Shock and Vibration

Volume 2018, Article ID 3619257, 8 pages

https://doi.org/10.1155/2018/3619257

## Experimental Study of a Broadband Parametric Acoustic Array for Sub-Bottom Profiling in Shallow Water

^{1}Guangdong Province Key Laboratory for Coastal Ocean Variation and Disaster Prediction, Guangdong Ocean University, Zhanjiang 524088, China^{2}College of Electronics and Information Engineering, Guangdong Ocean University, Zhanjiang 524088, China^{3}Shanghai Acoustic Laboratory, Chinese Academy of Science, Shanghai 200032, China

Correspondence should be addressed to Binbin Zou; nc.ca.aoi.liam@bbuoz

Received 24 June 2018; Revised 10 November 2018; Accepted 22 November 2018; Published 25 December 2018

Academic Editor: Zhixiong Li

Copyright © 2018 Ke Qu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Broadband parametric acoustic arrays appear to offer advantages for shallow water sub-bottom profiling. In this paper, the performance of a broadband parametric acoustic array system was experimentally evaluated. In tank experiments using the nonlinear parabolic wave (KZK) equation, the directivity, source level, parametric acoustic array length, and penetration depth were evaluated. Based on Berktay’s far-field solution, the system’s emission signal was designed. According to sea trials of the broadband parametric acoustic array system as designed, a clear sub-bottom profile was obtained. Moreover, buried pipelines in the seabed were effectively detected, verifying the system’s effectiveness.

#### 1. Introduction

In traditional sub-bottom profiling systems, due to the limitations of the linear sound source, the detector beam is relatively wide and has low resolution. To obtain a low-frequency sound source with high directivity, a transducer with a larger aperture is needed. Therefore, it is difficult to satisfy the device portability requirement in actual application. Based on a parametric acoustic array system of nonlinear sound sources, a small-aperture broadband beam with low frequency, high directivity, and without sidelobes can be realized. The parametric acoustic array system is very suitable for high-resolution detection of seabed stratigraphic profiles and represents an important development direction in sub-bottom profile detection technology [1].

The basic theory of parametric acoustic arrays was first proposed by Westervelt in the 1960s [2, 3]. Later, Berktay further deduced the relative emission theory of parametric acoustic arrays and promoted their application [4]. Because it offers a low-frequency sound source with a narrow beam and no sidelobes, the technology has been used in sub-bottom profiling [5], industrial flaw detection [6], medical examination [7], biological detection [8], target tracking [9], and underwater acoustic communication [10, 11]. However, its most mature application in underwater acoustics is still the sub-bottom profiler [12–14]. To satisfy measurement requirements at different depths, a single-frequency difference frequency signal is generally used in current parametric array sonar systems, and the original frequency is relatively low. During offshore detection, because the frequency is low, the parametric array will be truncated, which impacts far-field directivity. Moreover, because the signal bandwidth is insufficient, it is difficult to carry out high-resolution detection on the seabed.

To meet the demand for high-resolution offshore detection, especially for detecting profiles within 10 m of the seafloor sediment and detecting buried objects, a broadband parametric array system was designed in this study. By using a 20–30 kHz difference frequency signal generated by the 300 kHz original frequency, the vertical resolution can be effectively improved. Based on Berktay’s envelope modulation theory and the KZK (Khokhlov-Zabolotskaya-Kuznetsov) equation combined with tank experiments, the performance of the broadband difference frequency sound source was evaluated under various conditions, and the detection effect was deduced. Finally, sea trials were carried out for the system, and effective detection results were obtained. While parametric acoustic array has been received considerable attention over the past decade, relatively few engineering details have surfaced about a whole broadband parametric acoustic array system [15–20]. The key engineering issues and performance of the whole broadband parametric acoustic array system are presented in this paper.

#### 2. Theory

In the linear theory, there is no interaction when two sound waves at different frequencies are superposed. The total sound field is equal to the linear superposition of the two sound pressures. In the nonlinear theory, for sound waves and at different frequencies in a nondispersive medium, each sound wave is disturbed by the other one when it propagates in the medium. Interaction occurs when two sound waves at different frequencies are superposed. Besides the original frequency wave, the sum frequency wave at frequency , the difference frequency wave at frequency , and harmonic frequency waves at frequencies and all exist. During propagation, the original frequency wave generates acoustic scattering continuously. This forward scattering is repeatedly superposed on the sound scattering produced earlier, and as a result, it is gradually enhanced. The process can be regarded as involving a volume array consisting of virtual sources of various secondary sound fields in space. This volume array is called a parametric array. In the secondary sound field of the parametric array, the difference frequency sound field has attracted the most attention in sonar engineering.

Let us assume that the medium is an ideal fluid and that only one attenuation coefficient is introduced to characterize the attenuation effect of the medium on the sound wave. It is also assumed that the original frequency wave and the difference frequency wave propagate with small amplitude. The continuity equation, momentum conservation equation, and equation of state can be combined, and a second-order approximation, the Westervelt nonlinear equation, can be deduced [3]:where is the sound pressure, is the sound speed in the medium, is the medium density, is the time, and is the source strength density. Based on the study of the input broadband signal, Berktay proposed an amplitude modulation method. It is assumed that the emission signal is , where is the amplitude of the sound source at the original frequency and is the envelope of the emission signal, whose frequency should be much less than the original frequency . Then, the sound pressure at position on the sound axis can be expressed as follows:

By substituting into equation (1), the sound pressure of the difference frequency at position on the far-field sound axis can be obtained:where is the nonlinear coefficient, is the area of the transmitting transducer, and is the attenuation coefficient of the original frequency wave. Berktay’s theory can be used only to calculate the far-field solution on the sound axis. The KZK equation can more completely describe the nonlinear effect of the sound field at different positions, including near and nonaxial sound fields:where is the delay time and is a Laplace operator. In the following discussion, the emission signal of the parametric array is designed according to equation (3), and the simulation result is analyzed by equation (4).

Equation (3) shows that the sound pressure amplitude of the difference frequency wave on the axis is proportional to the second-order derivative of the square of the envelope signal versus time and that the results are valid in the weak nonlinear far field. Assuming constant total power and amplitude modulation, compared with a dual-frequency parametric array, the gain of the difference frequency signal of the broadband parametric array has improved by 2.1–6.0 dB [21]. Equation (3) also illustrates that the spectral range of the difference frequency signal can theoretically double the emission signal envelope. As a relatively high-frequency signal, the emission signal can easily generate a wider broadband using current underwater acoustic transducer technology. As a relatively low-frequency signal, the difference frequency signal also has wide broadband and sharp directivity, which cannot be achieved by the common low-frequency transducer.

#### 3. Tank Experiments

To study the performance of the broadband parametric array system, several experiments were carried out in a water tank. Figure 1 shows that the length, width, and height of the water tank were 10 m, 5 m, and 5 m, respectively. Sound-absorbing materials were laid on the walls and bottom. The center frequency of the parametric array emission system was 310 kHz, and the bandwidth at −3 dB was 120 kHz. The transducer diameter was 10 cm, and the receiving equipment was a B&K8103. The emission depth and the receiving depth were both 1.5 m. The oscilloscope was a Tektronix 2014B. The active power filter was a NF3828, and the low-pass filter was an eighth-order Butterworth filter.