methane measurements. 

The bubbler was installed at the base of the wing onto which the oil release nozzle 

was mounted. The bubbler was placed below the oil nozzle to allow gas bubbles to mix 

with any released oil without fouling the bubbler and rendering it inoperable. A single 

gas supply line was attached to a quick-disconnect fitting at the base of the manifold 

and extended to the surface where it was attached to a gas source, in this case a gas 

bottle for laboratory grade methane or a compressor for air. 
40

Figure 45. Left – A bubbler forced gas through a porous ceramic disc. Center – The transducer mounted 

to the ROV was aimed at the bubble and oil cloud created by the bubbler and oil release 

nozzle. Right – The ROV in Situ aimed at a bubble cloud.

3.1.1.2. Acoustics

The acoustic system used for the measurement of the bubble cloud size distribution 

is shown in Figure 46. A computer triggered a waveform generator which created a 

signal suited to the rest of the acoustic system, as described below. The signal passed 

through an amplifier to ensure the transmit signal strength was adequate for detecting 

the backscattered return. A diplexer was used to pass the high power transmit signal 

from the amplifier to the two-sided transducer and the low power received signal from 

the transducer to a filter/preamplifier. After passing through the filter/preamplifier, the 

signal was digitized by a data acquisition board for storage on the computer. The 

capabilities of this equipment is outlined in the following sections.

Figure 46. Setup for the acquisition of bubble cloud backscatter data. A computer-controlled arbitrary 

waveform generator creates a square wave impulse that is amplified, passed through a 

diplexer, and transmitted toward the bubble cloud. The received signal passes through the 

diplexer, is captured by a data acquisition board, and the waveforms are stored on the 

computer for further analysis.

Computer

The computer utilized for the effort was a laptop running a custom InspectionWare 

interface capable of controlling the function generator and data acquisition board 
41

through USB and ExpressCard connections, respectively. The use of the 

InspectionWare interface allowed for rapid changes to data collection routines and 

triage processing of datasets as they were collected to ensure high quality data was 

produced.

Function Generator

An Agilent arbitrary waveform generator was used to synthesize and generate the 

source signals for all tests. A single negative going square wave with an amplitude of 2 

V and varying durations was used as a source signal. When measurements were

performed using one side of the transducer to transmit and other to side to receive, the 

transmitted signals were tuned to the center frequency of the transmitting side of the 

transducer, either 50 or 110 kHz. When measurements were performed with both sides 

of the transducer transmitting simultaneously, a 50 kHz signal was generated.

Amplifier

The signal synthesized by the function generator was amplified by a QSC RMX 1450 

two channel amplifier. The signal was passed through one channel of the amplifier to 

the transmitting side of the transducer. Typical gain values provided by the amplifier 

were approximately 26 dB which resulted in a 40 V signal directed toward the 

transducer. 

Diplexer

A Ritec RDX-6-1K diplexer was used for each transmit channel to protect the receive 

electronics from the high voltage transmit signal. Damping was set to its minimum value 

of 10 Ohms to allow the broadband pulse to propagate through the system without 

being attenuated. The minimum low frequency cutoff of 1 kHz was also set to allow 

frequencies necessary for detection of larger bubbles to pass through the diplexer.

Transducer

An AirMar CM265LM transducer was used to project sound at and receive sound 

backscattered from the bubble cloud. For this device, the transducer housing has two 

independent transducers: one with an operational band of 42-65 kHz and the other with 

an operational band of 85-135 kHz. Each side is operated separately and is capable of 

transmitting and/or receiving the acoustic signal. For tests with air, one side of the 

transducer was used as a transmitter and the other as a receiver with each side used as 

both transmitter and receiver for different tests. For tests with methane, both sides of 

the transducer were excited simultaneously with each side of the transducer alternately 

recording.

Preamplifier

Each signal received from the diplexer was passed through a Teledyne Reson 

VP2000 voltage preamplifier powered by a Teledyne Reson EC6069 battery module. A 

1 kHz to 250 kHz hardware band pass filter was applied to the signal to remove 

radiofrequency interference and maintaining the lowest frequencies of interest. Gain 

was also applied to each signal with 20 dB of gain for the low frequency side of the 
42

transducer and 30 dB of gain for the high frequency side of the transducer to maximize 

the utilization of the dynamic range of the data acquisition system.

Data acquisition

An Acquisition Logic Data Acquisition Card [DAQ] housed in a Magma PCI 

expansion chassis for connection to the control computer. Five ms of data was digitized 

at a sampling rate of 2 MHz. For tests with air bubbles, the data was collected for one 

transmitter and receiver per dataset and for tests with methane bubbles the data was 

collected alternately between each transmitter at half second intervals. Once digitized, 

the data was stored for off-line analysis.

3.1.2. Analysis

3.1.2.1. Mathematical Derivation

Following the work from Freinert and Nützel, measurements of the bubble size 

distribution based on acoustic backscatter were derived from the sonar equation,

,

where Mv is the volume backscattering defined by 

,

TL is the transmission loss in seawater defined by

with α, the attenuation of sound in seawater, defined by Ainslie and McColm, V is the 

volume insonified by the acoustic beam, RL is the received pressure as a function of 

frequency from the receive transducer and TL is the transmitted pressure as a function 

of frequency from the transmit transducer. The backscattered signal per unit volume is 

defined as

where n(a) is the bubble size distribution and σs(a) is the scattering cross section for a 

bubble of radius a. The scattering cross section for a backscattering measurement is 
43

where fo is the resonance frequency of a bubble of radius a defined by Commander and 

Prosperetti k is the wavenumber in water, and f is the insonification frequency.

The equation can be reformulated to 

which can be used to extract the bubble size distribution term. Specifically, through a 

change of variables and using the approximation that the resonant bubbles will be the 

primary contributors to the backscattered signal as described in Section 8.3 of Medwin

and Clay, the integral portion of the equation is reduced to

where a0 is the resonant radius and δ0 is the damping term for a bubble resonant at 

frequency f0. The resonant radius is again determined by Medwin and Clay and the total 

damping term (sum of thermal, radiation, and viscous terms) is defined in Chapter 3 of 

Leighton. This approximation introduces an error of a few percent but is adequate for 

estimating the bubble size distribution. Therefore, the final equation used in the analysis 

is

.

When performing the measurements each of these terms, with the exception of the 

bubble size distribution is known.

3.1.2.2. Data Processing

Determining the bubble size distribution from the backscattered acoustic energy 

follows the following steps according to the analytical development above:

1. Record raw data

2. Subtract the mean signal from each signal

3. Perform a Fast Fourier Transform (FFT) on each signal

4. Adjust each signal for gain and transducer sensitivity (SL and RL terms)

5. Calculate the transmission loss for seawater (TL term)

6. Derive the volume scattering term (V term)

7. Derive the bubble size distribution

The signal processing steps will be outlined using the analysis for one dataset for a 

methane bubble plume in the following sections. 
44

Record

Figure 47 shows ten recordings of the acoustic backscatter measurement on a 

methane bubble plume. At the beginning of each signal, the recorded signal is clipped 

due to high amplitude acoustic cross-talk between the two sections of the transducer. 

The bubble signal is clearly visible as the time variable portion of the recordings 

whereas the crosstalk is the time invariant portion of the recordings.

Such recordings are collected at a rate of one per second per transducer and form a 

B-Scan which demonstrates the development of the bubble cloud with respect to time. 

Figure 48 shows a B-Scan for the bubble only case, bubbles plus ANS, and bubbles 

plus dispersed ANS. Each individual backscatter result is shown as a vertical line in the 

B-Scan with the evolution in time shown as the horizontal axis. Variation from green 

denotes oscillation about zero pressure. Each of these B-Scan images has 

approximately the same amount of color variation which demonstrates that this 

measurement is robust against the introduction of oil droplets.

Figure 47. Ten different acoustic backscatter signals from a methane bubble plume.
45

Figure 48: B-Scans for Methane, Test 39 (top); Methane and ANS, Test 47 (middle); and Methane and 

dispersed ANS, Test 53 (bottom).

Subtract

The mean signal from all of the recorded signals is found, as shown in Figure 49 -

Left. This signal is a composite of the transducer response, acoustic crosstalk, and 

persistent reflections from non-bubble sources. The mean signal is subtracted from the 
46

rest of the signals to produce the approximate backscattered bubble signal, as shown in 

Figure 49 – Right for the same signals shown in Figure 47. Note that the signal with the 

mean removed has a much higher signal to noise ratio than the raw data, thereby 

improving the automated detection and analysis routine. 

Figure 49: Top – The mean of 300 received signals used to represent the electrical and mechanical 

system response. Bottom – The same ten received signals from Figure 47 with the mean 

signal subtracted from each. These signals are taken to be the approximate backscatter 

response of the bubble column. 

Fourier Transform

To ascertain the frequency response of the bubbles, a Fast Fourier Transform (FFT) 

is performed on each signal. The resultant spectrogram (frequency vs. time) is shown in 

Figure 50. The frequency content fluctuates as the bubble size distribution changes in 

time. The evolution with time is shown along the horizontal axis with the individual 

frequency content for each backscattered signal shown as a line along the vertical axis. 
47

The brighter yellow the signal is, the more prevalent that frequency component is in the 

received signal.

Figure 50. The frequency content of the backscattered signal is found.

Gain/Sensitivity Adjustment

Correction of the average receive signal through removal of the transducer 

sensitivity is shown in Figure 51. The mean receive signal is shown in blue and is the 

average of all backscattered returns. The transducer calibration is shown in orange and 

was determined by performing an FFT on a signal reflected from the near-perfectly 

reflecting air-water interface. By subtracting the calibration (orange) from the received 

signal (blue), the effect of the frequency-dependence of the transmit and receive 

sensitivities of the transducer is removed, resulting in the yellow frequency response. 

This response is then used to derive the bubble size distribution.
48

Figure 51: Correction of the received signals to remove the transducer sensitivity is performed in 

processing step 4. The low frequency (top) and high frequency (bottom) transducers have 

different sensitivity curves shown in orange which correct the received signal in blue to the 

actual backscatter amplitude in yellow.

Transmission Loss (TL)

The TL term was determined from the known properties of the water and the range 

to target as shown in Figure 52.
49

Figure 52. The transmission loss term in the sonar equation is dependent upon range and acoustic 

attenuation in seawater.

Volume Term

By calculating the frequency-dependent spot size, the fraction of that diameter and 

the height of the column insonified can be determined. The range to the target is 

calculated based on time of arrival of the reflected pulse. The duration of the reflected 

signal is then used to determine the overall two-way travel time through the cloud which 

results in the bubble plume diameter; in these tests, the plume was determined to be 

approximately 0.26 m in diameter at the height of the measurement. Based on the 

transducer specification, the beam width was interpolated for each frequency and the 

spot size was determined. Based on this spot size, the volume term can be calculated, 

as shown in Figure 53.

Figure 53. The volume term is calculated from the transducer spot size and the bubble cloud diameter.
50

3.1.3. Bubble Size Distribution

Table 3. Different parameters for bubble properties were used in the inversion of the backscatter 

measurements for air and methane.

Parameter Name Air Methane Units

Density 1.21 0.716 kg/m3

Ratio of Specific Heats 1.4 1.32

Specific Heat at Constant 

Pressure

240.0 530.6 cal/kg-°C

Thermal Conductivity 5.6e-3 8.37e-3 cal/m-s

Thermal Diffusivity 1.9e-5 2.20e-5 m2/s

Surface Tension 75e-3 6.42e-4 N/m

Using the gas parameters appropriate for the given test, bubble size distributions 

were obtained, as shown in Figure 54. The bubble size distribution for each dataset was 

averaged for both the low frequency transducer (Channel A, left) and high frequency 

transducer (Channel B, right). Each ROV flight generated a new test. Variations 

between tests are primarily governed by the ability of the ROV operator to aim the 

acoustic transducer at the center of the bubble cloud; during tests with ANS and 

dispersed ANS, visibility of the cloud was diminished, thereby making aiming more 

difficult and reducing the average backscattered acoustic return.
51

Figure 54. Results of the data processed for the subsurface gas releases at Ohmsett. Bubble size 

distributions from the low frequency (left) and high frequency (right) transducers were obtained 

for methane only (top), methane and ANS (middle), and methane and dispersed ANS (bottom) 

test cases.

For testing with air bubbles where one half of the transducer transmitted and the 

other received, the low and high frequency (large and small bubble diameter) 

measurements demonstrate different peak frequencies due to the resonance 

frequencies of the individual transmitters, as shown in Figure 55. 
52

Figure 55. An example bubble size distribution calculations for air bubbles.

One benefit of using this measurement technique is the ability to observe the change 

in bubble population with respect to time. Figure 56 demonstrates the bubble size 

distribution evolution for both the high and low frequency transducers. It is noted that 

the size distribution is confined to the specific bands for each transmitter. 

Figure 56. Bubble size distribution over time for the high frequency transmitter (Left) and low frequency 

transmitter (Right).

3.1.4. Comparison between static and free swimming platform

Data from the air and methane bubble-only tests are shown in Figure 57. In air 

bubble tests, the two halves of the transducer produced narrow bubble size distributions 

focused specifically on each transducer’s operational band. In the methane 

measurements at Ohmsett, the signals are much more broadband. Therefore, for the 

bubble sizes generated by the bubblers used on this and other BSEE programs on 

which ARA performed, the low frequency transducer appears to be adequate to 

generate the bubble size distribution. 
53

Figure 57. Bubble size distribution measurements were obtained using both the high and low frequency 

sides of the AirMar transducer with air at VIMS in November 2016 (left) and with just the low 

frequency side of the AirMar transducer with methane at Ohmsett in February 2017 (right).

In the final report for BSEE Project 1002, the right pane of Figure 67, reproduced 

here in Figure 58, shows the bubble size distribution for seven tests performed with air 

bubbles and dispersed oil using transducers mounted to a fixed frame. Figure 58 also 

shows the bubble size distribution for seven tests performed from a free-flying ROV 

during the current program. Less variation is shown in the maximum gas concentration 

for the fixed from the fixed frame (~5%) compared to the variation in the maximum gas 

concentration from the free-flying ROV (~70%) due to the nature of the motion of the 

ROV. 

Figure 58. Bubble size distributions measured during BSEE Project 1002 (left) and during this project 

(right) for bubbles and dispersed oil. The variation in the gas concentration varies less for the 

measurements from the fixed from (left) than for the free-flying ROV (right).

One more point of comparison is use of a Laser In-Situ Scattering and 

Transmissometry (LISST) to obtain independent measurements of bubble size 

distribution. One such distribution, an average typical of an air bubble test, is shown in 

Figure 59. Both air and methane measurements, such as those shown in Figure 57, 
54

have mean bubble sizes near the LISST-measured mean bubble size and roll off toward 

larger and smaller bubble sizes at comparable rates.

Figure 59. LISST measurements performed on the air bubbler produced a bubble size distribution 

consistent with both the air and methane bubble measurements.

3.2. ACOUSTIC MEASUREMENT OF DISPERSANT EFFECTIVENESS FROM ROV

PLATFORM

Acoustic scattering data from plumes of methane bubbles and oil were measured 

with the transducers mounted to the ROV. A “sonar-like” image of the scattering from a 

plume of dispersed ANS and methane is shown in Figure 60. The resultant average 

backscattering amplitude as a function of frequency for 3 methane releases, 6 ANS with 

methane releases, and 7 dispersed ANS with methane releases is shown in Figure 61.

Figure 60. Acoustic sonar image from a plume of dispersed ANS and methane. The high scattering is 

red and low scattering is dark blue/black. Each vertical line is a single ping over the 80 second 

measurement time. The vertical axis is the distance from the center of the plume.
55

Figure 61. The backscattering amplitude as a function of frequency measured from the ROV platform

(top) and static platform (bottom) for methane, ANS and methane, and dispersed ANS and 

methane.

The backscattering results from the free swimming ROV platforms are similar to 

measurements from static platforms with the methane showing the highest 

backscattering followed by ANS with methane, then dispersed ANS and methane for 

frequencies less than 2.25 MHz. Importantly, the dependence on frequency of the 

backscattering increased as oil was added to the methane, and the dependence on 

frequency increased even more when the oil was dispersed. This increased 

dependence on frequency observed as the oil became more dispersed is similar to 

measurements we performed from a static platform submersed under the water at 

Ohmsett [Panetta et al. 2014]. Coupled with our systematic measurements from static 

platforms, these measurements from the ROV show the feasibility of measuring 

dispersant effectiveness from ROV platforms.

Dispersed ANS and Methane

ANS and Methane

Methane

Backscattering amplitude

Static Platform

ROV Platform

Dispersed ANS and Methane

ANS and Methane

Methane

Backscattering amplitude

Frequency (MHz)

Frequency (MHz)
56

4. DEPLOYMENT PLATFORMS FOR OIL SPILL RESPONSE 

We explored only two options for deployment on free swimming ROV and glider 

platforms and were the first team to the author’s knowledge to measure the slick 

thickness from ROV and glider platforms. To best transition these measurements to 

open water environments to characterize oil spills will require deployments on multiple 

platforms. The two main criteria that limit implementation on various platforms are 

power requirements and size. These restrictions are relaxed for ROV platforms since 

operations ROVs are large and carry power to the vehicle. More significant restrictions 

exist for AUV deployments because the payload space is small (typically 1 foot x 6 inch 

diameter) and the power requirements are stringent because the AUVs are battery 

operated.

5. SUMMARY AND CONCLUSIONS

In this project we have begun the transition of acoustic measurements of slick 

thickness, gas bubble size distribution, and oil dispersant effectiveness to free 

swimming ROV and glider platforms. Using a SeaBotix LBV150 ROV vehicle, we have 

demonstrated the ability to effectively measure both oil slick thickness as well as gas 

bubble/oil droplet size distribution while operating the ROV in free swimming mode in 

our labs and at Ohmsett. We also demonstrated the ability to measure the slick 

thickness using acoustic sensors mounted on a Slocum glider. The oil slick thickness 

measurements were performed both in the absence of waves as well as the presence of 

waves. Acoustic transducers were mounted externally on the frame of the ROV and the 

glider and tethered via cables to data collection and processing hardware.

While the extra sensors and cabling associated with oil slick thickness 

measurements do impact the performance and flight dynamics of the ROV, proper 

ballasting and mounting of the sensors allowed the vehicle to remain controllable and 

flyable. The existing setup could be deployable in an open water setting if the currents 

and waves are within specific limits.

The measurement of bubble size distribution required mounting of a relatively large 

and heavy low-frequency transducer and receiver on top of the ROV. This sensor 

configuration severely affected the stability, controllability and flight dynamics of the 

vehicle. While extensive ballasting measures allow the vehicle to become stable, it was 

still difficult to control and move. A larger ROV would be able to deal with the size and 

mass of the low frequency sensor much more effectively. For the purposes of research 

deployment at Ohmsett, the setup was functional but unlike the measurement of oil slick 

thickness, it would be too difficult to use in an open water deployment scenario.

To better understand the influence of sea state on vehicle motion and thus 

measurement precision, the team designed and built a custom inertial motion sensor 

package to quantify the motion of the vehicle while making oil slick thickness 
57

measurements as well as subsurface measurements of gas bubble distribution 

measurement and dispersant effectiveness. 

The technical progress made to measure the gas bubble size distribution using 

acoustic backscattering is significant and opens the opportunity to provide gas bubble 

size measurements as well as oil dispersant effectiveness from a single set of acoustic 

sensors on a single platform. The measurements of oil droplet scattering related to 

dispersant efficiency show the proof of concept from ROV platforms and produced 

results similar to static platforms from previous work. We advanced these capabilities to 

TRL 6 through multiple measurements at Ohmsett in many spill scenarios including 

surface slicks in various sea states and subsurface releases of methane and dispersed 

oil. 

6. REFERENCES

Greinert, J., & Nützel, B. (2004). Hydroacoustic experiments to establish a method for 

the determination of methane bubble fluxes at cold seeps. Geo-Marine Letters, 24(2), 

75-85.

Ainslie, M. A., & McColm, J. G. (1998). A simplified formula for viscous and chemical 

absorption in sea water. The Journal of the Acoustical Society of America, 103(3), 1671-

1672.

Commander, K. W., & Prosperetti, A. (1989). Linear pressure waves in bubbly liquids: 

Comparison between theory and experiments. The Journal of the Acoustical Society of 

America, 85(2), 732-746.

Medwin, H., & Clay, C. S. (1997). Fundamentals of acoustical oceanography. Academic 

Press.

Leighton, T. (2012). The Acoustic Bubble. Academic press

Panetta, P. D., McElhone, D., Carr, L., & Winfield, K. (2015). Acoustic Tool to Measure 

Oil Slick Thickness at Ohmsett For US Department of the Interior Bureau of Safety and 

Environmental Enforcement (BSEE).

Panetta, P. D., McElhone, D., Winfield, K., & Cartwright, G. (2014, May). Ultrasonic 

Scattering Measurements of Dispersed Oil Droplets in the Presence of Gas. In 

International Oil Spill Conference Proceedings (Vol. 2014, No. 1, pp. 266-282). 

American Petroleum Institute.
58

APPENDIX: INERTIAL POSITIONING MEASUREMENTS OF 

UNMANNED UNDERWATER VEHICLE (UUV) DYNAMICS 

INTRODUCTION 

This report is part of an ongoing study, of which main purpose is to develop 

innovative techniques for characterizing the size and flow rate of crude oil slicks and 

subsurface release, respectively. These techniques include (1) the measurement of oil 

slick thickness using the compression wave speed of oil and (2) the measurement of 

subsurface oil droplet size using ultrasonic backscattering. Both of these techniques 

are implemented using ultrasonic transducers, which emit and receive sound at an 

angle nominally normal to the slick surface or plume. However, limited UUV 

controllability in a stochastic open water environment prevents a singular transducer 

from remaining continuously normal to the slick or plume. 

This problem is overcome by considering an array of several transducers positions 

at a range of off-axis angles, such that the probability of at least one transducer being 

sufficiently perpendicular to the target is substantially increased. For this reason it is 

important to characterize the dynamic response of an acoustic measurement UUV in 

stochastic conditions. Identifying the probabilistic angular orientation of a UUV will (1) 

improve the understanding of how angular displacements from normal influence 

effectiveness of the current technique and (2) aid in transducer array design for a future 

acoustic measurement UUV prototype.

The purpose of this paper is to characterize the dynamic response of UUVs during 

wave tests at OHMSETT, where acoustic measurements were made in conjunction with 

dynamic measurements. A Seabotix LBV150^2 ROV and a Teledyne Slocum Electric 

Glider were each used as platforms for measurement of oil slick thickness. The ROV 

was subsequently used as a platform for measurement of subsurface oil release in calm 

conditions; however, this paper principally addresses dynamics of UUVs during slick 

thickness measurement. (Data regarding ROV dynamics during subsurface release 

measurement is included separately in section 5). Of primary interest are the pitch 

(fore-to-aft rotation) and roll (port-to-starboard rotation) of each UUV during acoustic 

measurement, as well as the probabilistic distribution of these rotations. Additional 

investigated properties include the body-fixed 3-axis acceleration of each UUV, as well 

as the measurable oscillatory motion of the UUV (if present) that was induced by the 

amalgamation of deliberate control input and wave conditions.

BACKGROUND

Data was recorded using a Bosch 9-DOF absolute orientation sensor and a 

Raspberry Pi Zero. The sensor uses a black box fusion algorithm to derive Euler angles 

and linear acceleration from accelerometer, rate gyroscope, and magnetometer data. 

To address concerns regarding the interference of iron trusses present in the 

OHMSETT facility and the linearization techniques used in the fusion algorithm, raw 

accelerometer and rate gyroscope measurements were also recorded to be used for a 
59

duplicate, posterior reconstruction of pitch and roll. Measurements were sampled at an 

effective rate of approximately 30Hz, which was substantially higher than Nyquist 

frequency of possible wave conditions in OHMSETT's wave tank. The maximum 

allowable data output rate for the Bosch 9-DOF sensor is 100Hz for all of fused absolute 

orientation, linear acceleration, acceleration, and angular velocity. The accelerometer is 

capable of measuring within the range and zero-g offset of ±39.2m/s^2 ± 1.47m/s^2, 

while the gyroscope is capable of measuring within the range and zero-rate offset of 

±34.91rad/s ± 0.05rad/s.

DATA PROCESSING

Coordinate Transformations

 The UUV body-fixed coordinate system is defined by the x-axis-to-forward, y-axisto-starboard, z-axis-to-downward convention. Positive angular position about each axis 

is defined using a counterclockwise convention. To circumvent the numerous differing 

conventions that can be used to define pitch and roll, angular positions from this point 

onward will be referred to as "X Euler," "Y Euler," and "Z Euler;" where "X Euler" is the 

counterclockwise rotation angle in degrees about the x-axis. The posterior 

reconstruction of X Euler will later be referred to as "Phi," while the posterior 

reconstruction of Y Euler will later be referred to as "Theta." 

 

Figure 1: UUV body-fixed coordinate system. Showing axes conventions used for linear acceleration 

and angular position. The demonstrated convention was used for both the Slocum Glider and 

the Seabotix ROV (shown). 
60

Electronic components of the measurement device were housed in a 1.4x3.1x 4.4cm 

waterproof, pressure-resistance case. This case was mounted on the ROV and Slocum 

Glider in a position that would allow for predicted minimal effect on the overall buoyancy 

and dynamics of each vehicle. 

Figure 2: Mounting of the measurement device. Showing position of measurement device on (a) 

Seabotix ROV and (b) Slocum Gilder. Waterproof case was placed inside of a protective 

pressure-resistant bag with air removed to protect from crude oil contamination. 

Measurements were subsequently transformed using a direction cosine matrix from 

the case-fixed coordinate system onto the UUV body-fixed coordinate system. The 

direction cosine matrix was used to transform measurements as follows [1]:

aa = �

aaxx

aayy

aazz

� RR = �

cos ψψxxxx,xxxx cos ψψxxxx,yy cos ψψxxxx,zz

cos ψψyy ,xxxx cos ψψyy ,yy cos ψψyy ,zz

cos ψψzz ,xxxx cos ψψzz ,yy cos ψψzz ,zz

� aabbbbbbbb = RRTT aacc cccc = RR−11 aacc cccc

EE = �

XXXXXXXXXXXX

YY

ZZ

� EEbbbbbbbb = EEcc cccc − �

ψψxxxx,xxxx

ψψyy ,yy

ψψzz ,zz

�

ψψxxxx,xxxx = ψψzz ,zz = ββ

ψψxxxx,zz = ππ

2

+ ββ

ψψzz ,xxxx = ππ

2 − ββ

ψψxxxx,yy = ψψyy ,xxxx = ψψyy ,zz = ψψzz ,yy = ππ

2

ψψyy ,yy = 0
61

In this system, aa is a vector of accelerations, EE is a vector of Euler angles, and ψψyy ,xxxx

is the angle between the case-fixed y-axis and the body-fixed x-axis. The angle ββ is the 

rotation angle about the (unchanging) y-axis from the body-fixed coordinate system to 

the case-fixed coordinate system. For both mounting cases shown in Figure 1, the 

angle ββ is acute and negative. The angle ββ is determined prior to coordinate 

transformation by plotting the pre-transformed Y Euler (and its posterior reconstruction 

Theta), locating a region of the plot for which the UUV was resting motionless on the 

deck or bottom of the wave tank, and recording this approximate angle. Angles were 

probed at the commencement of the resting period to avoid additional error from 

gyroscopic drift.

Data File Name Test 

Configuration

ββ (From Y Euler) ββ (From Theta) Averaged ββ

Feb-22_09_19_38.csv

(Test 12 through 18)

ROV Slick 

Thickness

-5.6° -5.6° -5.6°

Feb-22_13_13_06.csv

(Test 19a through 

20e)

ROV Slick 

Thickness

-5.7° -5.0° -5.35°

Feb-23_09_12_47.csv

(Test 29 through 30)

Glider Slick 

Thickness

-13.5° -13.7° -13.6°

Figure 3: Empirically determined approximate offset angle. Showing offset angle ββ to be used in 

coordinate transformation of accelerations using direction cosine matrix and rotational 

transformations of angular position vectors.

Posterior Approximation of Euler Angles

Angular position was posteriorly reconstructed from raw accelerometer and rate 

gyroscope data using a linear approximation algorithm. The posterior reconstructions of 

X Euler and Y Euler are referred to as "Phi" and "Theta," respectively. The 

approximation algorithm combines low-pass filtered acceleration data with high-pass 

filtered rate gyroscope data to prevent gradual gyroscopic drift. Frequency domain 

equations for Phi and Theta are given as follows [2]:

φφ(ss) = − aayy(ss)

gg � 1ττ + 1

� +

ωωxx(ss)

ss � ττ

ττ + 1

�

θθ(ss) = aaxx(ss)

gg � 1ττ + 1

� +

ωωyy(ss)

ss � ττττ + 1

�
62

In this system, aayy is the y-axis component of raw acceleration (m/s^2), gg is the 

gravitational acceleration (m/s^2) in the z-axis direction, and ωωxx is the x-axis component 

of angular velocity (rad/s). The parameter ττ is an approximate time constant of the 

linearized time-invariant system. A time constant of 1/3 was selected for the algorithm. 

The posterior approximation of angular was evaluated for similarity to the Bosch 

sensor's fusion algorithm using data collected during both Seabotix ROV and Slocum 

Glider movement.

Figure 4: Comparison of Bosch sensor fusion algorithm vs. posterior approximation for Test 14b. 

Showing Seabotix ROV angular position in wave conditions.
63

Figure 5: Comparison of Bosch sensor fusion algorithm vs. posterior approximation for Test 30. Showing 

Slocum Glider angular position during a diving and surfacing procedure.

Filtering

Linear acceleration data was filtered using a bilinear transform filter in order to 

remove high frequency electrical noise [2]. A bandwidth of 3Hz was selected for the 

filter. Raw and filtered linear acceleration data was examined to verify effectiveness of 

the selected bandwidth.
64

Figure 6: Comparison of raw linear accelerations vs. filtered linear accelerations for a 

preliminary maneuver that occurred before Test 29. Showing linear accelerations during a 

preliminary Slocum Glider diving and surfacing procedure.

Cross-Correlation

Cross-correlation of 3-axis acceleration signals was used to investigate the overall 

influence of wave conditions on UUV motion during each test. It is important to note that 

for the Seabotix ROV, periodicity of acceleration signals is the result of both stochastic 

conditions in the wave tank as well as active control from the ROV operator. A peak 

prominence algorithm was used to detect periodicity in each cross-correlation plot. 
65

Figure 7: Cross-Correlation plot of ROV linear acceleration for Test 19c. Showing peak detection using a 

minimum threshold height of 0.1. Frequency of UUV motion was approximated from the mean 

difference in peak locations within the time lag domain of contiguously detected peaks (shown 

with annotation). 

Metrics of Angular Position

Univariate histograms, bivariate histograms, and descriptive statistics were used to 

derive probabilistic information about the pitch and roll during wave tests. For tests 

using the Seabotix ROV, mean and standard deviation were of primary interest. Glider 

tests were characterized in terms of dive and climb angle, for the reason that mean and 

standard deviation of measurements for a full test would be of little meaning in a 

multimodal distribution.
66

Figure 8: Probability distribution through time of Seabotix ROV angular position for Test 13. 

Showing (a) a univariate histogram for pitch (Y Euler) derived from the Bosch fusion algorithm 

and (b) a bivariate histogram for pitch (Theta) vs. roll (Phi) derived from the posterior 

approximation.
67

Figure 9: Probability distribution through time of Slocum Glider angular position for Test 29. 

Showing bivariate histograms for pitch (Y Euler, Theta) vs. roll (X Euler, Phi) derived from (a)

the Bosch fusion algorithm and (b) the posterior approximation.
68

RESULTS

Test Mean Wave 

Height [m]

Significant 

(Highest 1/3) 

Wave Height [m]

Mean 

Wavelength [m]

WMO Sea 

State

Wave Frequency

[Hz]

12 0.4851 0.5867 12.3444 3 (Slight) 0.33

13 0.3302 0.3785 12.1615 2 (Smooth) 0.33

14a 0.4039 0.4267 12.1310 2 (Smooth) 0.33

14b 0.4039 0.4267 12.1310 2 (Smooth) 0.33

15 0.1219 0.2235 11.1862 2 (Smooth) 0.35

16 0.5029 0.5715 11.9786 3 (Slight) 0.33

17 0.5436 0.5918 11.9786 3 (Slight) 0.33

18 0.1676 0.2845 11.5824 2 (Smooth) 0.34

19a 0.0991 0.1219 6.4618 2 (Smooth), 0.49

19b 0.0533 0.0889 3.2004 1 (Calm) 0.70

19c 0.0635 0.1016 4.7244 2 (Smooth) 0.57

19d 0.1092 0.1803 5.9131 2 (Smooth) 0.51

20a 0.1702 0.2286 2.9261 2 (Smooth) 0.73

20b 0.1549 0.2388 3.6881 2 (Smooth) 0.65

20c 0.1524 0.2337 3.5357 2 (Smooth) 0.66

20d 0.0914 0.1448 3.6881 2 (Smooth) 0.65

20e 0 0 0 0 (Calm) None

29 0.0406 0.0711 16.3373 1 (Calm) 0.26

30 0.0432 0.0838 15.1486 1 (Calm) 0.28

Figure 10: Summary of wave conditions. Showing mean and significant wave heights, mean wavelength, 

World Meteorological Organization sea state code, and wave frequency. Wave frequency was 

determined using the intermediate dispersion relation and a wave tank depth of 2.4 meters. 

Test Wave 

Frequency 

[Hz]

Acceleration 

Cross-correlation 

(XY, YZ, ZX) [Hz]

Mean Angular 

Position

Standard 

Deviation

Time Interval 

[Min.]

12 0.33 0.34, 0.35, 0.34 Phi -1.30° Phi = 1.52° 73-82
69

Y Euler = 0.46°

Theta = 1.57°

Y Euler = 2.23°

Theta = 3.28°

13 0.33 0.34, 0.33, 0.33 Phi = -1.17°

Y Euler = 1.07°

Theta = 1.28°

Phi = 1.79°

Y Euler = 2.43°

Theta = 2.36°

84-91

14a 0.33 0.34, 0.34, 0.34 Phi = -0.77°

Y Euler = 1.33°

Theta = 1.79°

Phi = 2.08°

Y Euler = 2.23°

Theta = 2.97°

92-100

14b 0.33 0.34, 0.34, 0.34 Phi = -1.55°

Y Euler = 0.97°

Theta = 1.05°

Phi = 1.07°

Y Euler = 1.99°

Theta = 2.53°

115-117

15 0.35 Low, 0.25, 0.25 Phi = -1.09°

Y Euler = 0.81°

Theta = 1.36°

Phi = 1.59°

Y Euler = 2.40°

Theta = 2.91°

120-126

16 0.33 0.34, 0.34, 0.34 Phi = -1.50°

Y Euler = 0.61°

Theta = 2.05°

Phi = 1.44°

Y Euler = 2.47°

Theta = 3.64°

131-138

17 0.33 0.34, 0.34, 0.34 Phi = -1.15°

Y Euler = 0.37°

Theta = 1.55°

Phi = 1.69°

Y Euler = 2.94°

Theta = 4.36°

140-147

18 0.34 0.34, 0.34, 0.34 Phi = -0.60°

Y Euler = 0.20°

Theta = 1.05°

Phi = 2.33°

Y Euler = 2.71°

Theta = 3.40°

150-157

19a 0.49 0.50, 0.51, 0.50 Phi = -2.13°

Y Euler = 0.51°

Theta = 3.00°

Phi = 2.29°

Y Euler = 2.35°

Theta = 3.62°

27-34

19b 0.70 0.51, 0.51, 0.50 Phi = -2.48°

Y Euler = 0.32°

Theta = 2.06°

Phi = 2.40°

Y Euler = 1.94°

Theta = 1.99°

34-41

19c 0.57 0.51, 0.51, 0.52 Phi = -2.21° Phi = 2.60° 42-49
70

Y Euler = -0.51°

Theta = 1.77°

Y Euler = 3.94°

Theta = 4.70°

19d 0.51 0.51, 0.51, 0.50 Phi = -1.98°

Y Euler = 0.63°

Theta = 2.28°

Phi = 1.35°

Y Euler = 2.97°

Theta = 3.47°

52-59

20a 0.73 Low, 0.73, 0.73 Phi = -1.87°

Y Euler = -0.03°

Theta = 2.97°

Phi = 2.24°

Y Euler = 4.76°

Theta = 6.02°

75-82

20b 0.65 Low, 0.61, 0.62 Phi = -2.72°

Y Euler = -0.21°

Theta = 3.90°

Phi = 2.46°

Y Euler = 3.56°

Theta = 4.72°

84-91

20c 0.66 0.58, 0.58, 0.58 Phi = -1.75°

Y Euler = 1.71°

Theta = 3.14°

Phi = 1.79°

Y Euler = 1.68°

Theta = 2.08°

92-99

20d 0.65 Low, Low, Low Phi = -1.89°

Y Euler = 0.94°

Theta = 2.32°

Phi = 1.97°

Y Euler = 2.53°

Theta = 3.20°

99-107

20e None Low, Low, Low Phi = -1.84°

Y Euler = 1.77°

Theta = 3.56°

Phi = 1.22°

Y Euler = 1.58°

Theta = 2.62°

117-122

Figure 11: Summary of Seabotix ROV dynamic response. Showing ROV periodicity of motion in 

comparison to wave frequency, and descriptive statistics for angular position through time. 

Test Wave 

Frequency* 

[Hz]

Acceleration Crosscorrelation (XY, YZ, 

ZX) [Hz]

Peak Climb 

Angle

Dive Angle Time Step 

(Min.)

29 0.26 Low, 0.25, Low Y Euler = 25.50°

Theta = 25.35°

Y Euler = -15.77°

Theta = -15.60°

401-408

30 0.28 Low, 0.25, Low Y Euler = 25.64°

Theta = 25.68°

Y Euler = -17.37°

Theta = -17.49°

409-419

Figure 12: Summary of Slocum Glider dynamic response. Showing Glider periodicity of motion in 

comparison to wave frequency, and highest-mode (through time) angles during diving and 

surfacing procedures.
71

Figure 13: Distribution of Phi standard deviation as a function of wave frequency (x) and significant wave 

height (y). The linear fit is given by the equation f(x,y) = 1.391 + 1.373x - 0.4738y and carries 

a root-mean-square error of 0.3823.
72

Figure 14: Distribution of Y Euler standard deviation as a function of wave frequency (x) and significant 

wave height (y). The linear fit is given by the equation f(x,y) = 1.525 + 2.177x + 0.4492y and 

carries a root-mean-square error of 0.7628.
73

Figure 15: Distribution of Theta standard deviation as a function of wave frequency (x) and significant 

wave height (y). The linear fit is given by the equation f(x,y) = 2.222 + 2.027x + 0.9589y and 

carries a root-mean-square error of 1.059.
74

Figure 16: Standard deviation of angular position with respect to WMO sea state. Showing data and 

linear fits for all tests. The linear fit for Phi is given by the equation y = -0.024x + 1.920 and 

carries a root-mean-square error of 0.4831. The linear fit for Y Euler is given by the equation y 

= 0.318x + 1.995 and carries a root-mean-square error of 0.8143. The linear fit for Theta is 

given by the equation y = 0.506x + 2.392 and carries a root-mean-square error of 1.031.
75

DYNAMICS OF SUBSURFACE RELEASE ROV CONFIGURATION

Figure 17: Mounting of the measurement device on the ROV during subsurface release testing. Note 

that measurement device is mounted directly posterior to the low-frequency transducer (shown 

wrapped with buoyancy foam). 

Data File Name Test 

Configuration

ββ (From Y Euler) ββ (From Theta) Averaged ββ

Feb-24_10_38_32.csv

(Flights A through M)

ROV Subsurface 

Release

-8.1° -6.7° -7.4°

Figure 18: Empirically determined approximate offset angle of subsurface release configuration. Showing 

offset angle ββ to be used in coordinate transformation of accelerations using direction cosine 

matrix and rotational transformations of angular position vectors.
76

Figure 19: Intermittent flights during subsurface release testing. Showing angular position of Seabotix 

ROV while quipped with a low-frequency transducer. 

Flight Mean Angular Position Standard Deviation Time Interval [Min.]

A Phi = -2.40°

Y Euler = -1.73°

Theta = 0.51°

Phi = 3.64°

Y Euler = 5.63°

Theta = 6.53°

174.00-175.83

B Phi = -2.11°

Y Euler = -3.44°

Theta = -0.12°

Phi = 5.58°

Y Euler = 6.64°

Theta = 7.69°

176.5-178.40

C Phi = -1.75°

Y Euler = -3.40°

Theta = 1.95°

Phi = 6.41°

Y Euler = 6.68°

Theta = 9.36°

179.33-181.33
77

D Phi = -3.15°

Y Euler = -3.29°

Theta = -0.17°

Phi = 3.71°

Y Euler = 6.37°

Theta = 8.50°

181.83-183.50

E Phi = -2.44°

Y Euler = -2.74°

Theta = -0.71°

Phi = 4.16°

Y Euler = 5.59°

Theta = 5.79°

184.67-186.10

F Phi = -3.62°

Y Euler = -2.75°

Theta = 4.08°

Phi = 3.73°

Y Euler = 6.31°

Theta = 7.88°

186.67-188.40

G Phi = -1.64°

Y Euler = -2.44°

Theta = -0.22°

Phi = 4.68°

Y Euler = 5.28°

Theta = 6.43°

189.83-191.60

H Phi = -1.60°

Y Euler = -3.40°

Theta = -1.11°

Phi = 4.56°

Y Euler = 7.04°

Theta = 8.08°

192.83-194.30

I Phi = -0.50°

Y Euler = -2.31°

Theta = 0.59°

Phi = 6.23°

Y Euler = 5.83°

Theta = 6.68°

197.00-198.50

J Phi = -1.74°

Y Euler = -1.45°

Theta = 2.40°

Phi = 5.71°

Y Euler = 4.65°

Theta = 6.01°

201.50-204.50

K Phi = -1.61°

Y Euler = -1.74°

Theta = 0.13°

Phi = 4.88°

Y Euler = 5.81°

Theta = 6.43°

205.57-207.00

L Phi = -3.59°

Y Euler = -3.74°

Theta = 1.33°

Phi = 5.77°

Y Euler = 6.77°

Theta = 8.76°

208.00-211.00

M Phi = 1.99°

Y Euler = -1.61°

Theta = 1.08°

Phi = 4.49°

Y Euler = 5.19°

Theta = 5.82°

212.17-213.00
78

Pooled Standard Deviation: Phi = 5.25°

Y Euler = 6.05°

Theta = 7.58°

Figure 20: Summary of Seabotix ROV dynamic response during subsurface release testing. Showing 

mean and standard deviation of angular position through time for flights with low-frequency 

transducer.

Figure 21: ROV angular position in subsurface release configuration during Flight M. Showing 

substantial variation in pitch and roll due to amalgamation of control input and the moment 

created by the off-axis drag force of the low-frequency transducer.
79

Figure 22: ROV linear acceleration in subsurface release configuration during Flight M. Showing 

accelerations associated with substantial variation in angular position. Note that the ROV 

body-fixed coordinate system continues to be defined by the x-axis-to-forward, y-axis-tostarboard, z-axis-to-downward convention.
80

Figure 23: Probability distribution through time of Seabotix ROV angular position in subsurface release 

configuration during Flight M. Showing a bivariate histogram for pitch (Theta) vs. roll (Phi)

derived from the posterior approximation.

REFERENCES

[1] Diebel, James, 2006, Representing Attitude: Euler Angles, Unit Quaternions, and Rotation

Vectors, Stanford University, Stanford, CA.

[2] Hover, Franz S., 2016, Design of Electromechanical Robotic Systems: Worked Problems, 

MIT Center for Ocean Engineering, Cambridge, MA.