 Research
 Open Access
Selfsimilarity property of acoustic data acquired in shallow water environment
 Jin Chen^{1, 2},
 Fajie Duan^{2},
 Jiajia Jiang^{2},
 Baoju Zhang^{1},
 Ying Tong^{1}Email author and
 Jun He^{3}
https://doi.org/10.1186/16871499201391
© Chen et al.; licensee Springer. 2013
 Received: 29 December 2012
 Accepted: 4 March 2013
 Published: 28 March 2013
Abstract
Underwater acoustic modeling in shallow water environment is difficult since sound waves reflect several times between the surface and the water bottom. This article discusses an underwater acoustic characteristics analysis method based on selfsimilarity. It is found that acoustic signal has good selfsimilarity in shallow water. The actual towed hydrophone linear array was established and it was used for underwater acoustic signal acquisition experiment in Qilihai Reservoir which is located in the suburb of Tianjin, China. It can be derived that the signals acquired by hydrophones have selfsimilarity by the analysis of the variance of maggregated time series. It is proved that the characteristics of selfsimilarity can be used for the sound pulse propagation in shallow water.
Keywords
 Fractal
 Selfsimilarity
 Towed hydrophone linear array
 Shallow water environment
1. Introduction
The hydrophone array plays an increasingly important role in access to the ocean information. For example, active acoustic detection methods can also be used for realtime monitoring of marine fish density and behavior [1–3]. Compared with the traditional way, the method of ocean acoustic waveguide and hydrophone linear array can implement thousands of square kilometers of realtime imaging, and continuous monitoring in specified sea water. As a type of active acoustic detection, underwater seismic exploration is widely used in the detection of potential seabed oil, natural gas resources reservoir, combustible ice, and other resources. Norwegian Gullfaks oil field went into operation in 1986. In order to improve the efficiency of field collection, the four timelapse seismic measurements were fulfilled in 1985 (baseline data), 1995, 1996, and 1999, respectively. Through timelapse seismic data, they carried out analysis and forecasting the movement of water injected. As a result, the recovery factor of oil fields to increase about 2% [4]. In the monitoring oilfield mined, seismic data can also be used. Swanston et al. [5] compared the seismic data of a drilling platform in the Gulf of Mexico in before and after 8 years of mining, the difference of sound respond between water and the hydrocarbon compound can be used for resources monitoring [5]. Acoustic data also can be used for monitoring carbon fixation in the deep ocean. By analyzing the data of 1994, 1999, and 2001 in the same seismic reflection exploration region, it can clearly draw the conclusion that data reflected CO_{2} changes [6].
Results of recent studies have proved that many natural and artificial systems have selfsimilarity [7–16]. It is very useful that selfsimilarity is a considerable keyproperty in understanding of widely existing nonlinear physical systems. By dividing complex networks into boxes containing nodes within a given ‘size’, Song et al. [7] find that complex networks have the scalefree nature, which is one of the evidences in the selfsimilarity confirming. Selfsimilarity is a common characteristic of many communication networks [8–10]. For example, the traffic of World Wide Web, as a typical communication network, also has the characteristic of selfsimilarity [9]. Selfsimilarity is also in the Ad Hoc wireless network transmission. As a result, the traffic in Ad Hoc networks can be predicted by methods such as fuzzy logic system [10]. Fermann [11] studied the pulse propagation characteristics in nonlinear Schrödinger equation optic–fiber amplifier through the selfsimilarity method. From the study of Liang [12], it can be concluded that the signals of ultrawideband radar do not have selfsimilarity. Considering the case of the multiscale structure of the sea and the sea surface shape changes over time, Guan et al.[13] established the onedimensional fractal sea surface model and simulated the wave motions with the time variation using closeform solution of sea wave nonlinear differential equations. Qian [14] used Koch curve, instead of sine curve, to model the sea surface scattering properties with sound waves and electromagnetic waves approximately.
The main purpose of this article is to verify whether the acoustic signals in shallow water have selfsimilarity. We have established a hydrophone line array with 24 sensors in shallow water, and actual data acquisition experiment was conducted in Qilihai Reservoir, Tianjin, China. In Section 2, we introduced the property of hydrophone linear array and data acquisition experiments conducted in Qilihai Reservoir. Then the waveform of the original data sequence was presented. In Section 3, we analyzed the selfsimilarity of the multichannel hydrophone data sequence by variancetime plot.
2. Workbench testing and field data acquisition experiment
As shown in Figure 1, we implemented an maggregated hydrophone linear array and collected the acoustic signals in 4,000 samples per second. The actual system components and test instruments are listed below.

32channel hydrophones;

24bits analog–digital converter;

hydrophone space is 2 m;

40m flexible segment;

PCIinterface data reception card;

data realtime storage based on double pingpang structure;

Tektronix model 4104B oscilloscope.
The 32 sensors were evenly distributed within the exploration cable. Each node is responsible for a signal acquisition of 16 hydrophones. In order to ensure the synchronization of the collected data of each channel in the array, we designed a highprecision unified acquisition clock synchronous system of linear array. After sensing the changes of underwater sound intensity by hydrophones of each channel, signals were amplified and filtered through a fully differential conditioning circuit, then digitized by 8channel SigmaDelta ADC. At last these data were uploaded and stored in host computer through the cascadetype channel individually.
We use the temperaturecompensated crystal oscillator in the head of hydrophone linear array to generate the high stability of the clock as the master clock. Then it was transmitted over unshielded twisted pair to every data acquisition unit (DAU). The slave clock source in every DAU is voltagecontrolled temperaturecompensated crystal oscillator (VCTCXO). DAU is not using VCTCXO in an open loop environment, but letting the acquisition circuits of the data output pulses and the master clock locked to zero retardation by using phaselocked loop. With highprecision sampling clock generation and transmission system, the array can acquire signals simultaneously at submicrosecond level, which is important in offshore environment.
Characteristics of acoustic wave propagation in shallow water are more complex than that of in the deep water, because the ups and downs of the bottom of reservoir are analogous with the water depth. Sound reflection in underwater between surface and bottom is even more than deep water. Therefore, the shallow water acoustic modeling is more difficult. This article discusses the acoustic signal analysis method based on fractal, which can be used for forecasting or targeting an underwater artificial signal. Thereby, it will reduce the difficulty of establishing acoustic propagation model of shallow water environment.
3. Selfsimilarity properties of acoustic signals
For a detailed explanation of selfsimilarity in time series, see [8–14]. We can discuss its definition briefly here. Our discussion in this section and the next closely follows those sources.
Accordance with established practice, the parameter H is the Hurst parameter, which is calculated as $H=1\frac{\beta}{2}.$
In order to be able to verify whether a sequence is Hselfsimilar, we can use the variancetime plot method [9]. It mainly reflects the slowly decline variance of a selfsimilar sequences when parameter m increases continuously.
The concrete steps are listed below

Preprocesses sequence X to meet the requirement of zero mean and unit variance;

For different values of m (starting from two until a relatively large positive integer), generates a plurality of sequences;

Calculates the variance of the sequences X^{(m)}, respectively, and takes the log values;

Draws variance–time plot, the variance of X^{(m)} is plotted against m in a log–log twodimensional coordinate system.

If the variance is all above in the slope of –β, then the series X has selfcorrelation; otherwise, the series has no selfcorrelation characteristics.
If time series X still has selfsimilarity when m is a large integer, the sequence X can be said to have “longrange dependence.” Namely, in the seemingly haphazard sequence, the sequence values after a long time are closely associated with the current value of the sequence. In other words, the time series X elements value x_{0} on the impact of the subsequent element values x_{ t } “to be extended to the infinite.” This feature is also one of the potential applications of selfsimilarity in the field of underwater acoustic detection and target identification.
To further analyze the underwater acoustic signal from the universality of selfsimilarity, we selected and analysis the data sequence of CH2–CH5 hydrophones in the same time period, mainly to study the original sequence and variance–time law results.
4. Conclusion
Many research results show that the selfsimilarity is a common phenomenon in the optical fiber, World Wide Web,Ad Hoc Networks, and other communication network traffic data, and other complex systems. In this article, we discuss the selfsimilarity of underwater acoustic signals collected by towed hydrophone array in shallow water environment. We have collected the same period for four different channel underwater acoustic signal variance–time plot graphics, verified its stable selfsimilar characteristics.
One of the possible reasons for the selfsimilarity of underwater acoustic signal from shallow waters is the fractal characteristics in the scattering properties of surface and bottom of waters. The nature of water itself has fractal characteristics. After the reflection of the water surface and underwater, the sound signal received by hydrophone line array will contain selfsimilarity, as the reflective medium has selfsimilar fractal characteristics. In this article, the underwater acoustic signals’ selfsimilarity is studied in the reservoir environment through the analysis of the actual experimental data. It is proved in this article that the underwater acoustic signals have longrange dependence, which laid the foundation for the future research of underwater target detection and signal processing method from the selfsimilarity aspect.
Declarations
Acknowledgment
This study was supported by the grants Program for New Century Excellent Talents in University (NCET), TOA (KX20100006), TSTC (11ZCKFGX03600), DFTJNU (52XK1206) , and MYATRP(10zd2114) in China.
Authors’ Affiliations
References
 Nicholas MC, Purnima R, Deanelle ST, Srinivasan J, Lee S, Redwood NW: Fish population and behavior revealed by instantaneous continental shelfscale imaging. Science 2006, 311: 660663. 10.1126/science.1121756View ArticleGoogle Scholar
 Nicholas MC, Purnima R, Srinivasan J, Zheng G, Mark A, Ioannis B, Olav GR, Redwood NW, Michael JJ: Critical population density triggers rapid formation of vast oceanic fish shoals. Science 2009, 323: 17341737. 10.1126/science.1169441View ArticleGoogle Scholar
 Nicholas MC, Srinivasan J, Anamaria I: Ocean acoustic waveguide remote sensing: visualizing life around seamounts. Oceanography 2010, 23(1):204205. 10.5670/oceanog.2010.95View ArticleGoogle Scholar
 Landrø M, Strønen LK, Digranes P, Solheim OA, Hilde E: Timelapse seismic as a complementary tool for infill drilling. J. Petrol. Sci. Eng. 2001, 31: 8192. 10.1016/S09204105(01)00122XView ArticleGoogle Scholar
 Swanston AM, Flemings PB, Comisky JT, Best DP: Timelapse imaging at Bullwinkle Field, Green Canyon 65, offshore Gulf of Mexico. Geophysics 2003, 68(5):14701484. 10.1190/1.1620620View ArticleGoogle Scholar
 Arts R, Eiken O, Chadwick A, Zweigel P, van der Meer L, Zinszner B: Monitoring of CO2 injected at Sleipner using timelapse seismic data. Energy 2004, 29: 13831392. 10.1016/j.energy.2004.03.072View ArticleGoogle Scholar
 Song C, Havlin S, Makse HA: Selfsimilarity of complex networks. Nature 2005, 433: 392395. 10.1038/nature03248View ArticleGoogle Scholar
 Song S, Ng JK: Some results on the selfsimilarity property in communication networks. IEEE Trans. Commun. 2004, 52(10):16361642. 10.1109/TCOMM.2004.833136View ArticleGoogle Scholar
 Crovella ME: Selfsimilarity in world wide web traffic: evidence and possible causes. IEEE ACM Trans. Network 1997, 5(6):835846. 10.1109/90.650143View ArticleGoogle Scholar
 Liang QL: Ad hoc wireless network traffic—selfsimilarity and forecasting. IEEE Commun. Lett. 2002, 6(7):297299.View ArticleGoogle Scholar
 Fermann ME: Selfsimilar propagation and amplification of parabolic pulses in optical fibers. Phys. Rev. Lett. 2000, 84(26):60106013. 10.1103/PhysRevLett.84.6010View ArticleGoogle Scholar
 Liang Q: Radar sensor wireless channel modeling in foliage environment: UWB versus narrowband. IEEE Sens. J. 2011, 11(6):14481457.View ArticleGoogle Scholar
 Guan J, Liu NB, Huang Y: Fractal Theory and Applications of Radar Target Detection Publishing. House of Electronics Industry: Beijing; 2011.Google Scholar
 Qian ZW: The Nonlinear Acoustics. 2nd edition. Beijing: Science Press; 2009.Google Scholar
 Unser M, Blu T: Selfsimilarity: part I—splines and operators. IEEE Trans. Signal Process. 2007, 55(4):13521363.MathSciNetView ArticleGoogle Scholar
 Unser M, Blu T: Selfsimilarity: part II—optimal estimation of fractal processes. IEEE Trans. Signal Process. 2007, 55(4):13641378.MathSciNetView ArticleGoogle Scholar
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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.