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Study of vertical coherence in shallow water ambient noise.


Nearly 70% of earth surface is covered with water but the marine environment plays a very complex role in transmission of signals. This is due to the fact that in terrestrial communication electromagnetic waves are used for transmission whereas in underwater due to the dissipative nature of water especially salt water they get extremely attenuated and this limits their usage [3]. Similarly optical signals are also rapidly absorbed in sea water and get easily scattered by suspended particles and high level of ambient light in upper part of water column and this limits its applications, hence acoustic waves are the only means to carry information underwater. These have better transmission characteristics that air [1].

A. Ambient noise:

Ambient noise has a major role in underwater since these are the noises that are present after all easily identifiable sound sources are eliminated. Ambient noise in the ocean is represented as a superposition of independent, uncorrelated plane waves propagating in all directions.

The various sources of noise includes biological noise, thermal noise, human made noise and geophysical noise. These have to be processed and removed since it degrades the data collected. When compared to noise sources such as ship, rain, biological and human activities underwater ambient noise level is dominated by wind for a significant range of frequency [2]. Deane et al. [3], have reported shallow water noise coherence and showed the measured vertical coherence by a simple model in which the input parameters represent the known geoacoustic properties of the sediment bed.

Rest of the paper is organized in the following manner; Section II gives a brief explanation about vertical coherence, mathematical analysis and the spectral estimation for the signal. Section III describes about results and analysis obtained from coherence analysis. Finally, the conclusion and future work is discussed in Section IV.

B. Measurements:

A set of ambient noise data was collected at off shores, Chennai using the vertical linear array of hydrophones deployed at various locations at 15m depth, off shores Chennai. The data were collected at a wind speed of 2m/s to 7m/s. The sampling frequency range for the data is 20 kHz.

Fig. 1 shows the measurement set up for collecting the real time data. The collected data will be in the form of voltage readings that will be recorded in the data acquisition system (DAS) which will be placed in the data collecting vessel. This data will be converted to the pressure unit, upa and then their spectrum is calculated using Welch method of modified period gram using a Hamming window with 50% overlap.

Vertical Coherence:

Vertical coherence of ambient noise is an attractive area were more attention have been given to ambient noise in deep ocean but only few shallow water measurements have been reported during 1960's in the frequency range of less than 2kHz [5]. Coherence is defined as a measure of the phase and amplitude relationship between set of acoustic waves. It is the property by which two or more waves, fields are in phase with every other. The coherence of waves is quantified by cross-correlation function. The pressure sensors placed at various points will give same outputs only if the noise is perfectly coherent and vice-versa. The coherence function depends upon the separation and orientation of the two receivers, the frequency band employed, and integration time used. Especially important is the multipath structure of the sea between the sources and the two receivers, that is, upon the manner of propagation. When there is a strong dominant propagation path, as inside a convergence zone, the coherence is high. The coherence will be low when there are more number of multipath propagation in the medium.

A. Coherence function:

The coherence function is given by [tau] where it gives the noise pressure fluctuations at two hydrophones namely x and y.

[[tau].sub.xy] = [bar.[s.sub.xy]]/[square root of ([bar.[s.sub.xx]] x [bar.[s.sub.yy]])] (1)

Where [[tau].sub.xy] is the Coherence function between x and y, [bar.[S.sub.xy]] is the cross spectral density, [bar.[S.sub.xx]] and [bar.[S.sub.yy]] represents the power spectral density for x and y and the overbar is used to show that they give the ensemble avearge. Hence, as a result of normalization, [[tau].sub.xy] is independent to the spectral shape of the sources. If two spectrally distinct source mechanisms were present like shipping and surface waves, then [[tau].sub.xy] would depend only on the frequency-dependent relative weighing of the two source spectra [5]. In spatially homogeneous noise, coherence function depends only on the separation and orientation of the sensors, and not on their position in the water column. Real part of the coherence function gives the Symmetric component and the imaginary partgives the antisymmetric component. Spatial correlation of ambient noise between pairs of hydrophones is obtained as a function of frequency [6].

B. Vertical directional density function:

The vertical directional function is given by the real and imaginary components present in the signal. This vertical directional density function is given by, F([theta]) were [theta] gives the polar angle from upward direction. Hence the coherence function is given by its finite Fourier transform of the noises at two vertically separated sensors. The sensor separation is given by d, and k is the acoustic wave number k = [omega]/c, where [omega] angular frequency and c is sound speed.

[[tau].sub.xy](kd) = [1/2][[integral].sup.[pi].sub.0]F([theta])[exp.sup.(-jkdcos[theta])]sin[theta]d[theta] (2)

F([theta]) Is given by its even and odd components of the signal such as,

F([theta]) = [F.sub.e]([theta]) + [F.sub.o]([theta]) (3)

From the above equation the real and imaginary components can be given by,

Re[[[tau].sub.xy](kd)] = [1/2][[integral].sup.[pi].sub.0]Fe([theta])cos(kdcos[theta])sin[theta]d[theta] (4)


Im[[[tau].sub.xy](kd)] = [1/2][[integral].sup.[pi].sub.0][F.sub.o]([theta])sin(kdcos[theta])sin[theta]d[theta] (5)

The vertical coherence of surface generated noise in the shallow water is given by the following equation.

[[tau].sub.xy] = 2{[sin kd/kd + cos kd - 1/[k.sup.2][d.sup.2]] + j[cos kd/kd - sin kd/[k.sup.2][d.sup.2]]} (6)

This is used only if the incident sound is transparent to the bottom that is there would be no reflections from the seabed which is equivalent to the situation where the seabed is infinitely remote .In the noise field, the symmetric component is obtained from the real part and the ant symmetric component is obtained from the imaginary part of the signal. Since, coherence is to be stable over wide range of environmental conditions the normalized measurements are used.

C. Spectral Estimation:

The spectral estimation is very important for obtaining the coherence function. For this the power spectral density (PSD) is obtained for various locations and their corresponding cross spectral density (CPSD) is estimated. The PSD gives the strength of the signal spread over certain frequency range. The PSD can be normally estimated by two methods namely Non-Parametric and Parametric method. In this paper PSD is estimated using Non-Parametric method since it has less computational complexity and can be used when little knowledge about the signal is known. In order to obtain the PSD in Non-parametric method the Welch period gram method is applied. Welch method is used to obtain PSD of the signal since it gives the PSD by reducing the effect of noise [7].

PSD shows at which frequency the signal strength is strong and vice versa. Spectral estimation is based on the idea of finding the autocorrelation sequence of a random process and taking its Fourier transform to find the estimate of power spectrum. PSD is the Fourier transform of autocorrelation and CPSD is the Fourier transform of cross correlation.CPSD gives the relation between two set of data [8].

Fig. 3 and 4 gives the power spectral estimation separately obtained for location 1 and location 2, which is obtained with the Welch period gram estimation method using the hamming window technique. This is a nonparametric method and hence has less computational complexity when only little knowledge about the signal is known. Power spectrum gives the strength of the signal.

Fig. 5 shows the power spectral estimation by combining the data collected from location 1 and 2. It is clear that for certain power range, the effect of wind is large and the signal is attenuated to a larger extent. In the frequency range of 7-9 kHz a raise in the power level is noted and at lower frequencies much of variations is not found. Fig. 6 shows the cross spectral estimation for all the location. For the obtained cross spectrum the coherence is plotted

Fig. 7 gives the plot for coherence. It is observed that noise is dominated more by surface and due to which lesser spacing in the coherence occurs and amplitude also gradually decreases. Fig. 8 gives the real and imaginary part which is associated with the symmetric and anti-symmetric components of the signal. Imaginary component shows that the bottom is highly reflective which gives rise to noise field that is symmetric in the horizontal and is given by small oscillations at about zero

Conclusion and Future work:

Hence from the above results it is clear that Coherence is less sensitive to changes in surface condition. Since coherence is a normalized measurement, the ambient noise field is stable over wide range of environmental conditions. With respect to the theory coherence structure is primarily controlled by seabed reflectivity which depends on bottom properties depending on sound velocity profile of the water column. For the future work, this can be extended to obtain geo-acoustic inversion in order to get the properties of sea bed.


[1.] Robert, J. Urick, 1983. "Principles of Underwater Sound,"in McGraw Hill, 3rd Edition.

[2.] Christopher, T., Tindle, Grant B. Deane and Michael J. Buckingam, 1997. "Vertical Coherence of Ambient Noise in Shallow Water overlying a fluid seabed," in J.AcoustSoc.Am, pp: 0001-4966/97/102.

[3.] Robert, I. Odom, 2002. "An Introduction to Underwater Acoustic principles and applications," in association with Praxispublishing, Chichester, Springer, ISBN3, pp: 3/540/42967.

[4.] Latha, G., S. Ramji and S. Ramakrishnan, 2007. "Analysis of Fluctuations in wind dependent Shallow water ambient noise spectrum, Fluctuation and Noise," J. Acoust. Am, 7(3): 313-319.

[5.] Latha, G., M.C. Sanjana and V. Rajendran, 2009. "Vertical Coherence Of ambient noise in shallow water of Bay of Bengal," in the Proceedings of Sympol.

[6.] Hansa Rani Gupta, Sushila BAtan and Rajesh Mehra, 2013. "Power Spectrum Estimation using welch method for various Window techniques," in International Journal of Scientific Research and Technology, 2(6): 389-392.

[7.] Sanjana, M.C., G. Latha and K. Nithyanandam, 2014. "Stability of Vertical Coherence of Ambient Noise in Shallow water off the Indian Coast," in Indian Journal of Geo-Marine Sciences, 5: 444-727.

[8.] Ashokan, M., G. Latha, R. Ramesh and A. Thirunavukkarasu, 2014. "Analysis of Underwater rain noise from Shallow Water ambient noise measurements in Indian Seas," in Indian Journal of Geo-Marine Sciences, Am 67: 1988-1996.

(1) S. M. Asha Banu, (2) S. Sakthivel Murugan, (3) P. Venugopal

(1) Department of ECE SSN college of Engineering Chennai, India.

(2) Department of ECE SSN college of Engineering Chennai, India.

(3) Department of Mathematics SSN college of Engineering Chennai, India.

Received 7 June 2016; Accepted 12 October 2016; Available 20 October 2016

Address For Correspondence:

S. M. Asha Banu, Department of ECE SSN college of Engineering Chennai, India.


Caption: Fig. 1: Setup for data collection

Caption: Fig. 2: Block diagram for Coherence analysis

Caption: Fig. 3: Power spectral density for location 1

Caption: Fig. 4: Power spectral density for location 2

Caption: Fig. 5: Power spectral density for location 1 and 2

Caption: Fig. 6: Cross spectral density for location 1 and 2

Caption: Fig. 7: Plot for Coherence

Caption: Fig. 8: Real and imaginary coherence
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Author:Banu, S.M. Asha; Murugan, S. Sakthivel; Venugopal, P.
Publication:Advances in Natural and Applied Sciences
Article Type:Report
Geographic Code:9INDI
Date:Sep 15, 2016
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