Two Autonomous Underwater Multi-Dimensional Acoustic Recorders (AUMDAR) were deployed in the southeastern part of Lake Travis during the summer of 2018. Each AUMDAR system possessed a three-axis acoustic vector sensor capable of estimating the azimuthal and vertical arrival angles from discrete sound sources. A unique and complicated propagation environment existed during the experiment due to the mooring locations and the range-dependent lake bathymetry. The AUMDAR systems were almost entirely shielded from sound emanating from surface vessels to the south and southeast of the deployment location, while a larger, yet limited, direct acoustical field of view was realized to the north and northeast. During the evening hours, the low-frequency received level increased without a corresponding increase in the number of detected discrete surface vessels. During the same time, the predominant direction of the received sound pointed toward the bend in the river channel. A three-dimensional ray model was employed to assess the various arrival angles from a grid of source positions located throughout the lake. The model results are consistent with the observations and suggest that the ambient noise field originated from vessels physically located to the northwest of the sensors, but arriving at angles consistent with out-of-plane sound propagation.

In many underwater acoustic waveguides, there is sometimes an assumption of isotropic ambient noise, at least in some frequency bands.1 Such is the case where wind-driven ambient noise dominates and the acoustic field can be described by a uniform distribution of point sources at the air/water interface.2 However, it is also not uncommon for the ambient noise field to be anisotropic due to a nonuniform distribution of sources. Such can be the case for environments which are dominated by shipping traffic3 or for receivers which are shielded by bathymetric features on one or more sides.4 This work represents a somewhat unusual case where the low-frequency ambient noise directionality arises from a combination of a distribution of discrete sound sources and three-dimensional (3D) propagation effects.

The observation of directionality of the ambient noise sources was enabled by a pair of acoustic vector sensors. Previous work has demonstrated the use of vector sensors to measure 3D propagation effects for active sources in a nearshore environment with a sloping bottom.5 In this work, the vector sensors were deployed within a constrained environment formed by a flooded river channel. By cross-fixing signals from the two vector sensors, recreational vessels operating nearby are localized. The observation of more diffuse ambient noise propagating from vessel traffic outside the direct acoustic field of view of the sensors is explained through application of a 3D propagation model.

The paper is organized into the following sections. Section II introduces the vector sensor recording systems and describes the experimental layout. Section III is focused on the data from the experiment: what was collected, how it was processed, the resulting observations, and hypothesized explanations. The hypotheses of Sec. III are further explored through 3D numerical modeling presented in Sec. IV. Concluding remarks are found in Sec. V.

The Autonomous Underwater Multi-Dimensional Acoustic Recorder (AUMDAR) was developed by the first two authors at the Applied Research Laboratories at The University of Texas at Austin (ARL:UT). The fundamental components of AUMDAR include (1) a low-power, low-noise multichannel acoustic data recorder, (2) an environmental board which generates non-acoustic data such as platform pitch, roll, heading, and depth, (3) an acoustic sensor suite, and (4) an onboard battery pack. The data recorder, developed at ARL:UT, is a PC/104 form factor with 16-bit analog-to-digital converters. The modularity of the recorder design permits a number of configurable deployment options which include low-power functionality, scheduled recording intervals, interfaces for atomic clock boards, options for in-buoy processing, and interfaces for acoustic communications. The environmental board contains a 9-axis motion tracking chip (3-axis gyroscope, 3-axis accelerometer, and 3-axis magnetometer) as well as an interface for an external pressure sensor. In its standard configuration, AUMDAR accepts up to four acoustic channels but can be expanded to accept additional analog channels. The duration of the data collection of AUMDAR is limited by the battery pack and hard disk storage capacity and is generally configurable between 30 days continuous and 1 year duty-cycled deployment durations.

During the summer of 2018, two AUMDAR systems were readied for an at-sea deployment. Commercially available Wilcoxon VS-205 (MD, USA) acoustic vector sensors were integrated into AUMDAR as the acoustic sensor suite. Each VS-205 consists of an omnidirectional hydrophone and three orthogonal, directional particle acceleration transducers housed in single, neutrally buoyant sensor housing. Acoustic vector sensors permit direction of arrival (DOA) estimates by combining the omnidirectional and directional field components. Although the VS-205 is capable of generating its own non-acoustic data describing its spatial orientation with respect to the earth's gravitational and magnetic fields, this functionality was not utilized on AUMDAR, and the platform orientation was derived from the environmental board.

Lake Travis is a 63 mile long, man-made reservoir located about 13 miles northwest of Austin, TX that was formed by damming the Colorado River by Mansfield Dam. Figure 1(a) shows a satellite image of the southeastern region of the lake. Figure 1(b) is a closer view of the experimental region and is comprised of a visible satellite image overlain by high resolution data from forward-looking sonar (the rainbow color shading) and by coarser resolution elevation data provided by the Lower Colorado River Authority (LCRA), displayed as isobath contours. The Colorado River channel is distinguishable in Fig. 1(b) as the portion of the bathymetry between the 40 m isobaths and, for the purpose of this discussion, is divided into northern and southern river channel designations. The depth of the lake depends on regional rainfall and on downstream water demand and is controlled by floodgates located in the dam; the lake was 202.2 m above mean sea level (AMSL) on June 13, 2018 (207.5 m AMSL is considered full). On this day, two of the highest points on the “Sometimes” Islands were protruding above the air/water interface.

FIG. 1.

(Color online) (a) Satellite image of the southeast region of Lake Travis with weather stations W1 to W4 and AUMDAR locations A1 and A2 marked. (b) Detailed depiction of the submerged river channel near Mansfield Dam. Color bathymetry data from high-resolution, forward-looking sonar and labeled isobaths (in m) from LCRA elevation data are superimposed on the satellite imagery.

FIG. 1.

(Color online) (a) Satellite image of the southeast region of Lake Travis with weather stations W1 to W4 and AUMDAR locations A1 and A2 marked. (b) Detailed depiction of the submerged river channel near Mansfield Dam. Color bathymetry data from high-resolution, forward-looking sonar and labeled isobaths (in m) from LCRA elevation data are superimposed on the satellite imagery.

Close modal

Despite the southeastern basin of Lake Travis being covered by water (except for the exposed parts of the Sometimes Islands), the bathymetry is quite complex in the experimental region. The two AUMDAR units were deployed near the middle of the northern river channel, to the north of the Sometimes Islands, and to the east of the southernmost bend in the river channel. Two of the steepest bathymetry gradients in all of Lake Travis occur on the southern wall of the northern river channel, in the immediate vicinity of the AUMDAR deployment locations, labeled A1 and A2 in Fig. 1. The maximum slopes in these areas are nearly 50° with mean slopes between 20° and 30°. There is also a very steep gradient along a north/south line immediately west of Windy Point with slopes in excess of 30°.

As part of the system checkout process, both AUMDAR systems were deployed in Lake Travis for approximately 20 h spanning June 13–14, 2018. Each system was deployed on a vertical mooring line, with the vector sensor located approximately 5 m above the lake bed. The systems recorded continuously during the entirety of the deployment. The winds, measured at weather stations designated in Fig. 1(a) as W1 to W4, were relatively calm throughout the experimental period with a mean wind speed around 2 m/s, which diminished toward zero in the overnight and early morning hours.

1. Platform motion

The nine channels of non-acoustic motion data were sampled at 50 Hz and combined using the Madgwick motion fusion algorithm6 to produce estimates of platform pitch, roll, and heading on each AUMDAR system during the experiment. After correcting for the magnetic declination at the experimental location (3.85° east of north), A1 reported a stable heading of 231.1°±0.6°T and A2 reported a stable heading of 208.0°±0.4°T. The respective heading of each system was used to stabilize the acoustic data relative to true north (T). Throughout the remainder of this paper, all bearings are reported in degrees relative to true north (T). The pitch and roll estimates of both systems were less than 1° and 0.5°, respectively. Because the platforms were vertically oriented throughout the experiment to within 1°, no correction was made to the acoustic data for any vertical angle estimates.

1. Omnidirectional data

Time series acoustic data were recorded during the experiment at a sample rate of 9.6 kHz. The first post-processing step was to short-time Fourier transform the omni-, x-, y-, and z-channels to convert the data to power spectral density (PSD). Only a high signal-to-noise ratio (SNR) sound is considered in this paper. A SNR criterion was enforced through a time/frequency dependent mask applied to the PSD to discard any spectral data that were less than 12 dB above the early morning average PSD (defined by the period between 00:00 and 04:00, all times CDT). The resulting spectrograms are shown in Fig. 2(a) for A1 and Fig. 2(e) for A2. The black regions represent the masked data which are not utilized throughout the remainder of the manuscript. The first notable features in the spectrogram are broadband vertical striations. Each striation is an acoustic contact from a discrete surface vessel (fishing boat, ski boat, stand-up personal watercraft, etc.) passing within the direct acoustic field of view of the receiver. In this context, the direct acoustic field of view is defined as the underwater space in which acoustic energy arrives at the receivers along largely in-plane propagation paths. Regions of the lake where in-plane acoustic energy from surface vessels is blocked by the bathymetry is considered outside the direct acoustic field of view of the receivers. Any detectable out-of-plane energy arriving at the receivers from the same vessels is considered outside the direct acoustic field of view. The discrete vessel density is greatest between the hours of 12:00 and 20:00, tapers off toward midnight, and is lowest between the hours of midnight to 06:00 of the following day. The discrete vessel density remains relatively low from 06:00 to 08:00 AM on June 14.

FIG. 2.

(Color online) Omnidirectional PSD vs time for (a) A1 and (e) A2. Beamformed source bearing vs frequency and time for (b) A1 and (f) A2. Band-averaged (200 to 700 Hz) omnidirectional PSD vs time for (c) A1 and (g) A2. MBGF for azimuthal DOA verses time for (d) A1 and (h) A2.

FIG. 2.

(Color online) Omnidirectional PSD vs time for (a) A1 and (e) A2. Beamformed source bearing vs frequency and time for (b) A1 and (f) A2. Band-averaged (200 to 700 Hz) omnidirectional PSD vs time for (c) A1 and (g) A2. MBGF for azimuthal DOA verses time for (d) A1 and (h) A2.

Close modal

The second notable feature in the spectrogram data is a persistent narrowband tone at 116 Hz. This tone originates from a J13 projector submerged at 10 m depth at the Lake Travis Test Station (LTTS), cf. Fig. 1(b). The projector was turned on at 16:35 on June 13 and turned off at 07:26 on June 14. The primary purpose of the projector was to generate sound at a known bearing to each receiver so that the non-acoustic data from the environmental boards and the acoustic stabilization processing could be validated. The distance/line of bearing from A1 and A2 to the projector was 822 m/193° and 1232 m/205°, respectively. The received level was approximately 16 dB higher on A1 than on A2, which is likely attributed to the different receiver ranges and to the varying degree of bathymetric shielding between the source and receiver locations.

The third notable feature in the spectrogram data is an increase in the omnidirectional receive level between 200 and 700 Hz occurring between the hours of 16:00 and 00:00. This period of increased low-frequency energy does not appear to be directly correlated with the discrete vessel density within the direct field of view of each receiver. In the context of not appearing to emanate from discrete contacts, this energy will be referred to as diffuse. To better visualize the diffuse energy, the 200 to 700 Hz band averaged omnidirectional levels are, respectively, plotted for A1 and A2 in Figs. 2(c) and 2(g). In these figures, it is observed that despite the waning vessel density near the receivers, the broadband low-frequency energy slowly builds from about 70 dB at hour 16, peaks around 83dB at hour 20:15, and decreases to 72 dB at hour 23. In searching for potential correlations for this observation, it is noted that sunset occurred at 20:33 on June 13, 2018. This observation prompts the fundamental questions considered in this manuscript: (1) Is the increase in the diffuse, low-frequency noise related to an increase in recreational boating occurring between 16:00 and 20:30 (sunset), and (2) why is the increase in low-frequency noise not directly correlated to the density of discretely observable contacts? Evidence which provides answers to these questions will be explored in Secs. III B 2 and III B 3 through additional analysis of the measured data and in Sec. IV through numerical modeling.

2. DOA estimation

There are a variety of ways that the DOA can be estimated for narrowband and broadband sources. In this work, an established and straightforward approach is utilized to beamform the vector sensor data at each frequency and time sample to obtain the azimuthal and vertical angles with maximum sound intensity. This approach is described by multiple authors.7–10 The frequency domain beamforming technique is given by [cf. Eq. (9) of Ref. 9],

S(k)=w0O(k)+w1X(k)+w2Y(k)+w3Z(k),
(1)

where S is the beamformed data for a specific time sample and acoustic wavenumber k. The calibrated, omnidirectional complex pressure spectrum at each time sample is given by O and the calibrated directional spectra are X, Y, and Z. The beamformer weights are given by

w0=a0/ρcw1=a1cos(θ)sin(ϕ)w2=a2sin(θ)sin(ϕ)w3=a3cos(ϕ),
(2)

where θ is the azimuthal steering angle and ϕ is the vertical steering angle as measured from the z-axis (defined positive upward). The shape of the beam is controlled by the choice of the parameters a0, a1, and a2. In this work, the optimum null placement beampattern was selected where a0 = a1= a2 = 1. Although it has a wider main lobe than the maximum array gain beampattern, it does not have a backside lobe that can cause ambiguities in the azimuthal angle estimate in low SNR scenarios. The DOA estimate for each frequency and time sample is given by the steering angles that maximize |S(k)|2. In this work, beams were steered every 1° in the azimuthal angle and every 3° in the vertical angle.

The maximum azimuthal beam response angle for each frequency and time sample are shown for A1 and A2 in Figs. 2(b) and 2(f). As with the spectrogram data, acoustic contacts from discrete vessels appear as vertical striations in the beamformed data. The azimuthal localization allows one to conclude that almost all (if not all) of the contacts are broadband, and fill the entire spectrum between about 200 Hz and 1.5 kHz. Of particular interest is the beamformed arrival angles for the diffuse, low-frequency background noise. For A1, the vast majority of the angles are between 240° and 300°. There is more variability in the same frequency/time region for A2, but a high majority of these points fall between 150° and 250°. These observations suggest that there is some persistent directionality to this low-frequency background noise.

To create a simpler azimuthal DOA display, the broadband beamformed data shown in Figs. 2(b) and 2(f) are collapsed over frequency. A Maximized Broadband Gaussian Fit (MBGF) estimation approach estimates a single source bearing for each time sample. This approach is briefly described here. For a given time sample, a normalized histogram of the azimuthal DOA (0° to 359°) is constructed. Due to the acoustic masking removing nearly all of the frequency bins for some time samples, a broadband DOA is only estimated if the histogram contains more than 20% of the total number of frequency bins. The histogram is then mirrored about the 0° and 359° endpoints, and a Gaussian distribution with free parameters μ (mean) and σ (standard deviation) is fit to the normalized histogram data. The purpose of mirroring the histogram about the endpoints is to allow the Gaussian fit to take on mean values near the endpoints. Only a single Gaussian distribution is fit for each time sample, and so only the peak broadband arrival angle will be returned if there is a multimodal histogram.

The MBGF DOA angles for the two AUMDAR systems are shown in Figs. 2(d) and 2(h). There is a noticeable lack of broadband DOA angles between midnight and 06:00 due to the aggressive mask (with the exception of one contact near 01:45). During the time of high vessel density (hours 12:00 to 20:00), there is also a noticeable sparsity of angles between about 60° and 210° on both systems. The given explanation for this observation is that the combination of receiver depths, receiver locations in the northern river channel, the nearly exposed Sometimes islands, and the shallow source depths significantly limit the amount of acoustic energy arriving from sources located to the south and east of the receivers. The bathymetry creates an effective acoustic barrier to nearly half of the basin located at the southeast end of Lake Travis. There is one notable exception for A2. Intermittently between the hours of 17:00 and 20:00, and then more persistently between the hours of 20:00 and 23:00 there is a contact loitering between the angles of 120° and 150°. This contact was visually correlated to a small houseboat that lingered around the shallowest part of the Sometimes Islands in the vicinity of A2. The acoustic energy from this contact does not appear to be well received on A1.

Although computed, the vertical arrival angles are not shown in this manuscript. The justification for their exclusion is that the angles largely point toward the horizontal. Only in the case where a surface vessel passes nearly directly overhead of A1 or A2 does the vertical arrival angle migrate toward the surface for a short period of time. The typical excursion of the vertical angle above horizontal is on the order of 15° although it was as high as 60° for a few contacts.

3. Low-frequency noise directionality

To more clearly see the directionality of the diffuse, low-frequency ambient noise, a portion of Figs. 2(c), 2(d), 2(g), and 2(h) zoomed to hours 20:00 to 22:00 is shown in Figs. 3(a) and 3(b) where data from A1 and A2 are combined into a single plot and are color coded by receiver. This time period was selected to illustrate the peak of the ambient background noise despite the relative lack of discrete contacts within the direct acoustic field of view of the AUMDAR systems. Discrete surface vessels are identifiable as peaks in the 200 to 700 Hz band-averaged omnidirectional levels shown in Fig. 3(a) as well as smooth lines in the MBGF azimuthal angles shown in Fig. 3(b). Vertical lines have been added to Fig. 3(b) to bound time periods containing discrete contacts, which are also labeled C1 through C12. Contact tracks, estimated from cross-fixed MBGF DOA estimates from A1 and A2, are plotted on top of a bathymetric map in Fig. 3(c). The beginning of a track is marked with a small circle and the end of a track is marked with an arrowhead.

FIG. 3.

(Color online) (a) Band-averaged (200 to 700 Hz) omnidirectional PSD vs time for A1 and A2. (b) MBGF for azimuthal DOA for A1 and A2. (c) Contact tracks estimated by cross-fixing MBGF DOA estimates from A1 and A2, labeled C1 to C12.

FIG. 3.

(Color online) (a) Band-averaged (200 to 700 Hz) omnidirectional PSD vs time for A1 and A2. (b) MBGF for azimuthal DOA for A1 and A2. (c) Contact tracks estimated by cross-fixing MBGF DOA estimates from A1 and A2, labeled C1 to C12.

Close modal

An inspection of Fig. 3(c) reveals interesting information about the acoustic propagation environment and the direct acoustic field of view of the AUMDAR systems. Tracks C2, C3, C6, and C10 all originate in the vicinity of the 25 m isobath near the southernmost bend in the river channel. In a similar way, C4 and C5 terminate and C12 originates in a region that is close to a steep bathymetry gradient where the river channel is oriented along a north/south line. Seven of the 12 tracks either begin or end near the steep slope defined by the northern edge of the Sometimes Islands, again suggesting that this feature provides strong acoustic shielding from sources located to the south and east of the receivers.

Figure 3(b) also provides an estimate of the DOA for the diffuse background noise. Between the time periods containing discrete contacts, the MBGF DOA estimates from A1 fall in an angular aperture between 255° and 285°, a region geospatially illustrated by a wedge emanating from A1 in Fig. 3(c). The estimates from A2 fall in an angular aperture between 225° and 260°. As mentioned earlier, it is believed that the A2 DOA data points near 180° are generally attributed to a houseboat loitering in the vicinity of A2, a contact which may also appear as C9 for a brief time. The AUMDAR system at A2 may also be influenced by sound propagating along the river channel from the northeast, arriving at angles near 80°. However, the primary observation made here is that the directionality of the diffuse background noise on both systems generally points westward up the river channel. It is therefore hypothesized that this noise originates from some spatial distribution of surface vessels located in more northern parts of the lake and that the observed angular span of arrival angles results from horizontal reflection of sound in the river channel during its propagation to the receiver locations.

An acoustic model can yield valuable insights into the propagation environment for a given waveguide. As with any numerical computation, the fidelity of model outputs as compared to measured data often depends on the accuracy of the model inputs. Specifying model inputs that accurately reflect the waveguide properties for 3D propagation models can be especially challenging, a reality often arising from a sparsity of environmental observations. A 3D ray-based model, BELLHOP3D,11 is utilized in this work to provide reasonable evidence and plausible explanation to support the hypothesis that the diffuse, low-frequency noise arrives at the receivers because of horizontal reflection in the river channel. Perfect agreement between observations and model output is not expected.

This section describes the input parameters for the acoustic model. All of the acoustic sources in the analysis were assumed to be surface vessels with an effective source depth of 0.5 m. From a combination of the local water depth and the known mooring dimensions, the receiver depths were set at 41 m. A relatively dense ray fan was utilized, consisting of 100 vertically-launched Gaussian beams (between −40° and 0°, positive vertical angles defined upward) and 1000 horizontal beams spanning ±45° of the line of bearing between the source and receiver. The acoustic frequency modeled in this work is 400 Hz, a frequency located approximately in the center of the diffuse energy band spanning 200 to 700 Hz and hours 16:00 and 00:00 in the measured data.

The bathymetry is the primary mechanism causing out-of-plane acoustic propagation in this waveguide. The model bathymetry was derived from historical elevation data provided by the LCRA (latitude, longitude, and AMSL), combined with the reported lake level for June 13, 2018: 202.2 m AMSL. An additional 0.8 m decrease to the lake level was included such that parts of the Sometimes Islands were exposed above the air/water interface in the modeled bathymetry, as observed on the day of the experiment. It is noted that the LCRA data are somewhat coarse in resolution and does not contain surface roughness from rocks, boulders, submerged plants, shrubs, and trees, fences, vehicles, and structures, all of which are known to exist on the lake bed. Some of the limitations of the LCRA data are identifiable when compared with the higher-resolution data from the forward-looking sonar [cf. Fig. 3(c)]. However, the LCRA data are selected for the analysis because it spans the entire experimental region while the spatial coverage of the sonar data is limited.

A nominal geoacoustic description of the lake bed was drawn from prior inversion work in Lake Travis near the southern side of the southern river channel, and east of LTTS.12 The general description arising from that work consisted of an approximately 1.5 m thick unconsolidated sandy sediment layer overlying a high speed basement (likely regional limestone). The geoacoustic parameters provided to BELLHOP3D are given in Table I. While it is likely that the limestone basement is persistent throughout the region, it is unlikely that the first layer description is uniform over the entire lake bed. It is possible that nonuniform sediment accumulation has occurred over the past 76 years since the dam's construction. Unfortunately, there is not enough prior information to support anything other than a spatially uniform geoacoustic representation.

TABLE I.

Geoacoustic parameters for the modeled environment.

ParameterValueUnits
Layer 1 Compressional speed 1775 [m/s] 
 Thickness 2.31 [m] 
 Density 1.56 [g/cm3
 Attenuation 1.3057 [dB/(m kHz)] 
Layer 2 Compressional speed 2072 [m/s] 
 Thickness 28.5 [m] 
 Density 1.95 [g/cm3
 Attenuation 0.249 [dB/(m kHz)] 
Halfspace Compressional speed 2550 [m/s] 
 Density 2.05 [g/cm3
 Attenuation 0.233 [dB/(m kHz)] 
ParameterValueUnits
Layer 1 Compressional speed 1775 [m/s] 
 Thickness 2.31 [m] 
 Density 1.56 [g/cm3
 Attenuation 1.3057 [dB/(m kHz)] 
Layer 2 Compressional speed 2072 [m/s] 
 Thickness 28.5 [m] 
 Density 1.95 [g/cm3
 Attenuation 0.249 [dB/(m kHz)] 
Halfspace Compressional speed 2550 [m/s] 
 Density 2.05 [g/cm3
 Attenuation 0.233 [dB/(m kHz)] 

The water column sound speed profile (WCSSP) is measured by an automated logging device, located at LTTS, that scans the water column to a depth of 18 m at a frequency of approximately once per hour. The WCSSP measurements made on the days of June 13–14, 2018 suggested a stable, downward-refracting profile. The mean profile measured at LTTS is shown by the solid line in Fig. 4. The extrapolated region of the WCSSP that extends from the end of the LTTS record down to the deepest portion of the river channel is shown by the dashed line. The temperature at the bottom of the river channel was unknown, and therefore the extrapolation is a non-data driven approximation. It is not known whether the single, localized profile shown in Fig. 4 is representative of the larger Lake Travis region, but in the absence of additional information, this single profile is applied uniformly throughout the model domain.

FIG. 4.

WCSSP used in the acoustic propagation model. The solid black line indicates the average profile measured at LTTS for June 13, 2018 and the dashed line represents an extrapolation.

FIG. 4.

WCSSP used in the acoustic propagation model. The solid black line indicates the average profile measured at LTTS for June 13, 2018 and the dashed line represents an extrapolation.

Close modal

The standard ray trace output from BELLHOP3D is useful in visualizing the acoustic propagation pathways between a source and receiver. An example of the ray output is shown in Fig. 5(a) for an arbitrary source location to the northwest of A1. The black lines in the figure suggest that a direct path arrival is possible in the model for this source location, but that a large number of rays also reflect around the bend in the river channel. Six specific eigenrays that pass through the receiver position at A1 are highlighted in red. One of the eigenrays, labeled DP, represents the arrival from the line of bearing to the source, which is denoted as “direct path” in this manuscript. Eigenrays D1 and D2 travel along nearly the same line of bearing as DP but arrive at A1 after reflecting off the southern wall of the northern river channel. Eigenrays R1, R2, and R3 reflect from the western wall of the river channel and arrive at the receiver after either one or two distinct turns in the horizontal plane.

FIG. 5.

(Color online) (a) Bathymetric map overlain by a ray fan (black lines) and eigenrays (red lines). (b) Modeled TL vs azimuthal arrival angle for receiver A1. Specific ray arrivals are labeled in (a) and (b).

FIG. 5.

(Color online) (a) Bathymetric map overlain by a ray fan (black lines) and eigenrays (red lines). (b) Modeled TL vs azimuthal arrival angle for receiver A1. Specific ray arrivals are labeled in (a) and (b).

Close modal

To more clearly understand the azimuthal and vertical ray arrivals at the receivers, the source code of BELLHOP3D was modified to also include ray amplitude at the receiver as a function of the azimuthal arrival angle as a standard output. From this additional output, the modeled transmission loss (TL) as a function of arrival angle was calculated from a bivariate histogram of azimuthal receive angle and ray amplitude. The calculated result is depicted in Fig. 5(b), with the previously discussed eigenrays labeled at the appropriate peaks in the TL response curve. The minimum loss (i.e., the smallest TL) occurs for the direct path arrival DP with a TL of 59 dB and a DOA of 333°. The modeled acoustic pathways for D1 and D2, located at 137° and 163°, have approximately 15 and 23 dB more loss than DP. Three distinct reflected pathways, R1 to R3, have respective DOAs of 261°, 299°, and 217° and TL between 75 and 80 dB. It is interesting to note that the spread of arrival angles related to the reflected pathways is substantially less for R2 than it is for R1 and R3, a feature that may arise from a restricted set of ray paths caused by the narrow water inlet located in the vicinity of where R2 turns in the horizontal plane.

For the purpose of discussion, the strong bathymetry gradient oriented roughly along a north/south line to the west of Windy Point will be referred to as the Windy Point acoustic horizon. For a vessel that has transited northwest of this horizon and loses direct path propagation, then DP, D1, and D2 will no longer contribute to Fig. 5(b). However, the reflected pathways R1 to R3 will remain viable pathways between source and receiver. Qualitative analysis of the cross-fixed tracks from the experiment, a few of which are shown in Fig. 3(c), tend to suggest that the loss of the direct path arrivals occurs when the vessel crosses the Windy Point acoustic horizon, while the model allows the direct path arrivals to persist to locations northwest of this line. Due to approximate bathymetry, assumed homogeneity of the WCSSP, and an assumed source depth, there is understandable uncertainty in the model about the precise location where direct path arrivals would be inaccessible to the receiver. It is beyond the scope of the present analysis to provide higher fidelity or iterate on potential model inputs.

When multiple acoustic pathways exist between the source and receiver, an acoustic vector sensor located at the receiver can only resolve a single DOA. The apparent DOA will be an intensity-weighted average of all the arrival angles. For the example source location given in Fig. 5, and in the absence of direct path arrivals, the modeled vector sensor response angle would be about 261°. This modeled arrival angle lies within the observed spread of MBGF angles for A1 [cf. Figs. 3(b) and 3(c)] and provides plausible evidence that sound traveling down the river channel would be detectable at the receivers.

Section IV B provided a detailed examination of propagation from a single source to receiver A1. In this section, a grid of sources located to the west and northwest of the Windy Point acoustic horizon is considered. As shown in Fig. 6, the sources are spaced every 142 m in the longitudinal direction and every 122 m in the latitudinal direction for a total of 318 source positions. Position 1 is the southeastern-most point and the source numbering increases from south to north along each column. The source numbers for the top and bottom of each column are labeled in the figure.

FIG. 6.

(Color online) (a) Bathymetric map overlain by the locations of 318 modeled source positions relative to receiver locations A1 and A2. For reference, source numbers are included at the bottom and top of each column in the grid.

FIG. 6.

(Color online) (a) Bathymetric map overlain by the locations of 318 modeled source positions relative to receiver locations A1 and A2. For reference, source numbers are included at the bottom and top of each column in the grid.

Close modal

Modeled TL vs azimuthal angle, comparable to that of Fig. 5(b), is shown in Fig. 7 for all 318 source positions to each receiver. In this figure the data are stacked vertically by source number and colored by TL, with each block of data corresponding to a column of grid points. The same distinctive categories of arrivals that were discussed in Fig. 5 are present in Fig. 7. The approximate angular locations for the DP arrival for the first 100 source locations are marked by a solid line in the figure. Similarly, the approximate angular locations for the D1 and D2 arrivals are indicated by a dashed line. The various reflected paths (if present) occur between these two angular extremes. Figure 7 suggests that not every pathway is present for every source location. For example, consider propagation from the source to A1, which is shown in Fig. 7(a). Within the first column of gridded source positions, numbered 1 through 23, the direct path and D1 and D2 arrivals disappear after source number 10 (located near Windy Point). For source positions 11 through 23, the strongest reflected energy has a DOA of 282°. A second set of reflected arrivals for the same source locations occur at 207° but have about 22 dB more loss. A similar pattern of arrivals is observed from propagation from the source to A2 in Fig. 7(b).

FIG. 7.

(Color online) Ray amplitude vs azimuthal arrival angle for 318 gridded source locations to receivers (a) A1 and (b) A2. For the first 100 source positions, approximate locations of DP arrivals are marked by a solid line and D1 and D2 arrivals are marked by a dashed line.

FIG. 7.

(Color online) Ray amplitude vs azimuthal arrival angle for 318 gridded source locations to receivers (a) A1 and (b) A2. For the first 100 source positions, approximate locations of DP arrivals are marked by a solid line and D1 and D2 arrivals are marked by a dashed line.

Close modal

Figure 7 shows how the number and type of reflected pathways changes with the source location. For example, compare source number 20 to source number 160 in Fig. 7(a). Because of its nearly due-north location from Windy Point, source 20 contains one strong pathway at 282° and one weaker pathway centered at 217°. Source 160, which is located nearly due-west of Windy Point in a shallow part of the lake contains a more diffuse pathway, with out-of-plane sound arriving at a number of angles between 160° and 300°. It is also observed in Fig. 7 that the amplitude of all the arrivals decreases dramatically after source number 204. The reason for this decrease in arrival amplitude can be explained by the combination of source location and bathymetry (cf. Fig. 5). For sources located in the northwestern area of the map (sources 205 to 318), the sound is likely attenuated as it travels over the shallow area centered around 30.416° N, 97.911° W or as it requires additional reflections near the Windy Point outcropping before arriving at the receiver. This modeling result suggests that the largest contributions to the low-frequency ambient noise field observed at the receivers is limited to a relatively specific region of the lake corresponding to source numbers 1 to 204.

The direct pathways DP, D1, and D2 are not as strong in the observed data as they are in the model. This is potentially attributed to errors in one or more of the model inputs, likely the bathymetry or WCSSP, which were discussed at length in Sec. IV A. It is beyond the scope of the present analysis to iterate on or to invert for 3D model parameters which would preclude the direct pathways. An alternative approach, and the one taken in the present analysis, is to make modifications to the modeled data shown in Fig. 7. In this case, reasonable modifications to the modeled data are possible because each pathway can be adjusted independent of the others. A modified set of modeled data was generated where the contributions from the direct pathways were reduced by 10 dB. All of the model results from this point forward are generated from this modified data set.

Two questions remain and will be investigated from the model results. First, what would the modeled vector sensor DOA look like as a function of the number of sources present on the lake? Second, as the number of modeled sources increases, is the increase in the modeled level at the receiver consistent with the measured data? Since there is no independent supporting information regarding the spatiotemporal distribution of sources, a statistical approach is employed in this analysis.

There are two free parameters in the analysis, the number of sources and the location of the sources. For each possible number of sources N, 25 000 random realizations of the spatial source locations were generated. For example, for N =7, seven of the 318 precomputed source locations are chosen at random. Assuming a uniform source level, the TL as a function of arrival angle for those seven randomly chosen source locations are combined to estimate the DOA (a single number) and effective TL (a single number). Then 24 999 more random realizations are made in a similar manner, using seven sources each time. Then a normalized histogram of DOA and a normalized histogram of TL are constructed for the case of seven sources.

The aforementioned realization analysis was completed for N between 1 and 50. The estimated vector sensor DOA as a function of the number of sources is shown in Fig. 8, where the top row of the figure [Figs. 8(a)–8(c)] is for A1 and the bottom row [Figs. 8(d)–(f)] is for A2. The modeled DOA histogram as a function of the number of sources on the lake is shown in Fig. 8(a) for A1 and Fig. 8(d) for A2. The model suggests that in the absence of direct path arrivals, there is a strong probability that a distribution of sources on the lake will yield a vector sensor DOA of 275° for A1 and 243° for A2. It is also interesting to note that the width of the DOA distribution is largest when the number of sources is low and narrows as the number of sources increases. So, if the vessel traffic on the lake increased throughout the afternoon and early evening, then this model result suggests that the effective DOA should converge to a relatively stable angle. Of course, the acoustic intensity from contacts that had a direct pathway to the source would overpower the reflected arrivals while the contact was within the direct field of view of the receiver. This scenario was observed in Figs. 3(a) and 3(b), but is not specifically modeled here. For a more direct comparison between measured and modeled data, a normalized histogram of the MBGF data shown in Fig. 3(b) between the hours of 20:00 and 22:00 is included as Fig. 8(b) for A1 and Fig. 8(e) for A2. The measurement and model results are in good agreement during this period of time when the diffuse energy was at a maximum and discrete acoustic contacts within the acoustic horizon were at a minimum.

FIG. 8.

(Color online) Normalized histograms of modeled vector sensor arrival DOA from 25 000 realizations containing a variable number of sources for (a) A1 and (d) A2. Normalized histograms of MBGF data during the hours of 20:00 to 22:00 for (b) A1 and (e) A2. Normalized histograms of model TL for 25 000 realizations containing a variable number of sources for (c) A1 and (f) A2.

FIG. 8.

(Color online) Normalized histograms of modeled vector sensor arrival DOA from 25 000 realizations containing a variable number of sources for (a) A1 and (d) A2. Normalized histograms of MBGF data during the hours of 20:00 to 22:00 for (b) A1 and (e) A2. Normalized histograms of model TL for 25 000 realizations containing a variable number of sources for (c) A1 and (f) A2.

Close modal

Last, we turn our attention to the change in modeled level as the number of sources increases. To briefly revisit the measured data, Figs. 2(c) and 2(g) suggest an approximate 12 dB change in the PSD of the low-frequency background level between the hours of 16:00 and 00:00. The modeled histogram results for TL, shown in Fig. 8(c) for A1 and Fig. 8(f) for A2 indicate that a 12 dB swing in the reflected level is possible by changing the number of vessels on the lake from 1 to 28. This result is not necessarily presented as a method to predict vessel density, but as plausible evidence that the data in Fig. 2 are likely attributed to an increase in vessel density occurring in the late afternoon and early evening.

This paper presented experimental data from two AUMDAR vector sensor platforms moored in Lake Travis during a 20 h experiment. During this time, the DOA of sound propagation from many surface vessels was estimated at A1 and A2. By cross-fixing discrete contacts, it was clear that an acoustic horizon caused by the Sometimes Islands was present to the south of the receiver locations and that an acoustic horizon near Windy Point blocked direct path propagation from sources located about 900 m to the northwest of the receivers.

Despite this limited acoustic field of view, acoustic energy between 200 and 700 Hz exhibited a distinct increase between the hours of 16:00 and midnight, local time. It was hypothesized that the increase in the low-frequency broadband energy was correlated to an increase in recreational boating timed with the late afternoon and early evening hours. The azimuthal arrival angles for this energy was approximately confined between 255° and 285° for A1 and 225° and 260° for A2. The given hypothesis was that the energy originated from vessels located outside the direct acoustic field of view to the northwest and propagated down the river channel to arrive at the receiver locations.

The observed data and associated hypotheses were supported by 3D acoustic modeling efforts. A ray trace for an exemplary source revealed both direct and out-of-plane pathways for sound to arrive at the receiver locations. A statistical analysis based on thousands of random source point distributions confirmed that the expected distribution of arrival angles should be centered near 275° for A1 and 243° for A2. This result was in good agreement with the observation. Likewise, it was shown from the model that an increase in received level of 12 dB is possible as the number of sources increases from one to 28.

The directionality of ambient noise in this paper is somewhat unique in underwater acoustics, insomuch as it arises from the combination of a restricted field of view for direct path arrivals and bathymetry that supports very strong out-of-plane pathways. However, similar situations may arise in other constrained environments, including lakes, rivers, and harbors. The paper also shows the utility of vector sensor platforms in observing and understanding complex propagation environments.

This research was supported by the Internal Research and Development program at the Applied Research Laboratories. The 3D modeling was supported by ONR Award No. N00014-18-1-2401. The authors gratefully acknowledge the engineers, technicians, and staff who prepared the hardware and assisted with the lake deployment.

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