Observations of mid-frequency sound propagation on the Washington continental shelf with a subsurface duct Free

Over 60 years ago, Mackenzie¹ made the following acute observation after analyzing sound propagation data in shallow water over frequencies spanning 350–1400 Hz: “One of the most striking features of the long-range, shallow-water propagation of sonic frequencies is the fluctuation of the received signals. When a steady single-frequency tone is transmitted, the received signal level will vary over a range as much as 50 db.” Some of the 50 dB variation is now known to be due to narrowband interference, but even today, sound level variation on the continental shelf remains difficult to predict, due in large part to upper ocean variability. This difficulty is exacerbated by the operational need to make such predictions for any source/receiver geometry. With modern technological advancement, this is further complicated by the need to predict the temporal and spatial coherence of the acoustic field.

Several approaches can be adopted to improve predictions of mid-frequency sound (1–10 kHz) propagation and its variability. These include collecting in situ ocean data over space and time, incorporating historical data into acoustic models, and developing deterministic and stochastic ocean models that can adequately provide guidance to assist simulating sound propagation in space and time. We have begun an effort to investigate systematically the relative importance and efficacy of each approach and how to combine them in different scenarios. The work reported here is an initial step toward that goal and is aimed at reporting data and preliminary analysis from a mid-frequency sound propagation experiment conducted on the Washington continental shelf in the summer of 2022.

There are two aspects of mid-frequency propagation on the Washington shelf that this paper is focused on: the effect of a subsurface duct on sound propagation and the observed levels of sound intensity fluctuations. A subsurface duct refers to a channel with a sound speed minimum which effectively traps sound, enabling it to propagate to a long range within the duct. The most well-known of these is the deep and persistent SOund Fixing And Ranging (SOFAR) sound channel.² Ducts that form above this channel or in shallow water are sometimes referred to as secondary subsurface ducts. These ducts tend to be variable in time and space with their formation being driven by seasonal or episodic oceanographic processes.³ 

Early experimental work examining the physics of propagation within a subsurface duct, specifically the SOFAR channel, can be found in Fitzgerald et al.,² where its effects on deep water propagation were measured using explosive sources. One of the early numerical works on model/data comparison concerning a secondary subsurface duct is by Lawrence⁴ who considered the complex but interesting case where a subsurface duct is associated with a summertime eddy. Lately, a series of publications has been devoted to field work in the Beaufort and Chukchi seas,^5–8 where rapidly changing arctic climate conditions have resulted in the presence of a persistent subsurface duct. There has not been a systematic survey of secondary subsurface ducts in the world oceans; however, an initial effort in the climatology of such ducts over time and space has recently been given.⁹ As part of the effort leading to this 2022 experiment, Xu et al.³ surveyed sound speed profiles obtained from archived mooring and glider observations collected off the Washington coast and investigated potential oceanographic mechanisms that contribute to the formation of the subsurface duct.

The second area of focus is on the investigation of intensity fluctuations in mid-frequency sound propagation. Most of the research work on sound intensity fluctuations has been for low frequencies, typically at a few hundred Hertz. Notably, Headrick et al.¹⁰ investigated normal mode fluctuations in the presence of internal waves at the Mid-Atlantic Bight, Fredricks et al.¹¹ systematically analyzed scintillation statistics of acoustic signals from data taken at the New England shelf break, and Duda et al.¹² reported sound intensity fluctuation analysis of ASIAEX data taken from the South China Sea. A series of papers^13–16 reported 2–10 kHz sound fluctuation in the presence of internal waves during the Shallow Water 2006 (SW06) experiment off the New Jersey coast. Mid-frequency propagation has seen increased interest since that experiment. For example, DeFilippis et al.¹⁷ investigated the impact of small-scale sound speed variability on mid-frequency (1–10 kHz) acoustic propagation.

This paper reports data analysis from the 2022 experiment off the Washington coast. This is a joint field effort between oceanographers and acousticians in the hope that by combining ocean models, in situ ocean data, and historical ocean records, prediction of mid-frequency sound propagation and its fluctuations at different spatial and temporal scales can be improved. Harcourt et al.¹⁸ provides a preliminary account of the experiment, emphasizing work on ocean modeling and ocean measurements, as well as initial comparisons on the mean acoustic intensity field between data and simulations based on several ocean models. This paper primarily focuses on providing details of acoustic measurements and analysis, especially on the quantitative effects of subsurface ducts on sound propagation and on the statistics of sound intensity fluctuation. It is hoped that this analysis will lead to rational decisions on how to deterministically or stochastically model these effects. Section II provides a general description of the experiment, including acoustic measurements and various supporting ocean measurements. Section III is devoted to the analysis of subsurface duct effects and Sec. IV addresses the quantification of sound intensity fluctuations. Finally, in Sec. V, a discussion of the observations is provided, commenting on oceanographic mechanisms that potentially drive the observed acoustic behavior and on possible ways to improve mid-frequency sound propagation prediction at different spatial and temporal scales. Follow-on research topics based on the field data will also be briefly mentioned before concluding. Progress in modeling the acoustic measurements will be addressed in a separate publication.

The experiment took place July 22 to August 4, 2022, using the R/V Sally Ride on the Washington shelf roughly 30 km offshore from Gray's Harbor, WA. Acoustic transmissions were made using sources deployed at the westernmost end of the 20 km–long acoustics transmission line extending up the slope of the shelf with the water depth decreasing from 180 to 110 m at the easternmost end (Fig. 1). Receivers were deployed on moorings at the center of this line and at its end such that the acoustic transmissions were received at ranges of 10 and 20 km. In addition to the acoustic measurements, extensive oceanographic measurements were made using instruments deployed on five moorings as well as using a towed water column profiler, the Shallow Water Integrated Mapping System (SWIMS).¹⁹ 

Two acoustic sources were deployed at different times during the experiment. The first was the Autonomous Reverberation Measurement System (ARMS), a bottom lander consisting of a scanning directional source mounted 2.1 m above the seafloor. It also has a four-element receive array but the data on the array are not discussed in this paper. Henceforth, ARMS refers to the source only in this paper. The ARMS can be programmed to transmit 2–6 kHz sound in any direction within a 270° degree fan and can transmit any number of pings in each direction. It can transmit a peak source level of 200 dB at 3.5 kHz. The ARMS has a beam width of 20° in the horizontal direction and is approximately omnidirectional in the vertical at 3.5 kHz. Throughout the experiment, the ARMS was programmed to always transmit along the track shown in Fig. 1 with one exception: during a 1 h period on July 31, the ARMS was programmed to rotate to several different bearings, transmitting for roughly 6 min at each angle before moving to the next direction.

The second source was an ITC-1007 (Gavial ITC, Santa Barbara, CA) transducer which was suspended from the R/V Sally Ride stationed at the ARMS position (see Figs. 1 and 2) during a 2 h period on August 3, 2022. This source is omnidirectional and was deployed near 52 m depth (inside the subsurface duct) and at 30 m depth (above the duct). The water depth at the source location is nominally 177 m.

The acoustic signals transmitted were linear-frequency–modulated (LFM) pulses with 100 Hz bandwidth at center frequencies of 3500 and 6000 Hz. The ARMS source levels were 182 dB at 3500 Hz and 179 dB at 6000 Hz. The ITC-1007 source levels were 169 dB at 3500 Hz and 174 dB at 6000 Hz.

Acoustic receivers were deployed on two moorings: one at 10 km (labeled OM-C in Fig. 1) from the source and the other at 20 km [labeled receiver array mooring (RxM)] from the source. At OM-C, the water depth is 145 m, and two self-recording hydrophones (LS1, Loggerhead Instruments, Sarasota, FL) were attached to the mooring: one at 45 m depth and the other at 90 m. At RxM, the water depth is nominally 110 m and two self-recording, four-element arrays (SoundTrap ST4300) were attached to the mooring to span the water column from 26–86 m depth. Hydrophones were placed at 10 m increments over that span with the first array having hydrophones at 26, 36, 46, and 56 m and the second having hydrophones at 56, 66, 76, and 86 m. The locations and depths of the acoustic sources and receivers along the acoustic transmission line are shown in Fig. 2.

For illustration purposes, Fig. 3 shows ray trajectories with a source at 52 m depth, which is inside the subsurface duct. Figure 3(a) uses a range-independent sound speed field where the sound speed profile at 0 km in Fig. 2 is used. The launch angles for the rays are between ±3°. Here, one group of rays is trapped inside the duct and does not interact with the bottom. A second group of rays is confined between the surface mixed layer and 100 m depth where the sound speed has a maximum. A third group has steeper grazing angles and interacts with the bottom. Figure 3(b) uses the range-dependent sound speed field in Fig. 2. The same three groups of rays shown in Fig. 3(a) also appear here, but the range dependence of the sound speed field makes it possible that some of the trapped rays leak out of the duct, such as the rays that can be seen leaving the duct at close to 4 km range.

The acoustic source transmitted pulses at regular time intervals, which varied during this experiment, ranging from 10 s to 3 min. The received signal pulses from a group of transmissions are considered as a sequence with $j=1, 2, 3, …$ denoting the transmission number. The acoustic pressure pulse from the jth transmission received on a hydrophone at depth z is referred to as $sjt,z$⁠, its dependence on time (t) describes how the pulse changes shape over time. It is a real quantity that has been matched filtered. Figure 4 shows an example of two received signals after matched filtering. Unlike long-range propagation in the deep ocean where different arrivals are well-resolved, the arrival structure consists of only a couple of closely spaced peaks. The first peak at 100 ms is due to the multiple paths traveling in the duct, while the peaks at 115 and 150 ms correspond to multiple paths where the sound interacts multiple times with the seafloor. Due to bandwidth limitations, the individual path contributions within these peaks are not well-resolved and as a result, we will primarily consider the total integrated energy within the entire arrival instead.

In addition to the acoustic sources and receivers, five oceanographic moorings were deployed at the site: three along the acoustic transmission line (labeled as OM-W, OM-C, and OM-E in Fig. 1) and two located 5 km to the north-north-west (NNW) and to the south-south-east (SSE) of the central mooring (labeled OM-N and OM-S). Each mooring had five CTDs (Seabird Scientific SBE 37) and ten temperature sensors (Seabird Scientific SBE 56) evenly distributed over the mooring wire. The CTDs measured pressure, temperature, and salinity once every 10 s, while the temperature sensors collected one sample every 6 s. Each mooring also had a pair of upward-looking and downward looking ADCPs, which measured the full-depth water column current velocities. In addition to the moorings, a bottom lander with an upward-looking ADCP (Nortek Signature 100) was deployed near the central mooring (labeled JYL in Fig. 1). All five moorings and the bottom lander were deployed and collected data for the duration of the experiment.

To measure the water sound speed in three dimensions at the site, the SWIMS¹⁹ was towed behind the R/V Sally Ride for extended periods during the experiment. The system consists of a weighted tow body equipped with a SeaBird 9 CTD. The system was towed at 3–4.5 kts and cycled up and down through the water column at 60–80 m/min between 5 m beneath the sea surface and 10 m above the bottom as determined by an onboard altimeter. Over the course of the experiment, the SWIMS was towed along the 20 km–long acoustic line 64 times with each round trip along the track taking roughly 6 h. The sound speed field along the track can be found by interpolating the sound speed between the profiles, an example of which is shown in Fig. 2. The SWIMS measured sound speed fields are treated in initial analysis as a “snapshot” of the ocean, cognizant of the fact that the data are not taken in a single moment in time, and hence are temporally and spatially aliased.

To monitor sea surface roughness, a surface wave buoy (Spotter Buoy, Sofar Ocean, San Francisco, CA) was deployed during the experiment. Although detailed modeling of the surface roughness effect is yet to be conducted, the sea surface roughness is not expected to play a major role in acoustic propagation because the strong sound speed gradient below the warm surface mixed layer prevented sound from interacting with the surface at the range of interest. To assist the assessment of the geoacoustic properties at the experiment site, the Kongsberg SBP29 subbottom profiler (Kongsberg Maritime AS, Bergen, Norway) on board of R/V Sally Ride took data along the acoustic line. In addition, sediment samples are available from previous cruises.

During the entire experiment period, both the moorings and the SWIMS data exhibited the presence of a persistent subsurface duct, 10–50 m-thick, over the outer shelf and connected to thicker, deeper layers offshore.¹⁸ Along the acoustic line, as seen in Figs. 2 and 5, the sound speed profile has a complex structure near the surface extending from a mixed layer in the first 5–6 m to about 30 m, beneath which is the subsurface duct with its axis near 50 m depth. In this example, the duct is about 20 m-thick and it is a rather weak duct: the sound speed minimum is only about 1 m/s smaller than the maximum below it. Another important feature of the duct is that it has apparent range-dependence. Both the duct axis depth and duct thickness vary over space, and the duct weakens for water depths shallower than 125 m. In the example in Fig. 2, the mean width of the duct is 36.7 m with a standard deviation of 4.3 m. The mean change in sound speed between the sound speed minimum and the duct boundary (sound speed maximum below the duct axis) is 1.16 m/s with a standard deviation of 0.17 m/s. These numbers ignore the apparent bifurcation in the duct at 5 km and assume the duct boundary as the local maximum in sound speed between 60 and 80 m. While this structure within the duct has an impact on mid-frequency propagation, as will be seen later in the paper, it has little impact on the number of locally trapped modes (3–5) or the cutoff frequency of the lowest mode (300 – 500 Hz).

Analysis of the SWIMS and mooring data indicates that internal waves of varying amplitude and wavelength contribute to this duct spatial dependence. Examples of these internal waves are seen in the sound speed field data shown as background in Fig. 2, especially apparent in depths between 20 and 50 m. In summary, the subsurface duct has these three characteristics: weakness in the magnitude of its sound speed minimum, variability in range and time, and persistence over weeks. It is not obvious that such a weak and variable duct would support guided sound propagation with any efficiency at mid-frequencies.

To investigate the impact of this subsurface duct on sound transmission, we compare measured transmission loss (TL) with the sound source deployed at three depths: close to the duct axis depth, above the duct at 30 m, and near the seafloor at 175 m (2.1 m above the bottom). As designated in Fig. 2, the source was always at the western-most end of the track, at 0 km, and the TL was recorded at both 10 and 20 km ranges. Transmitted signals were at two center frequencies: 3500 and 6000 Hz.

For the two shallow source depth measurements, the ITC-1007 omnidirectional source was hung from the ship to depths either inside the duct or above the duct. At 3500 Hz, the source was lowered to 54 m depth, roughly inside the subsurface duct, and transmitted 30 pings at a rate of 1/min. Then, the source was raised to a shallower depth of 30 m where it transmitted 30 pings at a rate of 1/min. This sequence was repeated with a center frequency of 6000 Hz. For this second measurement, the in-duct source depth was 50 m. The entire set of measurements was conducted in a 2 h period on August 4, 2022.

For the ARMS source at 2.1 m above the bottom, 3500 Hz transmissions were made every 3 min for two long periods: one from July 27–31, the other from August 1–3. We report in this section a 12 h segment of data from July 27 when data were obtained on all receivers. At 6000 Hz, transmissions were also made every 3 min for 24 h on August 3 and 4.

At 3500 Hz and at 10 km range [Fig. 6(a)], when both the source and receiver are inside the duct, TL is about 8 dB smaller than that of all other source/receiver position combinations. This ducting effect is understandable: when both the source and receiver are inside the duct, a stronger signal is received because the duct traps sound and guides it to propagate with reduced loss. However, when either the source or receiver is outside the duct, TL is greater because the received sound propagates outside the duct spreading out to more of the water column and interacting with the seafloor. The same is true when both are outside the duct.

At 6000 Hz and at 10 km range [Fig. 6(c)], the results are similar but the TL difference is 13 dB greater for the receiver inside the duct. However, unlike the 3500 Hz case, an 8 dB TL difference remains for the source inside or outside the duct when the receiver is at 90 m, which may be due to increased bottom loss at the higher frequency.

At 20 km range, the duct effect is more complex due to duct range-dependency. While detailed acoustic modeling of propagation in subsurface ducts is deferred to a later publication, an initial modeling effort was conducted using the parabolic equation (PE) method to illustrate the range-dependent effects of the subsurface duct on sound propagation. The range-dependent SWIMS sound speed field shown in Fig. 2 and collected on August 3, 2022, was used in the model. The bottom is assumed to be a sandy fluid half-space with sound speed 1600 m/s, density of 2000 kg/m³, and attenuation coefficient of 0.3 dB per wavelength. This bottom model is not expected to faithfully reflect the field conditions but assumed sufficient for the purpose of assessing the effect of the range-dependent subsurface duct on sound propagation. Figure 7 shows the simulation results at 6000 Hz. (Results from simulations at 3500 Hz are similar to those at 6000 Hz and are not reported here.) The left column is for a source at 30 m, the middle column for a source at 50 m, and the right column is for a source near the bottom. The upper row has simulations assuming a range-independent sound speed profile where the sound speed profile at the source location is used. This is to demonstrate the ducting effect without the complications due to range dependence. The lower row uses the range-dependent sound speed field measured by SWIMS.

When the range-independent sound speed profile is used (upper row of Fig. 7), the classic ducting effect is clear when the source is inside the duct, even though the subsurface duct is weak. Quantitative modeling of sound leaking out of the duct due to range-dependence, including duct termination, will be conducted in follow-on research. When the source is either above the duct or near the bottom, the sound field shows no ducting effect near 50 m as expected. The higher sound speed above the duct is shown to refract sound downward and propagation is confined between the higher sound speed region above the duct and the seafloor.

When the range-dependent sound speed profile is used (lower row of Fig. 7), a more complex picture emerges: when the sound source is inside the duct, the ducting effect remains. However, the sound is found to leak out of the duct, leading to higher sound levels at depths deeper than the duct. This is especially true beyond 10 km, as was observed in the data shown in Fig. 6. Compared to the range-independent case, the ducting effect is not as clearly confined in depth and the sound level inside the duct is weaker by as much as 10 dB at 20 km range and 50 m depth. When the source is above duct, compared to the range-independent case, as the sound speed profile changes with range, the propagation conditions change as well, and the difference in the PE results reflects that. When the source is near the bottom, the propagation is affected by a bottom duct, evident in Fig. 7 at 10 km range, leading to enhanced propagation near the bottom in both the top and bottom panels of the third column in Fig. 7. The range-independent sound speed profile (top panel of Fig. 7) leads to enhanced bottom interaction as seen in the field plot, while for the range-dependent sound speed profile (bottom panel), the bottom duct weakens with range reducing the bottom interaction and resulting in sound propagation farther down range.

The interval between neighboring pings is 3 min for all data reported; hence, the SI is estimated over 3 M minutes. The estimated SI is available at 45 and 90 m depths at 10 km range and 26 to 86 m depths with 10 m spacing at 20 km range (see Fig. 2). Figure 8 shows a typical SI vs time estimated from a moving boxcar window spanning 60 min (M = 20) using data measured at 46 m depth and at 20 km range. The data are recorded continuously for two segments at 3500 Hz: one lasting roughly 4 days, July 27–31, the other just about 1 day, August 2 and 3. These were followed by a 1 day recording at 6000 Hz. The SI is high and variable; the low values are close to 0.5 and the high values are greater than unity. The overall SI at 3500 Hz found using all of the pings in the first segment is 1.4, in the second segment is 1.0, and at 6000 Hz, is 0.74. It is surprising that the overall SI at 3500 Hz is greater than that at 6000 Hz, opposite to the expectation that SI is higher for higher frequency. Note that the overall SI values for the 3.5 kHz segments in Fig. 8 are significantly higher than most of the SI values obtained with the shorter, 60 min–long moving window and is a result of the nonlinear dependence of SI on energy in Eqs. (4) and (5).

Next, we compare SI estimated from a moving window spanning 60 min (M = 20) at 10 and 20 km for 3500 Hz at 45 m depth and 46 m depth, respectively. As seen in Fig. 9, the SI is substantially greater at 20 km than at 10 km. The SI estimated from the entire first segment of data is 0.83 at 10 km and 1.40 at 20 km; and the second segment is 0.66 at 10 km and 1.00 at 20 km. This increased SI at longer range is true at 90 m depth as well.

It is worthwhile to examine in more detail the behavior of integrated energy fluctuation at different frequencies. Data from those shown in Fig. 8 at a range of 20 km were used to compare different statistical quantities at 3500 and 6000 Hz. In order to make the comparison based on similar statistical samples, we selected two sets of data: one at 3500 Hz, the other 6000 Hz. The datasets have the same 305 pings at 3 min/ping, a total of 15 h in duration. The 3500 Hz data were taken on July 27, the 6000 Hz data on August 3 and 4. Figure 10 compares the SI at the two frequencies vs depth. Here, a more complex situation appears: at shallow depths (<60 m), the SI is slightly greater for 3500 Hz than that for 6000 Hz except for that at 26 m, whereas at deeper depths, the opposite is true. The reverse of order of the SI between the 56 and 66 m is intriguing, and is a topic we hope to address through more detailed simulation studies. Recall that when all available data were used, the SI at 6000 Hz is smaller than that at 3500 Hz at 46 m depth as in Fig. 8. The result there is consistent with that found here using the same number of pings for the two frequencies. At 26 m, which is above the subsurface duct and close to the bottom of the mixed layer, the SI is the greatest, and SI at 3500 Hz is abnormally large at 2.8, and at 6000 Hz is 3.6. As shown in Ref. 20, bottom interaction in shallow-water propagation can lead to SI values significantly greater than 1.

Finally, the probability density function (PDF) of the integrated energy is presented in detail for the multi-day 3500 Hz data taken at 56 m depth and 20 km range. The PDFs taken at other range and depths have similar behavior and are not shown in the paper. Following Fredricks et al.,¹¹ the data vs time is low-pass filtered by a 2 h sliding window in order to compare long- and short-time statistical behavior. The two upper panels of Fig. 11 show the unfiltered data and low-pass filtered data. The low-pass is achieved by taking the mean of the 2 h boxcar sliding window. The lower two panels show the PDFs of the data in the two upper panels as well as the lognormal distribution. The SIs for the two cases are also given in the panels. Several features are noticeable in these panels: first, the low-pass filtered data show the approximate 12 h tidal effect, especially in the early part. Second, the low-pass filtered data have smaller variation compared to the unfiltered data: the corresponding SI are 0.14 and 1.16. Therefore, the short-time fluctuation dominates the total fluctuation. Third, the lognormal distribution fits well for both the unfiltered data and the low-pass filtered data; however, the distribution for the low-pass filtered data has a symmetric peak, whereas that for the unfiltered data has its peak biased toward the very small values, approaching an exponential distribution. Reference 11 suggests that it is not surprising that a lognormal distribution occurs for the integrated energy in a shallow water environment.

It is tempting to also analyze the scintillation and PDF of the high-passed filtered data, such as done by Fredricks et al.¹¹ where the high-pass data are obtained by subtracting the low-passed data from the unfiltered data. It is found that such a procedure applied to the current dataset results in negative values for the high-pass filtered data, making it unsuitable for scintillation analysis.

A small set of data was taken during ARMS calibration over an hour on July 31, 2022 where the ping-to-ping interval is 10 s, and the center frequency is 3500 Hz. (Recall that the ARMS source is 2.1 m above the seafloor.) This set of rapid transmissions, although limited in number, allows one to examine sound intensity correlations at short time scales. Figure 12 shows integrated energy vs time and the shortest significant temporal variation is around 5–10 min, which is consistent with the locally measured buoyancy frequency. A spectral comparison of the temporal variation of the sound energy and the temporal variation of the sound speed taken by a CTD on a mooring at the receiver location is also given in Fig. 12, showing remarkable similarity. The temporal variations of integrated energy falloff rapidly beyond frequencies of roughly 0.1–0.2 cycles/min (or time scales of 5–10 min), which is close to the expected local buoyancy frequency. This is consistent with the notion that no internal waves exist at frequencies higher than the buoyancy frequency.

At the longtime scale, Fig. 13 shows the 3500 Hz TL variation over a longer time scale at 10 km. The TL has been smoothed by a 5 h moving average of the integrated energy. A dominant semi-diurnal frequency is apparent in the TL data at both depths, similar to the temporal variation in the temperature data. Spectral analysis of the integrated energy shows that there is a broad peak corresponding to the semi-diurnal variation. At higher frequencies, the spectral level is flat, suggesting multiple scales of ocean variability contributing to the sound energy variation. Combined, these observations suggest that internal waves are one important cause for the observed sound level fluctuations, consistent with observations in deep ocean propagation and low-frequency shallow-water propagation.²¹ However, the details of the interaction between internal waves and sound propagation remain to be worked out. Other ocean processes, such as turbulence and fine structure, may also play roles contributing to the variability in the received signal.

In our study of mid-frequency sound propagation in shallow water, the main focus is a systematic investigation of TL prediction and its uncertainty at different spatial and temporal scales. This paper reports two main findings. First, a subsurface duct was found to persist for two weeks during the end of July and early August 2022 on the Washington shelf. It was a very weak duct with only a 1 m/s difference between the sound speed minimum and the maximum at the bottom of the duct. However, up to a 10 dB decrease in TL was found at 20 km range at frequencies of 3.5 and 6 kHz for a source in the duct, compared to a source outside the duct. The duct had strong range-dependence, likely due to internal waves, resulting in strong TL fluctuation and leakage of ducted energy to below the duct. It is demonstrated that using a range-independent sound speed profile taken from one location may result in a 10 dB underestimation of TL. Worth noting was that although the duct was weak, and it existed at a relatively restricted portion of the water column, the duct had a substantial impact on sound propagation if a sound source is placed in the duct. The duct was persistent over two weeks, possibly over months, consistent with immediately preceding and subsequent regional surveys of the joint field experiment, which recorded a largely contiguous subsurface duct over the outer continental shelf and upper shelf slope of the Washington coastal ocean. Understanding the physical processes responsible for production of this feature will improve TL prediction predicated upon the skill of ocean models in determining the ocean sound speed field.

The second finding was the strong ping-to-ping fluctuations (with pings just 3 min apart). The SI and probability density distribution of the integrated energy was analyzed over time, range, depth, and frequency. Strong scintillation is found for data taken at 10 and 20 km. The PDFs are well fit with a lognormal distribution. However, no consistent SI frequency dependence is observed, as indicated in Fig. 10. The 2022 field work only collected data at 100 Hz bandwidth, and there is a need for data with much wider bandwidth to assist in determining the detailed oceanographic mechanism causing the fluctuation. It is inferred from limited rapid-ping data that the shortest time scale of significant intensity variations is roughly 5–10 min, close to the time scale of the buoyancy frequency at the site, suggesting that the oceanographic origin of the strong fluctuation is likely internal waves. A better understanding of the time scales of intensity variations might be exploited to help mitigate the impact of strong fluctuations in applications.

Looking ahead to future measurements, data at much wider bandwidth than the 100 Hz band used, or on vertical and horizontal arrays, may prove valuable in mitigating the effects of strong fluctuations. More detailed measurements on the growth of fluctuations from short to long range should also be instructive.

In addition to linear internal waves that may often be present, there is some evidence of more infrequent nonlinear internal waves that may be correlated in time with the tidal cycle. Understanding the impact of nonlinear internal waves on TL could have an important role in acoustic prediction. The impact of fine spatial structures at scales smaller than that for internal waves might be important but remains to be explored. Finally, in order to take advantage of ocean modeling to improve acoustic TL predictability, TL variability at semi-diurnal and longer time scales needs to be measured and its oceanographic mechanisms investigated.

This work was supported by the U.S. Office of Naval Research Grant Nos. N00014-21-1-2524 and N00014-21-1-2419.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.