# Imaging of Artificial Bubble Distribution Using a Multi-Sonar Array System

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## Abstract

**:**

## 1. Introduction

## 2. Imaging Technique for Bubble Distribution

## 3. Design of the Sea Experiment

#### 3.1. Experiment Configuration

#### 3.2. Development of a Measurement System

#### 3.3. Artificial Bubble Generation

#### 3.4. Data Measurement

#### 3.5. Data Preprocessing

## 4. Results

#### 4.1. Synthetic Data Application

#### 4.2. Artificial Bubble Estimation Using Envelope RTM

#### 4.3. Quantitative Approach for Artificial Bubble Boundary

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- La Prairie, A.J.C. Method of Blasting. U.S. Patent 2,699,117, 11 January 1955. [Google Scholar]
- Wind Farm Noise Reduced by Air Bubble Curtain. Available online: https://www.engineerlive.com/content/wind-farm-noise-reduced-air-bubble-curtain (accessed on 20 November 2022).
- Fessenden, R.A. Method and Apparatus for Sound Insulation. U.S. Patent 1,348,828, 3 August 1920. [Google Scholar]
- Direction of Commander, Naval Sea Systems Command. Chapter 5. Masker Emitter Belts. In Underwater Ship Husbandry Manual; S0600-AA-PRO-050; Naval Sea Systems Command: Washington, DC, USA, 23 February 1995. [Google Scholar]
- Lee, H.; Moon, Y.; Kang, S. Tests on Ventilation Control of PRAIRIE for Improving Acoustic Stealth Performance. J. Korea Inst. Mil. Sci. Technol.
**2020**, 23, 602–608. [Google Scholar] [CrossRef] - Moon, Y.; Lee, H.; Choi, J.-Y.; Kim, S.-Y. A Study on Underwater Radiated Noise Characteristics of Naval Vessel with PRAIRIE According to Air Leakage Condition. Trans. Korean Soc. Noise Vib. Eng.
**2022**, 32, 268–273. [Google Scholar] [CrossRef] - Lamarre, E.; Melville, W.K. Instrumentation for the measurement of sound speed near the ocean surface. J. Atmos. Ocean Technol.
**1995**, 12, 317–329. [Google Scholar] [CrossRef] - Terrill, E.; Melville, W.K. Sound-speed measurements in the surface-wave layer. J. Acoust. Soc. Am.
**1997**, 102, 2607–2625. [Google Scholar] [CrossRef] [Green Version] - Vagle, S.; Farmer, D.M. The measurement of bubble-size distributions by acoustical backscatter. J. Atmos. Ocean Technol.
**1992**, 9, 630–644. [Google Scholar] [CrossRef] - Bae, H.S.; Kim, W.-K.; Son, S.-U.; Kim, W.-S.; Park, J.-S. An Estimation of the Backscattering Strength of Artificial Bubbles Using an Acoustic Doppler Current Profiler. Sensors
**2022**, 22, 1812. [Google Scholar] [CrossRef] - Johnson, B.D.; Cooke, R.C. Bubble populations and spectra in coastal waters: A photographic approach. J. Geophys. Res. Ocean.
**1979**, 84, 3761–3766. [Google Scholar] [CrossRef] - Stokes, M.D.; Deane, G.B. A new optical instrument for the study of breaking waves at high void fractions within breaking waves. IEEE J. Ocean Eng.
**1999**, 24, 300–311. [Google Scholar] [CrossRef] - Park, C.; Jeong, S.W.; Kim, G.D.; Park, Y.; Moon, I.; Yim, G. An empirical model of air bubble size for the application to air masker. J. Acoust. Soc. Korea
**2021**, 40, 320–329. [Google Scholar] - Medwin, H.; Brietz, N.D. Ambient and transient bubble spectral densities in the quiescent seas and under spilling breakers. J. Geophys. Res.
**1989**, 94, 12751–12759. [Google Scholar] [CrossRef] - Farmer, D.M.; Vagle, S.; Booth, A.D. A free-flooding acoustical resonator for measurement of bubble size distributions. J. Atmos. Ocean. Technol.
**1998**, 15, 1132–1146. [Google Scholar] [CrossRef] - Woodward, M.J. Wave-equation tomography. Geophysics
**1992**, 57, 15–26. [Google Scholar] [CrossRef] - Shen, X.; Clapp, R.G. Random boundary condition for memory-efficient waveform inversion gradient computation. Geophysics
**2015**, 80, R351–R359. [Google Scholar] [CrossRef] - Zhang, P.; Wu, R.S.; Han, L. Source-independent seismic envelope inversion based on the direct envelope Fréchet derivative. Geophysics
**2018**, 83, R581–R595. [Google Scholar] [CrossRef] - Chang, W.F.; McMechan, G.A. Elastic reverse-time migration. Geophysics
**1987**, 52, 1365–1375. [Google Scholar] [CrossRef] - Shin, C.; Min, D.J.; Yang, D.; Lee, S.K. Evaluation of poststack migration in terms of virtual source and partial derivative wavefields. J. Seism. Explor.
**2003**, 12, 17–37. [Google Scholar] - McMechan, G.A. Migration by extrapolation of time-dependent boundary values. Geophys. Prospect.
**1983**, 31, 413–420. [Google Scholar] [CrossRef] - Zhou, H.W.; Hu, H.; Zou, Z.; Wo, Y.; Youn, O. Reverse time migration: A prospect of seismic imaging methodology. Earth-Sci. Rev.
**2018**, 179, 207–227. [Google Scholar] [CrossRef] - Chung, W.; Pyun, S.; Bae, H.S.; Shin, C.; Marfurt, K.J. Implementation of elastic reverse-time migration using wavefield separation in the frequency domain. Geophys. J. Int.
**2012**, 189, 1611–1625. [Google Scholar] [CrossRef] [Green Version] - Wu, R.S. Multiple scattering and energy transfer of seismic wave separation of scattering effect from intrinsic attenuation. I: Theoretical modeling. Geophys. J. Int.
**1985**, 82, 57–80. [Google Scholar] [CrossRef] [Green Version] - Wu, R.S.; Chen, G.X. New Fréchet Derivative for Envelope Data and Multi-Scale Envelope Inversion. In Proceedings of the 79th EAGE Conference and Exhibition 2017, Paris, France, 12–15 June 2017; pp. 1–5. [Google Scholar]
- Liu, B.; Sacchi, M.D. Minimum weighted norm interpolation of seismic records. Geophysics
**2004**, 69, 1560–1568. [Google Scholar] [CrossRef] [Green Version] - Alford, R.M.; Kelly, K.R.; Boore, D.M. Accuracy of finite-difference modeling of the acoustic wave equation. Geophysics
**1974**, 39, 834–842. [Google Scholar] [CrossRef] [Green Version] - Turkel, E.; Yefet, A. Absorbing PML boundary layers for wave-like equations. Appl. Numer. Math.
**1998**, 27, 533–557. [Google Scholar] [CrossRef] - Liu, Q.H.; Tao, J. The perfectly matched layer for acoustic waves in absorptive media. J. Acoust. Soc. Am.
**1997**, 102, 2072–2082. [Google Scholar] [CrossRef]

**Figure 2.**Measurement system (marine buoy component) configuration: (

**a**) mounted boards and (

**b**) assembled electronic unit.

**Figure 3.**Acoustic sensors of the measurement system: (

**a**) receiving sensor (hydrophone), depth sensor, and (

**b**) transmitting sensor (projector).

**Figure 4.**Characteristics of acoustic sensors: (

**a**) receiving voltage sensitivities of hydrophones and (

**b**) source levels of projectors. Black solid lines indicate mean values.

**Figure 5.**Photographs of the sea experiment: (

**a**) measurement system deployment and (

**b**) acoustic data acquisition.

**Figure 9.**(

**a**) True sound speed structure for generating the synthetic data and estimated results of bubble distribution (

**b**) by using a 250 Hz Ricker wavelet and (

**c**) the 160 Hz first derivative of a Gaussian wavelet. The solid black circles represent the transmitting sensors, whereas the open circles represent the receiving sensors.

**Figure 10.**Comparison of acoustic sources used for numerical modeling: (

**a**) time domain and (

**b**) frequency domain.

**Figure 11.**Two-dimensional sections indicated by the gray slice in Figure 9c: (

**a**) X–Y section, (

**b**) X–Z section, and (

**c**) Y–Z section.

**Figure 12.**Estimation results of artificial bubble distribution using envelope RTM: (

**a**) t = 60 s (cycle #10), (

**b**) 102 s (#17), (

**c**) 162 s (#27), and (

**d**) 222 s (#37). The solid black circles represent the transmitting sensors, whereas the open circles represent the receiving sensors.

**Figure 13.**Sectional views at the gray slice location in Figure 12c: (

**a**) Y–Z section, (

**b**) X–Z section, and (

**c**) Y–Z section.

**Figure 14.**Backscattering strength of the artificial bubble cluster obtained through ADCP observation data.

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**MDPI and ACS Style**

Bae, H.S.; Kim, W.-K.; Son, S.-U.; Park, J.-S.
Imaging of Artificial Bubble Distribution Using a Multi-Sonar Array System. *J. Mar. Sci. Eng.* **2022**, *10*, 1822.
https://doi.org/10.3390/jmse10121822

**AMA Style**

Bae HS, Kim W-K, Son S-U, Park J-S.
Imaging of Artificial Bubble Distribution Using a Multi-Sonar Array System. *Journal of Marine Science and Engineering*. 2022; 10(12):1822.
https://doi.org/10.3390/jmse10121822

**Chicago/Turabian Style**

Bae, Ho Seuk, Won-Ki Kim, Su-Uk Son, and Joung-Soo Park.
2022. "Imaging of Artificial Bubble Distribution Using a Multi-Sonar Array System" *Journal of Marine Science and Engineering* 10, no. 12: 1822.
https://doi.org/10.3390/jmse10121822