A function that closely resembles the two-point time-domain Green's function (TDGF) representing the time delays associated with multipath between the two sensors can be recovered by correlating the noise field measured by two sensors. Here, a technique for extracting the TDGF from ambient ocean noise using acoustic vector sensors is presented. Experimental results suggest that the averaging time to extract TDGF is greatly reduced if sound pressure sensors (hydrophones) are replaced by acoustic vector sensors. The direct arrival and bottom bounce arrival were extracted successfully with only 1 min of vertical velocity data, while the bottom bounce arrival was not extracted with even 10 min of sound pressure data.

## 1. Introduction

Correlating apparently random signals to extract their coherent aspects has been applied theoretically and experimentally in both terrestrial seismic^{1} and ocean environments.^{2–5} A long averaging time is generally necessary to form the time-domain correlation function with data measured by sound pressure.^{6} However, long averaging time is probably not reasonable for survey tool applications. Thus, beamforming is used in the end-fire direction to emphasize the coherent part of the noise field coming originating directly over the vertical array,^{7–10} which can greatly reduce the averaging time. However, this method is limited by the requirement for a dense array.^{10}

In the ocean waveguide, although maximum energy is horizontally propagating, whereas the time delays associated with different ray paths between two vertically aligned sensors are contained in the vertically propagating noise. Vertical velocity sensors are sensitive in a pattern similar to a vertical dipole and are thus blind to horizontally propagating energy. Gerstoft^{10} pointed out that, if velocity sensors are used instead of sound pressure sensors, time delay sequences can be extracted with one sensor only.

The approach proposed in this study is inspired by the work of Gerstoft. A simplified theoretical description is developed to extract time delays associated with multipath using sound pressure and vertical particle velocity. Simulation and experimental results suggest that vector sensors provide better performance in Green's function reconstruction than sound pressure sensors.

## 2. Theory

The time-domain correlation function of ambient noise between two points is directly proportional to TDGF.^{7} This function can be acquired through an inverse Fourier transform on the frequency-domain correlation function. The frequency-domain correlation functions for sound pressure and vertical particle velocity component are derived as follows.

Consider a finite circular wind-generated noise sources plane parallel to the surface and located below the surface at depth $zs$. The noise sources are assumed to be random and incoherent. The correlation function is given as follows:^{11}

where the asterisk denotes the complex conjugation operation, $q2$ denotes the intensity of the noise source, and $G(\omega )$ is the Green's function in the frequency-domain. Here, $R$ is the radius of the ambient noise circular plane considered in our model. A radius of 20 km is wide enough for TDGF extraction. The sound pressure Green's function $Gp(\omega )$ and vertical velocity Green's function $Gvz(\omega )$ are given below,

where $km$ is the eigenvalue, $um$ the eigenfunction, and the superscript on the eigenfunction denotes partial derivative. Substituting the Green's functions from Eqs. (2) and (3) into Eq. (1) and performing the range integration results in the following sound pressure correlation function $Cp(\omega )$ and vertical particle velocity correlation function $Cvz(\omega )$:

Using Fourier synthesis, the frequency-domain correlation of the noise field between two (vertically separated) receivers at $z1$ and $z2$ is transformed to a time series as follows:

The TDGF can be approximated by the time derivative of the time domain correlation function as follows:

The propagation time delay of multipath can be extracted from Eq. (7). If the sound speed profile $c(z)$ in water is known, then the theoretical propagation time delay between two receivers at $z1$ and $z2$ can be calculated by the following equation:

For illustration, consider a vertical array in a water depth of 86 m. The array covers the water column with receivers every meter from 20 to 80 m. The reference sensor is located at a depth of 20 m. The sound speed in water is 1500 m/s. The bottom is a half-space seabed with 1600 m/s sound speed, density of 1.7 g/cm^{3}, and attenuation of 0.45 dB/λ. The wind-generated noise sources are located at 0.1 m below the sea surface. The frequency ranges from 100 to 2000 Hz.

Figure 1(a) depicts the derivative of the sound pressure correlation function using Eqs. (4), (6), and (7). The head wave first reaches the receivers. The direct arrival, the surface bounce, and bottom bounces arrived later. Theoretical propagation times from the reference sensor to the bottom sensor for the first four propagation paths were 0.0139, 0.040, 0.048, and 0.0667 s. The propagation times extracted from correlation function coincide with the theoretical values.

The time-domain correlation function of the vertical particle velocity using Eqs. (5) and (6) are illustrated in panel (b) of Fig. 1. The vertical particle velocity time-domain correlation function in Fig. 1(b) also show the multipath propagation structure. Compared with the sound pressure correlation results, almost no head wave propagation structure is observed. This result is due to the fact that vector sensors have dipole directivity in the vertical direction and are insensitive to the sound wave propagating horizontally. Since the head wave front always propagates close to the horizontal direction, hence, almost no head-wave propagation arrival was observed. Among all the extracted propagation arrivals, the direct arrival exhibited maximum amplitude, followed by the bottom bounce arrival, and finally the surface bounce arrival.

Vector sensors are advantageous in extracting multipath propagation arrivals, because the vertical directivity of a vector sensor can effectively inhibit the disturbance from distant non-stationary noise sources. This characteristic, in turn, greatly reduces the averaging time. This phenomenon is verified through experimentation as described in Sec. 3.

## 3. Experimental results

### 3.1 Data

The experiment was conducted in a shallow-ocean region in the South China Sea at a depth of approximately 86 m. The experimental setup and the sound velocity profile are illustrated in Fig. 2. Sea surface wind speed was measured to be approximately 10 m/s during the experiment. An array with two vector sensors placed 18 m apart was deployed from the side of the ship, with the top sensor at 25 m below the sea surface. The sensitivity of sound pressure for these sensors is −185 dB ($ref\u20091\u2009V/\mu Pa$), while the vertical acceleration sensitivity is 26 dB ($ref\u20091\u2009V/g$). During the experiment, the main and auxiliary engines of the experimental ship were brought to a halt. In addition, the experimental region was chosen to be far away from shipping lanes. Consequently, wind-induced noise was the dominant noise recorded during the experiment. The overall data acquisition time was approximately 1 h, but only approximately 10 min of ambient noise data were not contaminated.

### 3.2 Results

The sampling rate of the signals was 65 536 Hz, and each channel was transformed to the frequency domain using 32 768 point fast Fourier transforms (FFTs) using 0.5 s of data. These 0.5 s snapshots can be averaged over many snapshots to form cross correlation functions. The frequency band ranges from 200 to 2000 Hz.

Figures 3(a)–3(d) illustrate the correlation function derivative results between the two sensors with averaging times of 30, 60, 120, and 600 s of sound pressure data, respectively. The direct arrival was evident by averaging the snapshots over 30 s, but the correlation function fluctuated significantly. In addition, several interference peaks, which may have been caused by transient interference sources, were also observed. The fluctuation amplitude of the correlation function decreased with increase in averaging time. The bottom bounce was weak but visible when the averaging time was increased to 10 min. However, the amplitude of this peak was comparable to the interference peak. If the theoretical propagation time delay of the bottom bounce is unknown, whether this peak corresponds to a bottom bounce arrival cannot be established.

Figures 4(a)–4(d) describe the correlation function results between the two sensors with averaging times of 30, 60, 120, and 600 s of vertical particle velocity data, respectively. Compared with Fig. 3, vector sensors were remarkably superior to sound pressure sensors for extracting Green's function. For the same averaging time, the amplitude fluctuation of the vertical velocity correlation function was much smaller than that of the sound pressure correlation function. The correlation peaks were weak, except for the peak corresponding to the direct arrival (Fig. 1), and these weak peaks may be submerged in the fluctuations of the correlation function exactly as illustrated in Fig. 3. The necessary averaging time was reduced when velocity sensors were used instead of sound pressure sensors. The direct and bottom bounce arrivals were clearly observed with only 60 s of vertical particle velocity data (Fig. 4). That mean, the averaging time can be reduced by more than 10 times if sound pressure sensors replaced by acoustic vector sensors. If the length of the averaging time is increased further, the amplitude fluctuation of the correlation function is decreased, and correlation peaks corresponding to the direct arrival and the bottom bounce become more prominent.

Table 1 lists the theoretical and measured propagation times for the first three propagation paths. According to previous simulations and analysis, the correlation peak corresponding to the surface bounce is much weaker than the direct and bottom bounce arrivals. Consequently, the surface bounce arrival was not detected successfully. The arrival times of the direct and bottom bounces were consistent with the measured results, with the maximum time difference error of as small as 0.0004 s. The time difference between the direct arrival and the bottom bounce was twice as much as the propagation time of the sound wave from the bottom sensor to the sea bottom. During this experiment, the measured average sound velocity was 1531.5 m/s, and the bottom sensor was at a depth of 43 m. The ocean depth obtained by the data analysis was 85.5 m, which was surprisingly close to the measured value (86 m).

. | Direct arrival . | Surface bounce . | Bottom bounce . |
---|---|---|---|

Theoretical propagation time(s) | 0.0117 | 0.0442 | 0.0679 |

Experimental propagation time (s) | 0.0120 | 0.0675 | |

Time difference(s) | 0.0003 | 0.0004 |

. | Direct arrival . | Surface bounce . | Bottom bounce . |
---|---|---|---|

Theoretical propagation time(s) | 0.0117 | 0.0442 | 0.0679 |

Experimental propagation time (s) | 0.0120 | 0.0675 | |

Time difference(s) | 0.0003 | 0.0004 |

## 4. Discussions and conclusions

For extracting the TDGF between two points in the vertical direction, sounds that arrive in the horizontal direction were interference signals, while sounds propagating in the vertical direction were the expected signals. Vertical velocity sensors are not sensitive to the horizontally propagating noise. Using this feature, a TDGF extraction method based on vector sensors is presented. The simulation and experimental results showed that vector sensors had more remarkable performance in TDGF extraction. In particular, the extraction efficiency was reasonably high, with averaging time reduced by more than 90% compared with sound pressure sensors.

## Acknowledgments

This work was supported by Science and Technology Foundation of State Key Laboratory, China under Contract No. 9140C200103120C2001, the Natural Science Foundation of GuangDong province under Contract No. 2014A030310256.