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Array tilt effect induced by tidal currents in the northeastern East China Sea
Ocean Engineering 194 (2019) 106654
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Array tilt effect induced by tidal currents in the northeastern East China Sea Jungyong Park a, Woojae Seong b, c, Haesang Yang b, c, *, SungHyun Nam d, e, Seung-Woo Lee d a
Agency for Defense Development, Jinhae, P.O. Box 18, Changwon 51678, Gyeongsangnamdo, South Korea Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, 08826, South Korea c Research Institute of Marine Systems Engineering, Seoul National University, Seoul, 08826, South Korea d School of Earth and Environment Sciences, Seoul National University, Seoul, 08826, South Korea e Research Institute of Oceanography, Seoul National University, Seoul, 08826, South Korea b
A R T I C L E I N F O
A B S T R A C T
Keywords: Arrival structure Channel impulse response Tidal current SAVEX-15
The relation between the tidal current and the acoustic signal measured at vertical line arrays (VLAs) is inves tigated from data of the shallow-water acoustic variability experiment 2015 performed in the northeastern East China Sea. From the channel impulse response, the arrival structure measured on the VLA was observed to vary with semidiurnal tidal period. To explain this phenomenon, the direction of the array tilt is assumed to be consistent with the current flow direction. The modeling results based on ray tracing prove the relation between the variation of the arrival structure and array tilt angle in a time-varying form, yielding an estimation of tidal currents in the region. We compared the projected time series of horizontal currents to the acoustic paths with the curvature variation in the arrival structure to validate our results and confirmed that they are consistent with each other.
1. Introduction Deformation of an array shape can affect the performance of beam forming and may degrade the source localization performance of matched field processing (Kim et al., 2009) and array invariant (Cho and Song, 2017). Additionally, acoustic tracking using the time difference of arrival is affected by the inclination angle of the towed array (Thode, 2005). To overcome these limitations, the tilt angle of vertical line array (VLA) has been considered as a parameter for matched field processing (Kim et al., 2009), and robust matched field processing methods, such as ones based on the frequency difference have been proposed (Cho and Song, 2017; Worthmann et al., 2015). Furthermore, various acoustic methods have been developed for estimating and compensating for array shape deformation (Byun et al., 2018; Cho and Song, 2017; Lee et al., 2017; Nichols and Bradley, 2017; Rockah and Schultheiss, 1987; Sabra et al., 2005; Weiss and Friedlander, 1989). Most studies on array shape estimation have focused on towed hor izontal arrays (Lee et al., 2017; Nichols and Bradley, 2017; Rockah and Schultheiss, 1987; Sabra et al., 2005; Weiss and Friedlander, 1989). Some studies on VLAs have demonstrated the time-dependent variation of array tilt (Byun et al., 2018; Cho and Song, 2017; Yuan et al., 2018). These studies suggest that this variation occurs owing to changes in
environmental variability such as ocean surface waves (Cho and Song, 2017) and currents (Byun et al., 2018). Ocean surface waves induce subsurface buoy motions, which can result in an array tilt. In the Kauai Acomms MURI 2011 (KAM11) experiment, the array tilt angle of VLA was estimated by using an active source (Cho and Song, 2017). This study confirmed that the tilt angle is related to the ocean surface waves based on the period of estimated change in array tilt corresponding to the period of the surface waves (Cho and Song, 2017). The ocean current not only induces a nonreciprocal effect (Roux et al., 2004; Sabra and Dowling, 2003; Wang et al., 2003; Worcester, 1977; Worcester et al., 1985; Zheng et al., 1997) but induces a drag force that can be imposed on the array to change the position of the bottom moored array (Nichols and Bradley, 2017). In the shallow-water acoustic variability experi ment 2015 (SAVEX-15), the current was assumed to induce array tilt (Byun et al., 2018; Yuan et al., 2018) according to the estimated tilt direction which corresponded to the measured current trend in other time. However, the analyzed acoustic data were insufficient to demon strate the acoustically estimated, time-varying currents that may match to the measured current variation, e.g., primarily tidal currents varying at semidiurnal tidal period (Nam et al., 2018). Hence, previous results of studies (Byun et al., 2018; Yuan et al., 2018) are insufficient to confirm a link between the array tilt and time-varying tidal current in the
* Corresponding author. Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, 08826, South Korea. E-mail address: [email protected] (H. Yang). https://doi.org/10.1016/j.oceaneng.2019.106654 Received 5 June 2019; Received in revised form 2 September 2019; Accepted 26 October 2019 Available online 6 November 2019 0029-8018/© 2019 Elsevier Ltd. All rights reserved.
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SAVEX-15. We investigated the time-varying horizontal current-induced array tilt and determine the ground truth by using the current measurements during the SAVEX-15 from year day (YD) 140–141. Because both active acoustic source and ship-mounted acoustic Doppler current profiler (ADCP) were used simultaneously during this time, the relation between the current and array tilt can be obtained by using the acoustic mea surements. The acoustic data show that the arrival structure in the channel impulse response (CIR) varies with semidiurnal period. We assumed that the drag force induced by the current causes the array to tilt. Under this assumption, the ray tracing model results showed a trend similar to the variation in the measured arrival structure. The measured acoustic variability was compared with the mean current speed pro jected with the acoustic path (source to receiver array). This result supports the hypothesis that the tidal current, which dominates the time-varying horizontal current, has a significant effect on the array tilt in the SAVEX-15. The paper is organized as follows. Section 2 summarizes the SAVEX15. Section 3 describes the measured acoustic variability. Section 4 analyzes the relation between acoustic variability and the horizontal current by the arrival time difference. Section 5 describes the relation between acoustic variability and the time-varying current by the time domain beamforming method. Section 6 concludes the paper.
transducers (ITC-1001). In this study, we focus on a source at 72.5 m as shown in Fig. 1(b). The horizontal range was approximately 5.88 km between SRA and VLA1, and approximately 4.82 km between SRA and VLA2. The linear frequency modulation (LFM) chirp probe signal was emitted during this time. The center frequency of the source signal was 22 kHz, and its bandwidth was 20 kHz. The source level was approxi mately 180 dB along the bandwidth. The LFM probe signal was repeated 457 times during each transmission. Each pulse had 60 ms pulse length and a burst period of 120 ms; the total transmission time was 54.84 s. The LFM signal was transmitted every 37-min past the hour. The horizontal current data (u: zonal and v: meridional components in Fig. 2(a)) collected using the ship ADCP were vertically averaged over water depth ranging from around 20 to 70 m (7 depth cell bins). Each component is moving averaged over 2 h with 50% overlapping. The semidiurnal period is shown distinctly during YD 140–141. This domi nant current fluctuations at the semidiurnal tidal (principal lunar semidiurnal) period and the tidal ellipse are consistent with the results reported in the SAVEX-15 region during YD 135–141 (Nam et al., 2018) and previously (Hu et al., 2016; Kang et al., 2002; Yanagi et al., 1997). The trajectory of the horizontal current vector (Fig. 2(b)) forms the tidal ellipse more aligned into the northwest-southeast direction, which is consistent with previously known tidal currents in the region (Hu et al., 2016; Kang et al., 2002; Yanagi et al., 1997).
2. SAVEX-15
3. Qualitative analysis using acoustic data and ray tracing modeling
2.1. Experimental description
3.1. Preprocessing for the channel impulse response
The SAVEX-15 was conducted in the northeastern East China Sea during 14–28 May 2015 to collect the acoustic and environmental data and study the coupling of acoustics, oceanography, and underwater communication in the region. The bathymetry of the experimental site was nearly flat around 100 m depth. Environmental data were measured during the experiment, including temperature, salinity, and density as well as the direction and speed of wind and current vectors. The two kinds of active acoustic source (towed and moored arrays) are used with transmission frequency in the range of 0.5–32 kHz (Byun et al., 2018; Song et al., 2017, 2018; Yuan et al., 2018; Park et al., 2019). In yearday (YD) 140–141, the horizontal current vector (both speed and direction) was measured in a sampling interval of 5 min and depth cell bin size of 8 m for the full water column by using the 150 kHz ADCP mounted on the R/V Onnuri. The acoustic source was also operated for this time interval. Fig. 1(a) depicts the SAVEX-15 experimental region and locations of measurement devices of interest in this study. Fig. 1(b) shows the sound speed profile at YD 141, which was measured by a vertical profiling of Sea-Bird Electronics 9/11 plus standard conductivity, temperature, and depth (CTD) sensor (Cast 21). Two VLAs were moored at Stations 2 (VLA1) and 4 (VLA2). Each VLA consisted of 16 hydrophones (HTI-94SSQ) at 3.75 m spacing from 24.00 to 80.25 m depth, as shown in Fig. 1 (b). At the same time, a ship-tethered source-receiver array (SRA) was deployed at Station 1. The SRA functioned as a source and consisted of 8
The CIR is employed to show the variation in the arrival time structure with the depth. Every CIR is obtained after matched filter processing on the recorded data. Before calculating the mean CIR per minute at each transmission cycle, Delay compensation was applied on the measured data at every ping because the SRA was tethered to the research vessel which leads to significant arrival time shifts since the research vessel drifted (van Walree, 2013). Fig. 3(a) shows a sample of the CIR demonstrating a significant quadratic arrival time (fast time) shift. Fig. 3(b) shows the delay-compensated CIR for the same time and location as in Fig. 3(a). Once this significant delay shift was compen sated, the acoustic intensity from each ping was averaged to improve the signal-to-noise ratio which is given by, pðz; h; tÞ ¼
N 1 X p2 ðz; h; tÞ; N i¼1 i
(1)
where z is the receiver depth, h is the index for hour, N is the number of repetitions during the transmission interval, is the time series of the matched-filtered acoustic pressure at the depth z received at the hth hour (slow time) and t second (fast time, delay). After gathering pðz; h; tÞ from each receiver at every hour, the CIR per hour can be obtained. 3.2. Channel impulse response Fig. 4(a), (c), and (e) provide an example of the measured CIR after arrival time delay compensation. In these figures, the structure of measured CIR at VLA1 changes over time. The acoustic intensity of rays with a positive shooting angle (toward the sea-surface direction) is sometimes weaker than that of rays with a negative shooting angle (toward the bottom direction), and rays with a positive shooting angle are seldom observed in the measured CIR. Because the first bottom re flected signal was strong and the arrival time was easily analyzed, we focused on the first bottom reflected signal that is the earliest to arrive at the VLA. This bottom reflected signal arrives at the VLA in a sequen ce—from the element near the seafloor to the element near the surface. In Fig. 4(a), the signal which arrives at the element near the 60 m depth seems to be the earliest. The curvature of the arrival structure formed by
Fig. 1. (a) Top view of SAVEX-15 region during YD 140–141 and (b) sound speed profile and depths of source and receivers. 2
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Fig. 2. (a) Depth-averaged zonal (u, blue solid) and meridional (v, red dashed) currents and (b) hodograph of horizontal tidal currents observed in the northeastern East China Sea during YD 140–141.
Fig. 3. Example of the channel impulse response at YD 140.901 during 1 min. The source was located at 72.5 m and the receiver was located at 80.25 m. (a) The channel impulse response before delay compensation and (b) the channel impulse response after delay compensation.
the first bottom reflected signal increases, compared to that observed in Fig. 4(c). However, when more time has lapsed, Fig. 4(e) shows that the arrival time of the first bottom reflected signal is delayed more when the array element is closer to the surface. The delayed arrival time decreases the curvature of the arrival structure. At the same time, the curvature of the arrival structure at VLA2 demonstrates a similar period but a different phase compared with that of VLA1 at each time (not shown in the paper). The CIR is modeled assuming that the VLA tilting direction follows the direction of the current. Fig. 4(b), (d), and (f) depict the CIR modeling results obtained by using ray tracing. To model the CIR, rangeindependent bathymetry was applied and the sound speed profile as shown in Fig. 1(b) was used. The ray model calculates each ray tracing under the assumption that the sound speed profile is a piecewise linear function (Medwin and Clay, 1997). The color denotes the shooting angle of each ray in degrees. In this model, the relative sound speed variation induced by the current is neglected. Because signal strength of rays with a positive shooting angle appear quite weak in the measured data, only refracted rays and rays with a negative shooting angle are considered to compare the measured data and modeling results. The estimated array tilt angles from other days during the SAVEX-15 (Byun et al., 2018; Yuan et al., 2018) are used to model the variation in the VLA element location. The blue circle and the red triangles shown in Fig. 4(b), (d), and (f) denote the source depth and relative VLA location with the array tilt, respectively. The vertical array tilt diagrams in Fig. 4(b), (d), and (f) show that the change in receiver location in the horizontal direction is more significant than that in the vertical direction. To analyze the arrival structure variation of CIR, we focus on the first bottom arrival ray that have 1.2� shooting angle because these rays show significant similarity between the measured data and the modeled results. The modeled CIR in Fig. 4(b) represents the case in which the array elements are tilted toward the source, i.e., opposite to the direction of acoustic propagation. The curvature of the CIR structure in this case is similar to that observed in Fig. 4(a). In case the array elements are tilted away
from the source, the modeled CIR as shown in Fig. 4(f) resembles the results depicted in Fig. 4(e). Although there is a slight difference be tween the modeling results and the measured data, which mainly arises owing to the time-dependent variations in the sound speed profile, the modeling result can qualitatively demonstrate the arrival structure of the CIR. The eigenray tracing results toward the bottom are shown in Fig. 5. The receiver depths are 27.75 m (2nd element) in Figs. 5(a), 42.75 m (6th element) in Figs. 5(b), 69 m (13th element) in Figs. 5(c), and 80.25 m (16th element) in Fig. 5(d), respectively. The number of boundary interactions of each eigenray is limited for easy comparison with the measured data and the array does not tilt in this case. The white dashed lines in Fig. 5 denote the first bottom reflected rays (shooting angle of 1.5� in Fig. 4(d)), and the arrival time of the first bottom re flected rays is the earliest in this geometry. As the boundary interaction (including surface and bottom) increases, the ray path becomes longer. Lastly, the trapped rays with relatively long ray paths in the channel region also reach the receiver. The eigenray tracing results according to the receiver depths are entirely consistent with the CIR modeling and those would help to understand the acoustic propagation in this region. 4. Quantitative analysis using parameter and current measurements 4.1. Parameter for representing curvature of CIR arrival structure To represent the curvature of the CIR arrival structure and its vari ation quantitatively, the first arrival (first bottom reflected ray) time difference between the two receivers is used. The 2nd order differenti ation of a curve is the usual method to calculate the curvature of the curve. However, it is difficult to apply the 2nd order differentiation to calculate the curvature in our data because the data from receivers near the surface often do not show distinct arrival owing to the low signal to noise ratio. Instead, the first arrival time difference is effective to show 3
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(d) zs=72.5 m, tilt angle=0°
6
Depth (m)
VLA
3
40
0
60 Source 80 -20
-3
-10
0
10
Relative delay (ms)
20
30
-6
Shooting angle (deg)
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Fig. 4. (Color online) The measured CIR at VLA1; (a), (c), and (e). The colors denote the acoustic intensity in the dB scale. Modeled CIR using rays toward the bottom direction only; (b), (d), and (f) represent the effect of the array tilt induced by tidal current. The colors denote the shooting angle of rays. Blue circles denote the source depth and red triangles denote the relative location of VLA with tilt angle.
Fig. 5. (Color online) The eigenray tracing results toward the bottom direction. The receiver depths are (a) 27.75 m, (b) 42.75 m, (c) 69 m, and (d) 80.25 m, respectively. The white dashed lines denote the first arrival rays (the first bottom reflected rays).
4
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the vertical array tilt effect. To simplify the analysis, the sound speed profile is set to be constant along depth. Fig. 6(a) shows the schematic diagram of the first bottom reflected ray path when the receiver array is not tilted. The first bottom reflected rays can be a sample of rays with a negative shooting angle. In this case, the arrival time difference between two receivers is given by, � li lj 1 Δti;j ¼ zi zj � 2rc c qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi li ¼ r2 þ ð2H zs zi Þ2 ;
� 4H þ 2zs þ zi þ zj ;
ray at each receiver is obtained by measuring the time lag between the time-windowed data (5 ms). This value is used as the parameter for the curvature of CIR arrival structure. The blue dashed lines with circles in Fig. 7 indicate the relative arrival time at the 13th element from two VLAs. If the parameter moves toward a negative value, the curvature of the CIR arrival structure increases, as shown in Fig. 4(a) and (b). If the parameter moves toward a positive value, the curvature of the CIR arrival structure decreases, as shown in Fig. 4(e) and (f). The curves in Fig. 7 show semidiurnal period during the 23 h, which are consistent with the measured CIR arrival structure trend. The results from other receivers (12th–15th) also show similar semidiurnal periodicity.
(2)
where li is the ray trajectory length between the source and the ith receiver, zs is the source depth, zi is the depth of the ith receiver, r is the range between the source and the receiver, and H is the waveguide depth measured from the sea surface to bottom. When zj is fixed, Δti;j shows a quadratic curve as a function of zi with monotonic behavior. When the array is tilted and its angle is θt (Fig. 6 (b)), which is assumed to be small, the variation for every receiver depth can be ignored. In this case, the arrival time difference between two receivers can be approximated by the Taylor series expansion and is given by, � � � 0 0 θ t zj zi li lj H zi H zj 0 Δti;j ¼ ; (3) rθ � Δti;j þ � Δti;j þ c c li lj qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 where li ¼ ðri 0 Þ2 þ ð2H zs zi Þ2 and ri � r þ θt ðH
4.2. Time-varying currents projected to the acoustic paths The effects of the ocean current on the acoustic propagation is related to the acoustic path (between source and receiver) and hori zontal direction of the current. In previous papers, acoustic methods for estimating direction and speed of horizontal current were used to pro vide the projected values of the acoustic path (Wang et al., 2003; Worcester, 1977; Worcester et al., 1985; Zheng et al., 1997). The cur vature variation of CIR arrival structure is also affected by current speed in the direction projected to the acoustic path, which is given by,
zi Þ. The final
where u denotes the horizontal current vector and d denotes the direc tion of the acoustic path between the source and VLA. Time-series of horizontal current speed projected to the acoustic path as a function of time toward the receiver (positive) or source (negative) show correlated variations with the CIR arrival structure curvature (Fig. 7), proving that our modeling assumption is valid. Comparing the results of Fig. 7(a) and (b), the maximum projected mean current speed at VLA2 is greater than that at VLA1. Because the drag is related posi tively to the current speed, the projected current speed could be corre lated to the array tilt angle in the acoustic path direction. This can be confirmed by comparing parameters for the curvature of the CIR arrival structure, i.e., the maximum parameter value for the curvature of the CIR arrival structure at VLA2 is larger than that at VLA1.
approximation is valid when r � li � lj . This equation shows that the arrival time varies with the array tilt angle. From this analysis, the array tilt can be represented by using the arrival time variation which is consistent with the variation in CIR arrival structure. For instance, when the array tilt angle is 3� , zi ¼ 69 m, zj ¼ 80.25 m, and c ¼ 1500 m/s, then 0
Δti;j
Δti;j �
θt ðzj zi Þ c
(5)
up ¼ u⋅d;
¼ 0:39 ms.
To calculate the arrival time difference using acoustic data, we first obtain the arrival time of rays with a negative shooting angle at the 16th element satisfying a certain threshold. Since the arrival pattern at the 16th element is usually more apparent than the arrival pattern at other VLA elements, the arrival time of the signal at the 16th receiver can be easily obtained and it is used as a reference time of signal arrival. Using this reference value, the relative arrival time of the first bottom reflected
5. Time domain beamforming To represent the effect of time-varying current to the acoustic data concretely, this section shows the variation in arrival angle of a specific ray using beamforming. As shown in Fig. 6, the arrival angle of the first bottom reflected ray increases with the array tilt angle, θt , when array is tilted away from the source. Hence, the array tilt variation represents the arrival angle (Yuan et al., 2018). We use time domain delay-and-sum beamforming (Jensen et al., 2011) because the analyzed acoustic data are obtained from high frequency broadband signals. To calculate time domain beamforming, we obtain first bottom re flected rays by appropriate windowing. We select a rectangular window and its length is 20 ms. The window center is selected as the arrival time of the first bottom reflected ray at the 16th receiver. Using the first bottom reflected signal, the ambiguity surface of the time domain beamforming result, Bðt; θa Þ, is obtained by, 16 X
τi ðθa ÞÞ;
(6)
z16 Þsinðθa Þ=c;
(7)
~si ðt
Bðt; θa Þ ¼ i¼1
τi ðθa Þ ¼ ðzi
where ~si ðtÞ is the windowed signal measured at ith vertical array element and τi ðθa Þ is time delay under a plane wave assumption. This assumption is valid when the range between the source and receiver is far enough. The acoustic data sampled at 100 kHz is upsampled to 400 kHz for the time domain beamforming. Examples of Bðt; θa Þ are shown in Fig. 8(a)–
Fig. 6. Schematic diagram of first bottom reflected ray path when (a) receiver array is not tilted and (b) receiver array is tilted. 5
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Fig. 7. Comparison between acoustic arrival time difference and ocean current data. The arrival time difference is denoted by the blue dashed line with circles, and its axis is located on the left. The projected mean current speed is denoted by the red solid line, and its axis is located on the right. (a) The acoustic data measured at VLA1 and mean current projected to the SRA to VLA1 and (b) the acoustic data measured at VLA2 and mean current projected to the SRA to VLA2.
Fig. 8. Ambiguity surface of the time domain beamforming result using windowed data. The color denotes the normalized amplitude and the red circle denotes maximum peak (estimated arrival time and delay). (a) YD 140.484, (b) YD 140.693, and (c) YD 140.818.
(c) and the data obtained are identical to those shown in Fig. 4(a), (c) and (e), respectively. The peak of ambiguity function is marked by the red circle, which represents the estimated relative delay and arrival angle of the first bottom reflected ray. The estimated arrival angle changes over time and corresponds to the curvature variation of the CIR arrival structure. Hence, the arrival angle trend also represents the array tilt effect (curvature variation of CIR arrival structure). For instance, the arrival angle of the first bottom reflected ray increases in Figs. 8(c), and Fig. 4(e) shows that the curvature of CIR arrival structure decreases at the same time. Both results represent the array tilt away from the source. The time series of estimated arrival angles of the first bottom re flected rays at VLA 1 and 2 are shown in Fig. 9(a) and (b), respectively, with the projected mean current speed. The variation in the arrival
angles are consistent with the projected mean current speed trend, which shows that the vertical array tilt induces the variation of arrival angle of specific rays, as shown in Fig. 8(a) and (b). This result is consistent with the comparison between the CIR arrival structure vari ation and horizontal current direction shown in Fig. 7(a) and (b). From the beamforming result, we conclude that the vertical array tilt can be induced by the current. 6. Conclusion The relation between the array tilt and time-varying (primarily semidiurnal tidal) currents is shown by using active acoustic data. The results prove that the curvature of CIR arrival structure varies at
Fig. 9. Comparison between estimated arrival angle of the first bottom reflected ray and time-varying current data. The estimated arrival angle denoted by the blue dashed line with circles. The projected mean current speed denoted by the red solid line. (a) The acoustic data measured at VLA1 and mean current projected to the SRA to VLA1, and (b) the acoustic data measured at VLA2 and mean current projected to the SRA to VLA2. 6
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semidiurnal tidal period. Under the assumption that the array tilt di rection is same with the current flow direction, the modeling result using ray tracing shows curvature of CIR arrival structure changes with ver tical array tilt. To parameterize the curvature of CIR arrival structure, arrival time difference of first bottom reflected ray path measured at the receivers near the bottom is utilized. For validation of the assumption, the measured currents which are vertically averaged over depth are projected to the direction of acoustic path. Time-series of the projected depth-averaged current are consistent with acoustic parameters: the parameter for curvature of CIR arrival structure and arrival angle of first bottom reflected ray. The comparison result of acoustic data and pro jected currents provides the significant effect of time-varying ocean currents such as tidal currents on the acoustic arrival data, contributing to field of remote sensing measurement of horizontal current using VLAs.
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Acknowledgements This work was funded by U. S. Office of Naval Research (N00014-131-0510) via the joint experiment between US and Republic of Korea (SAVEX-15), and Ministry of Oceans and Fisheries via KIOST (PE99331 and ‘Construction of Ocean Research Stations and their Applications in Studies’), and KRISO (PES1940). References Byun, G., Cho, C., Song, H.C., Kim, J.S., Byun, S.-H., 2018. Array invariant-based calibration of array tilt using a source of opportunity. J. Acoust. Soc. Am. 143, 1318–1325. Cho, C., Song, H.C., 2017. Impact of array tilt on source-range estimation in shallow water using the array invariant. J. Acoust. Soc. Am. 141, 2849–2856. Hu, Z., Wang, D.P., Pan, D., He, X., Miyazawa, Y., Bai, Y., Wang, D., Gong, F., 2016. Mapping surface tidal currents and Changjiang plume in the East China sea from geostationary ocean color imager. J. Geophys. Res. Oceans. 121, 1563–1572. Jensen, F.B., Kuperman, W.A., Porter, M.B., Schmidt, H., 2011. Computational Ocean Acoustics. Springer, New York. Kang, S.K., Foreman, M.G., Lie, H.J., Lee, J.H., Cherniawsky, J., Yum, K.D., 2002. Twolayer tidal modeling of the Yellow and East China Seas with application to seasonal variability of the M2 tide. J. Geophys. Res. Oceans. 107, 6-1-6-18. Kim, K., Seong, W., Lee, K., Kim, S., Shim, T., 2009. Range-dependent geoacoustic inversion of vertical line array data using matched beam processing. J. Acoust. Soc. Am. 125, 735–745. Lee, K., Seong, W., Kim, S., 2017. Estimation of the roll angle in a triplet towed array using oceanic surface-generated ambient noise. J. Acoust. Soc. Am. 142, EL123–EL129.
7
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Array tilt effect induced by tidal currents in the northeastern East China Sea Jungyong Park a, Woojae Seong b, c, Haesang Yang b, c, *, SungHyun Nam d, e, Seung-Woo Lee d a
Agency for Defense Development, Jinhae, P.O. Box 18, Changwon 51678, Gyeongsangnamdo, South Korea Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, 08826, South Korea c Research Institute of Marine Systems Engineering, Seoul National University, Seoul, 08826, South Korea d School of Earth and Environment Sciences, Seoul National University, Seoul, 08826, South Korea e Research Institute of Oceanography, Seoul National University, Seoul, 08826, South Korea b
A R T I C L E I N F O
A B S T R A C T
Keywords: Arrival structure Channel impulse response Tidal current SAVEX-15
The relation between the tidal current and the acoustic signal measured at vertical line arrays (VLAs) is inves tigated from data of the shallow-water acoustic variability experiment 2015 performed in the northeastern East China Sea. From the channel impulse response, the arrival structure measured on the VLA was observed to vary with semidiurnal tidal period. To explain this phenomenon, the direction of the array tilt is assumed to be consistent with the current flow direction. The modeling results based on ray tracing prove the relation between the variation of the arrival structure and array tilt angle in a time-varying form, yielding an estimation of tidal currents in the region. We compared the projected time series of horizontal currents to the acoustic paths with the curvature variation in the arrival structure to validate our results and confirmed that they are consistent with each other.
1. Introduction Deformation of an array shape can affect the performance of beam forming and may degrade the source localization performance of matched field processing (Kim et al., 2009) and array invariant (Cho and Song, 2017). Additionally, acoustic tracking using the time difference of arrival is affected by the inclination angle of the towed array (Thode, 2005). To overcome these limitations, the tilt angle of vertical line array (VLA) has been considered as a parameter for matched field processing (Kim et al., 2009), and robust matched field processing methods, such as ones based on the frequency difference have been proposed (Cho and Song, 2017; Worthmann et al., 2015). Furthermore, various acoustic methods have been developed for estimating and compensating for array shape deformation (Byun et al., 2018; Cho and Song, 2017; Lee et al., 2017; Nichols and Bradley, 2017; Rockah and Schultheiss, 1987; Sabra et al., 2005; Weiss and Friedlander, 1989). Most studies on array shape estimation have focused on towed hor izontal arrays (Lee et al., 2017; Nichols and Bradley, 2017; Rockah and Schultheiss, 1987; Sabra et al., 2005; Weiss and Friedlander, 1989). Some studies on VLAs have demonstrated the time-dependent variation of array tilt (Byun et al., 2018; Cho and Song, 2017; Yuan et al., 2018). These studies suggest that this variation occurs owing to changes in
environmental variability such as ocean surface waves (Cho and Song, 2017) and currents (Byun et al., 2018). Ocean surface waves induce subsurface buoy motions, which can result in an array tilt. In the Kauai Acomms MURI 2011 (KAM11) experiment, the array tilt angle of VLA was estimated by using an active source (Cho and Song, 2017). This study confirmed that the tilt angle is related to the ocean surface waves based on the period of estimated change in array tilt corresponding to the period of the surface waves (Cho and Song, 2017). The ocean current not only induces a nonreciprocal effect (Roux et al., 2004; Sabra and Dowling, 2003; Wang et al., 2003; Worcester, 1977; Worcester et al., 1985; Zheng et al., 1997) but induces a drag force that can be imposed on the array to change the position of the bottom moored array (Nichols and Bradley, 2017). In the shallow-water acoustic variability experi ment 2015 (SAVEX-15), the current was assumed to induce array tilt (Byun et al., 2018; Yuan et al., 2018) according to the estimated tilt direction which corresponded to the measured current trend in other time. However, the analyzed acoustic data were insufficient to demon strate the acoustically estimated, time-varying currents that may match to the measured current variation, e.g., primarily tidal currents varying at semidiurnal tidal period (Nam et al., 2018). Hence, previous results of studies (Byun et al., 2018; Yuan et al., 2018) are insufficient to confirm a link between the array tilt and time-varying tidal current in the
* Corresponding author. Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, 08826, South Korea. E-mail address: [email protected] (H. Yang). https://doi.org/10.1016/j.oceaneng.2019.106654 Received 5 June 2019; Received in revised form 2 September 2019; Accepted 26 October 2019 Available online 6 November 2019 0029-8018/© 2019 Elsevier Ltd. All rights reserved.
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SAVEX-15. We investigated the time-varying horizontal current-induced array tilt and determine the ground truth by using the current measurements during the SAVEX-15 from year day (YD) 140–141. Because both active acoustic source and ship-mounted acoustic Doppler current profiler (ADCP) were used simultaneously during this time, the relation between the current and array tilt can be obtained by using the acoustic mea surements. The acoustic data show that the arrival structure in the channel impulse response (CIR) varies with semidiurnal period. We assumed that the drag force induced by the current causes the array to tilt. Under this assumption, the ray tracing model results showed a trend similar to the variation in the measured arrival structure. The measured acoustic variability was compared with the mean current speed pro jected with the acoustic path (source to receiver array). This result supports the hypothesis that the tidal current, which dominates the time-varying horizontal current, has a significant effect on the array tilt in the SAVEX-15. The paper is organized as follows. Section 2 summarizes the SAVEX15. Section 3 describes the measured acoustic variability. Section 4 analyzes the relation between acoustic variability and the horizontal current by the arrival time difference. Section 5 describes the relation between acoustic variability and the time-varying current by the time domain beamforming method. Section 6 concludes the paper.
transducers (ITC-1001). In this study, we focus on a source at 72.5 m as shown in Fig. 1(b). The horizontal range was approximately 5.88 km between SRA and VLA1, and approximately 4.82 km between SRA and VLA2. The linear frequency modulation (LFM) chirp probe signal was emitted during this time. The center frequency of the source signal was 22 kHz, and its bandwidth was 20 kHz. The source level was approxi mately 180 dB along the bandwidth. The LFM probe signal was repeated 457 times during each transmission. Each pulse had 60 ms pulse length and a burst period of 120 ms; the total transmission time was 54.84 s. The LFM signal was transmitted every 37-min past the hour. The horizontal current data (u: zonal and v: meridional components in Fig. 2(a)) collected using the ship ADCP were vertically averaged over water depth ranging from around 20 to 70 m (7 depth cell bins). Each component is moving averaged over 2 h with 50% overlapping. The semidiurnal period is shown distinctly during YD 140–141. This domi nant current fluctuations at the semidiurnal tidal (principal lunar semidiurnal) period and the tidal ellipse are consistent with the results reported in the SAVEX-15 region during YD 135–141 (Nam et al., 2018) and previously (Hu et al., 2016; Kang et al., 2002; Yanagi et al., 1997). The trajectory of the horizontal current vector (Fig. 2(b)) forms the tidal ellipse more aligned into the northwest-southeast direction, which is consistent with previously known tidal currents in the region (Hu et al., 2016; Kang et al., 2002; Yanagi et al., 1997).
2. SAVEX-15
3. Qualitative analysis using acoustic data and ray tracing modeling
2.1. Experimental description
3.1. Preprocessing for the channel impulse response
The SAVEX-15 was conducted in the northeastern East China Sea during 14–28 May 2015 to collect the acoustic and environmental data and study the coupling of acoustics, oceanography, and underwater communication in the region. The bathymetry of the experimental site was nearly flat around 100 m depth. Environmental data were measured during the experiment, including temperature, salinity, and density as well as the direction and speed of wind and current vectors. The two kinds of active acoustic source (towed and moored arrays) are used with transmission frequency in the range of 0.5–32 kHz (Byun et al., 2018; Song et al., 2017, 2018; Yuan et al., 2018; Park et al., 2019). In yearday (YD) 140–141, the horizontal current vector (both speed and direction) was measured in a sampling interval of 5 min and depth cell bin size of 8 m for the full water column by using the 150 kHz ADCP mounted on the R/V Onnuri. The acoustic source was also operated for this time interval. Fig. 1(a) depicts the SAVEX-15 experimental region and locations of measurement devices of interest in this study. Fig. 1(b) shows the sound speed profile at YD 141, which was measured by a vertical profiling of Sea-Bird Electronics 9/11 plus standard conductivity, temperature, and depth (CTD) sensor (Cast 21). Two VLAs were moored at Stations 2 (VLA1) and 4 (VLA2). Each VLA consisted of 16 hydrophones (HTI-94SSQ) at 3.75 m spacing from 24.00 to 80.25 m depth, as shown in Fig. 1 (b). At the same time, a ship-tethered source-receiver array (SRA) was deployed at Station 1. The SRA functioned as a source and consisted of 8
The CIR is employed to show the variation in the arrival time structure with the depth. Every CIR is obtained after matched filter processing on the recorded data. Before calculating the mean CIR per minute at each transmission cycle, Delay compensation was applied on the measured data at every ping because the SRA was tethered to the research vessel which leads to significant arrival time shifts since the research vessel drifted (van Walree, 2013). Fig. 3(a) shows a sample of the CIR demonstrating a significant quadratic arrival time (fast time) shift. Fig. 3(b) shows the delay-compensated CIR for the same time and location as in Fig. 3(a). Once this significant delay shift was compen sated, the acoustic intensity from each ping was averaged to improve the signal-to-noise ratio which is given by, pðz; h; tÞ ¼
N 1 X p2 ðz; h; tÞ; N i¼1 i
(1)
where z is the receiver depth, h is the index for hour, N is the number of repetitions during the transmission interval, is the time series of the matched-filtered acoustic pressure at the depth z received at the hth hour (slow time) and t second (fast time, delay). After gathering pðz; h; tÞ from each receiver at every hour, the CIR per hour can be obtained. 3.2. Channel impulse response Fig. 4(a), (c), and (e) provide an example of the measured CIR after arrival time delay compensation. In these figures, the structure of measured CIR at VLA1 changes over time. The acoustic intensity of rays with a positive shooting angle (toward the sea-surface direction) is sometimes weaker than that of rays with a negative shooting angle (toward the bottom direction), and rays with a positive shooting angle are seldom observed in the measured CIR. Because the first bottom re flected signal was strong and the arrival time was easily analyzed, we focused on the first bottom reflected signal that is the earliest to arrive at the VLA. This bottom reflected signal arrives at the VLA in a sequen ce—from the element near the seafloor to the element near the surface. In Fig. 4(a), the signal which arrives at the element near the 60 m depth seems to be the earliest. The curvature of the arrival structure formed by
Fig. 1. (a) Top view of SAVEX-15 region during YD 140–141 and (b) sound speed profile and depths of source and receivers. 2
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Fig. 2. (a) Depth-averaged zonal (u, blue solid) and meridional (v, red dashed) currents and (b) hodograph of horizontal tidal currents observed in the northeastern East China Sea during YD 140–141.
Fig. 3. Example of the channel impulse response at YD 140.901 during 1 min. The source was located at 72.5 m and the receiver was located at 80.25 m. (a) The channel impulse response before delay compensation and (b) the channel impulse response after delay compensation.
the first bottom reflected signal increases, compared to that observed in Fig. 4(c). However, when more time has lapsed, Fig. 4(e) shows that the arrival time of the first bottom reflected signal is delayed more when the array element is closer to the surface. The delayed arrival time decreases the curvature of the arrival structure. At the same time, the curvature of the arrival structure at VLA2 demonstrates a similar period but a different phase compared with that of VLA1 at each time (not shown in the paper). The CIR is modeled assuming that the VLA tilting direction follows the direction of the current. Fig. 4(b), (d), and (f) depict the CIR modeling results obtained by using ray tracing. To model the CIR, rangeindependent bathymetry was applied and the sound speed profile as shown in Fig. 1(b) was used. The ray model calculates each ray tracing under the assumption that the sound speed profile is a piecewise linear function (Medwin and Clay, 1997). The color denotes the shooting angle of each ray in degrees. In this model, the relative sound speed variation induced by the current is neglected. Because signal strength of rays with a positive shooting angle appear quite weak in the measured data, only refracted rays and rays with a negative shooting angle are considered to compare the measured data and modeling results. The estimated array tilt angles from other days during the SAVEX-15 (Byun et al., 2018; Yuan et al., 2018) are used to model the variation in the VLA element location. The blue circle and the red triangles shown in Fig. 4(b), (d), and (f) denote the source depth and relative VLA location with the array tilt, respectively. The vertical array tilt diagrams in Fig. 4(b), (d), and (f) show that the change in receiver location in the horizontal direction is more significant than that in the vertical direction. To analyze the arrival structure variation of CIR, we focus on the first bottom arrival ray that have 1.2� shooting angle because these rays show significant similarity between the measured data and the modeled results. The modeled CIR in Fig. 4(b) represents the case in which the array elements are tilted toward the source, i.e., opposite to the direction of acoustic propagation. The curvature of the CIR structure in this case is similar to that observed in Fig. 4(a). In case the array elements are tilted away
from the source, the modeled CIR as shown in Fig. 4(f) resembles the results depicted in Fig. 4(e). Although there is a slight difference be tween the modeling results and the measured data, which mainly arises owing to the time-dependent variations in the sound speed profile, the modeling result can qualitatively demonstrate the arrival structure of the CIR. The eigenray tracing results toward the bottom are shown in Fig. 5. The receiver depths are 27.75 m (2nd element) in Figs. 5(a), 42.75 m (6th element) in Figs. 5(b), 69 m (13th element) in Figs. 5(c), and 80.25 m (16th element) in Fig. 5(d), respectively. The number of boundary interactions of each eigenray is limited for easy comparison with the measured data and the array does not tilt in this case. The white dashed lines in Fig. 5 denote the first bottom reflected rays (shooting angle of 1.5� in Fig. 4(d)), and the arrival time of the first bottom re flected rays is the earliest in this geometry. As the boundary interaction (including surface and bottom) increases, the ray path becomes longer. Lastly, the trapped rays with relatively long ray paths in the channel region also reach the receiver. The eigenray tracing results according to the receiver depths are entirely consistent with the CIR modeling and those would help to understand the acoustic propagation in this region. 4. Quantitative analysis using parameter and current measurements 4.1. Parameter for representing curvature of CIR arrival structure To represent the curvature of the CIR arrival structure and its vari ation quantitatively, the first arrival (first bottom reflected ray) time difference between the two receivers is used. The 2nd order differenti ation of a curve is the usual method to calculate the curvature of the curve. However, it is difficult to apply the 2nd order differentiation to calculate the curvature in our data because the data from receivers near the surface often do not show distinct arrival owing to the low signal to noise ratio. Instead, the first arrival time difference is effective to show 3
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(d) zs=72.5 m, tilt angle=0°
6
Depth (m)
VLA
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40
0
60 Source 80 -20
-3
-10
0
10
Relative delay (ms)
20
30
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Shooting angle (deg)
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Fig. 4. (Color online) The measured CIR at VLA1; (a), (c), and (e). The colors denote the acoustic intensity in the dB scale. Modeled CIR using rays toward the bottom direction only; (b), (d), and (f) represent the effect of the array tilt induced by tidal current. The colors denote the shooting angle of rays. Blue circles denote the source depth and red triangles denote the relative location of VLA with tilt angle.
Fig. 5. (Color online) The eigenray tracing results toward the bottom direction. The receiver depths are (a) 27.75 m, (b) 42.75 m, (c) 69 m, and (d) 80.25 m, respectively. The white dashed lines denote the first arrival rays (the first bottom reflected rays).
4
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the vertical array tilt effect. To simplify the analysis, the sound speed profile is set to be constant along depth. Fig. 6(a) shows the schematic diagram of the first bottom reflected ray path when the receiver array is not tilted. The first bottom reflected rays can be a sample of rays with a negative shooting angle. In this case, the arrival time difference between two receivers is given by, � li lj 1 Δti;j ¼ zi zj � 2rc c qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi li ¼ r2 þ ð2H zs zi Þ2 ;
� 4H þ 2zs þ zi þ zj ;
ray at each receiver is obtained by measuring the time lag between the time-windowed data (5 ms). This value is used as the parameter for the curvature of CIR arrival structure. The blue dashed lines with circles in Fig. 7 indicate the relative arrival time at the 13th element from two VLAs. If the parameter moves toward a negative value, the curvature of the CIR arrival structure increases, as shown in Fig. 4(a) and (b). If the parameter moves toward a positive value, the curvature of the CIR arrival structure decreases, as shown in Fig. 4(e) and (f). The curves in Fig. 7 show semidiurnal period during the 23 h, which are consistent with the measured CIR arrival structure trend. The results from other receivers (12th–15th) also show similar semidiurnal periodicity.
(2)
where li is the ray trajectory length between the source and the ith receiver, zs is the source depth, zi is the depth of the ith receiver, r is the range between the source and the receiver, and H is the waveguide depth measured from the sea surface to bottom. When zj is fixed, Δti;j shows a quadratic curve as a function of zi with monotonic behavior. When the array is tilted and its angle is θt (Fig. 6 (b)), which is assumed to be small, the variation for every receiver depth can be ignored. In this case, the arrival time difference between two receivers can be approximated by the Taylor series expansion and is given by, � � � 0 0 θ t zj zi li lj H zi H zj 0 Δti;j ¼ ; (3) rθ � Δti;j þ � Δti;j þ c c li lj qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 where li ¼ ðri 0 Þ2 þ ð2H zs zi Þ2 and ri � r þ θt ðH
4.2. Time-varying currents projected to the acoustic paths The effects of the ocean current on the acoustic propagation is related to the acoustic path (between source and receiver) and hori zontal direction of the current. In previous papers, acoustic methods for estimating direction and speed of horizontal current were used to pro vide the projected values of the acoustic path (Wang et al., 2003; Worcester, 1977; Worcester et al., 1985; Zheng et al., 1997). The cur vature variation of CIR arrival structure is also affected by current speed in the direction projected to the acoustic path, which is given by,
zi Þ. The final
where u denotes the horizontal current vector and d denotes the direc tion of the acoustic path between the source and VLA. Time-series of horizontal current speed projected to the acoustic path as a function of time toward the receiver (positive) or source (negative) show correlated variations with the CIR arrival structure curvature (Fig. 7), proving that our modeling assumption is valid. Comparing the results of Fig. 7(a) and (b), the maximum projected mean current speed at VLA2 is greater than that at VLA1. Because the drag is related posi tively to the current speed, the projected current speed could be corre lated to the array tilt angle in the acoustic path direction. This can be confirmed by comparing parameters for the curvature of the CIR arrival structure, i.e., the maximum parameter value for the curvature of the CIR arrival structure at VLA2 is larger than that at VLA1.
approximation is valid when r � li � lj . This equation shows that the arrival time varies with the array tilt angle. From this analysis, the array tilt can be represented by using the arrival time variation which is consistent with the variation in CIR arrival structure. For instance, when the array tilt angle is 3� , zi ¼ 69 m, zj ¼ 80.25 m, and c ¼ 1500 m/s, then 0
Δti;j
Δti;j �
θt ðzj zi Þ c
(5)
up ¼ u⋅d;
¼ 0:39 ms.
To calculate the arrival time difference using acoustic data, we first obtain the arrival time of rays with a negative shooting angle at the 16th element satisfying a certain threshold. Since the arrival pattern at the 16th element is usually more apparent than the arrival pattern at other VLA elements, the arrival time of the signal at the 16th receiver can be easily obtained and it is used as a reference time of signal arrival. Using this reference value, the relative arrival time of the first bottom reflected
5. Time domain beamforming To represent the effect of time-varying current to the acoustic data concretely, this section shows the variation in arrival angle of a specific ray using beamforming. As shown in Fig. 6, the arrival angle of the first bottom reflected ray increases with the array tilt angle, θt , when array is tilted away from the source. Hence, the array tilt variation represents the arrival angle (Yuan et al., 2018). We use time domain delay-and-sum beamforming (Jensen et al., 2011) because the analyzed acoustic data are obtained from high frequency broadband signals. To calculate time domain beamforming, we obtain first bottom re flected rays by appropriate windowing. We select a rectangular window and its length is 20 ms. The window center is selected as the arrival time of the first bottom reflected ray at the 16th receiver. Using the first bottom reflected signal, the ambiguity surface of the time domain beamforming result, Bðt; θa Þ, is obtained by, 16 X
τi ðθa ÞÞ;
(6)
z16 Þsinðθa Þ=c;
(7)
~si ðt
Bðt; θa Þ ¼ i¼1
τi ðθa Þ ¼ ðzi
where ~si ðtÞ is the windowed signal measured at ith vertical array element and τi ðθa Þ is time delay under a plane wave assumption. This assumption is valid when the range between the source and receiver is far enough. The acoustic data sampled at 100 kHz is upsampled to 400 kHz for the time domain beamforming. Examples of Bðt; θa Þ are shown in Fig. 8(a)–
Fig. 6. Schematic diagram of first bottom reflected ray path when (a) receiver array is not tilted and (b) receiver array is tilted. 5
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Fig. 7. Comparison between acoustic arrival time difference and ocean current data. The arrival time difference is denoted by the blue dashed line with circles, and its axis is located on the left. The projected mean current speed is denoted by the red solid line, and its axis is located on the right. (a) The acoustic data measured at VLA1 and mean current projected to the SRA to VLA1 and (b) the acoustic data measured at VLA2 and mean current projected to the SRA to VLA2.
Fig. 8. Ambiguity surface of the time domain beamforming result using windowed data. The color denotes the normalized amplitude and the red circle denotes maximum peak (estimated arrival time and delay). (a) YD 140.484, (b) YD 140.693, and (c) YD 140.818.
(c) and the data obtained are identical to those shown in Fig. 4(a), (c) and (e), respectively. The peak of ambiguity function is marked by the red circle, which represents the estimated relative delay and arrival angle of the first bottom reflected ray. The estimated arrival angle changes over time and corresponds to the curvature variation of the CIR arrival structure. Hence, the arrival angle trend also represents the array tilt effect (curvature variation of CIR arrival structure). For instance, the arrival angle of the first bottom reflected ray increases in Figs. 8(c), and Fig. 4(e) shows that the curvature of CIR arrival structure decreases at the same time. Both results represent the array tilt away from the source. The time series of estimated arrival angles of the first bottom re flected rays at VLA 1 and 2 are shown in Fig. 9(a) and (b), respectively, with the projected mean current speed. The variation in the arrival
angles are consistent with the projected mean current speed trend, which shows that the vertical array tilt induces the variation of arrival angle of specific rays, as shown in Fig. 8(a) and (b). This result is consistent with the comparison between the CIR arrival structure vari ation and horizontal current direction shown in Fig. 7(a) and (b). From the beamforming result, we conclude that the vertical array tilt can be induced by the current. 6. Conclusion The relation between the array tilt and time-varying (primarily semidiurnal tidal) currents is shown by using active acoustic data. The results prove that the curvature of CIR arrival structure varies at
Fig. 9. Comparison between estimated arrival angle of the first bottom reflected ray and time-varying current data. The estimated arrival angle denoted by the blue dashed line with circles. The projected mean current speed denoted by the red solid line. (a) The acoustic data measured at VLA1 and mean current projected to the SRA to VLA1, and (b) the acoustic data measured at VLA2 and mean current projected to the SRA to VLA2. 6
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semidiurnal tidal period. Under the assumption that the array tilt di rection is same with the current flow direction, the modeling result using ray tracing shows curvature of CIR arrival structure changes with ver tical array tilt. To parameterize the curvature of CIR arrival structure, arrival time difference of first bottom reflected ray path measured at the receivers near the bottom is utilized. For validation of the assumption, the measured currents which are vertically averaged over depth are projected to the direction of acoustic path. Time-series of the projected depth-averaged current are consistent with acoustic parameters: the parameter for curvature of CIR arrival structure and arrival angle of first bottom reflected ray. The comparison result of acoustic data and pro jected currents provides the significant effect of time-varying ocean currents such as tidal currents on the acoustic arrival data, contributing to field of remote sensing measurement of horizontal current using VLAs.
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