This is an investigation of sound propagation over a muddy seabed at low grazing angles. Data were collected during the 2017 Seabed and Bottom Characterization Experiment, conducted on the New England Mud Patch, a 500 km^{2} area of the U.S. Eastern Continental Shelf characterized by a thick layer of muddy sediments. Sound Underwater Signals (SUS), model Mk64, were deployed at ranges of 1–15 km from a hydrophone positioned 1 m above the seafloor. SUS at the closest ranges provide measurements of the bottom reflection at low grazing angles (<3 deg). Broadband analysis from 10 Hz to 10 kHz reveals resonances in the bottom reflected signals. Comparison of the measurements to simulated signals suggest a surficial layer of mud with a sound speed lower than the underlying mud and overlying water. The low sound speed property at the water–mud interface, which persists for less than 1 m, establishes a sound duct that impacts mid-frequency sound propagation at low grazing angles. The presence of a low-speed surficial layer of mud could be universal to muddy seabeds and, hence, has strong implications for mid-frequency sound propagation wherever mud is present.

## I. INTRODUCTION

The speed of sound in muddy marine sediments can be lower than the speed of sound in seawater near the seafloor. This low sound speed property is prominent in the lutocline, the opaque surficial layer of low-density (i.e., high porosity) fluid mud resting atop a muddy seabed.^{1} By settling processes and overburden pressure, the bulk modulus increases below the lutocline, leading to an increase in the sound speed with depth. The resulting geoacoustic profile can establish a sound duct near the water–mud interface. Very shallow-angle reflections are sensitive to this feature, and the duct can impact mid-frequency sound propagation. Here, we examine how the geoacoustic profile of marine mud affects broadband bottom reflection measurements (in the range of 10 Hz–10 kHz) using data collected during the 2017 Seabed and Bottom Characterization Experiment (SBCEX17). Although the conclusions herein are based on data taken in one area, the existence of a surficial duct may well be a universal characteristic of muddy seabeds.^{2,3}

The SBCEX17 experiment took place on the New England Mud Patch (NEMP), a large area along the 70–80 m bathymetric contour of the U.S. Continental Shelf where the seabed has a layer of mud approximately 10 m in thickness, referred to here as the mud-interval, resting on top of older sediments with a significantly higher sound speed.^{4} A distinct low-density surficial layer of mud on the NEMP is not unexpected. For example, bottom instruments landing on the seabed sank tens of centimeters into the mud rather quickly,^{5,6} and the instrument platform supporting the hydrophone used in this study settled an additional 10 cm over 5 h post deployment. Extensive core sampling^{4} and direct *in situ* measurements confirm the speed of sound within the mud is lower than in the overlaying water and the speed of sound increases with the depth into the seabed.^{5,7}

Several studies have used acoustic propagation and bottom reflection measurements made during SBCEX17 to invert the geoacoustic profile of the NEMP.^{8} Whereas these studies report a sound speed ratio across the water–mud interface of less than one and the sound speed below the mud-interval increases significantly, the geoacoustic profile over the entire mud-interval remains ambiguous.^{9} Here, we contribute to the discussion of the sound speed profiles within the mud-interval using shallow-angle (at grazing angles <3°) broadband reflection data recorded by a near bottom hydrophone^{10} of the shock front, generated by Mk64 Sound Underwater Signals (SUS) sources. The waveform of this broadband reflected signal appears to have a complex structure, which is quite different from the incident pulse. We show how this observation can be attributed to a “resonant” phenomenon^{11} caused by the low speed of sound within the lutocline.

The goal of this paper is to provide critical information from shallow-angle reflection measurements to constrain the geoacoustic profile of the NEMP mud-interval. Owing to the short 1 ms analysis window and shallow propagation angles, the data studied here are not sensitive to the deeper sediments at the bottom of the mud-interval. Models are presented to demonstrate the effects of a surficial layer, and the geoacoustic inversion results suggest that the low-speed property of mud is confined to a layer near the water–mud interface. The remainder of this paper is organized as follows: Section II describes the measurements. Section III presents a model for the bottom reflection and a recipe to simulate the measured waveforms. Section IV presents the results of a data/model comparison to identify the properties of the surficial mud layer and underlying mud and demonstrates how the data constrain the geoacoustic profile. Section V summarizes the findings and discusses implications for mid-frequency sonar operation.

## II. MEASUREMENTS

On 18 March 2017, a series of SUS was deployed off the stern of the R/V *Neil Armstrong*. The SUS were set to detonate at a 60 ft (18.3 m) depth, and radiated shockwaves were recorded by a hydrophone on the benthic Intensity Vector Autonomous Recorder (IVAR) platform. The IVAR hydrophone (ITC-1042, International Transducer Corporation) was sampled at 25 kHz and contains a high-pass anti-aliasing filter at 10 kHz. The IVAR platform settled ∼30 cm into the muddy sediment over 5 h such that its hydrophone was 1.1 m above the water–mud interface.

The IVAR received a total of 145 SUS signals during SBCEX17, comprised of 5 SUS each deployed at 29 locations, ranging from 1.3 to 13.4 km (see Ref. 10). Additionally, a “pure” Mk64 SUS shock front (i.e., reflection free) was also measured at 6 m range off the stern of the same research vessel during a follow-on experiment in 2021, which provides a reference waveform for the source signal (Fig. 1). The Mk64 SUS waveform is highly reproducible^{12} and follows an exponential decay lasting no more than 2 ms. The analysis herein focuses on the SUS deployed at the two closest stations: 1.3 km (40.4744° N, 70.6394° W) and 2.27 km (40.5006° N, 70.6191° W) from the IVAR (40.4866° N, 70.6383° W).

Figure 1 shows the measured pressure level of the shock front at 6 m (gray line) and the five waveforms from the two closest stations, which are at 1.30 km (black lines) and 2.27 km (red lines); the levels are compensated for spherical spreading to the 1 m range. The data are low-pass filtered at 10 kHz and resampled to a common 100 kHz to produce smooth waveforms. Immediately upon comparison with the source signal, the effect of the bottom reflection is apparent. This is, in part, because the receiver is very close to the seafloor; the direct and bottom reflected arrivals are not separated in time. The destructive interference of the direct arrival and reflection from the water–mud interface cause the acoustic pressure to return to zero between zero and 0.1 ms, which forms a narrow pulse. Such cancellation is expected for near horizontal reflection from an interface as the phase of the reflection coefficient corresponding to any homogeneous sediment trends toward *π* at small grazing angles.

Of great interest is the signal at 0.1–1 ms, which starts as a positive pressure and then moves to a negative, returning to zero within 0.5 ms before trending positive again. On top of this arrival is a higher frequency oscillation, which upon counting the number of cycles is estimated at about 8 kHz. Evidently, the sediment structure played the role of a filter. Particular attention is given to this unique part of the received signal as it is sensitive to the geoacoustic profile of the mud.

Note that the five measured waveforms at each station are effectively identical until the onset of the surface reflection (after 1.3 ms at 1.30 km and after 0.8 ms at 2.27 km). The surface arrival timing depends on the SUS detonation depth, and while the intended detonation depth is 18.3 m, it actually varied between 14 and 27 m over the ten deployed SUS (as determined by the timing of the bubble-pulse). Although the surface reflection appears to be an inverted version of initial arrival complex, its waveform is slightly modified due to the effect of the rough sea surface as well as the steeper angle of incidence on the bottom. To avoid these uncertainties, we focus on the bottom reflection and truncate the analysis at sea surface arrival. Data from the closest 1.3 km station affords the most time separation in the arrival sequence and will be the focus of the following analysis.

## III. MODEL

The first 1 ms of the measured waveform can be understood with a simple model. Given that our data are measured in the far-field of a source positioned well away from the interface, we approximate the phase and amplitude of the reflection with a plane-wave reflection coefficient. The received signal is a superposition of the direct arrival and its reflection from the seafloor, constructed with the reflection coefficient, is evaluated at the grazing angle determined by the source-receiver geometry.

Before continuing with the model development, we first note a few considerations. To make sure that the plane-wave ray-based model is adequate, we also used broadband parabolic equation (PE) methods to verify all of the results. These comparisons also confirm that simplifying the water column as isovelocity does not compromise the results derived from the actual sound speed profile, which, in SBCEX17, has a subtle increase of 1 m/s from the sea surface to seafloor (see Fig. 2 of Ref. 10). The measured sound speed at the bottom is 1468.8 m/s.

In the following, we develop the most basic description for the muddy seabed that will reproduce the observations. This is a uniform surficial layer of sediment overlying a halfspace of mud, giving three distinct sound speeds: in water (*c _{w}*), in the muddy surficial layer (

*c*), and in the mud halfspace (

_{L}*c*). A more sophisticated sediment model is also developed in which all of the parameters in the thin surficial layer are allowed to have a gradient, and additional basement layers can be added. However, this added sophistication does not improve or modify the model/data comparison and is only used later, at the end of Sec. IV, to generate waveforms for more complex sediment profiles cited in the literature.

_{H}The key to matching the observations to the model is a geoacoustic profile that supports a surficial sound duct. A sound duct arises when the index refraction for the surficial mud ($n=cL/cw$) is less than one *and* the index of refraction in the underlying mud ($n=cH/cw$) is greater than one. The duct establishes a set of resonant frequencies that depend explicitly on the geoacoustic properties of the surficial mud layer, its thickness, and the properties of the underlying mud.

One can best understand such resonances by studying the total reflection coefficient as a function of the grazing angle, *θ _{g}*, and frequency,

*f*. The total reflection coefficient from a seabed comprised of a layer overlying a halfspace is

where *L* is the thickness of the surficial layer, $kw=2\pi f/cw,\u2009kL=2\pi f/cL$, and $kH=2\pi f/cH$ are the wave numbers in water, the surficial layer, and halfspace, respectively, and

is the plane wave reflection coefficient at the water–mud interface, and the plane wave reflection coefficient at the layer–halfspace interface is

where *ρ _{w}*,

*ρ*, and

_{L}*ρ*are the densities in water, the surficial layer, and halfspace, respectively. The numerator of Eq. (1) represents the reflections from the top and bottom interfaces of the sediment layer while the denominator indicates any resonances caused by internal reflections within the sediment layers. Attenuation is included by making the sound speed complex.

_{H}Figure 2 shows the magnitude and phase of $R(\theta g,f)$ for an environment we find characteristic of the NEMP, a sediment layer with *n *=* *0.98 and *L* = 0.50 m, overlying a mud halfspace with *n *=* *1.005; the density ratio of the layer and halfspace are set as $\rho L/\rho w$=1.4 and $\rho H/\rho w$=1.6, respectively, and attenuation is 0.025 dB/*λ* throughout. Inspection of the reflection coefficient at small propagation angles reveals local minima in $|R|$ [see Fig. 2(a)]. The effect of the intrinsic attenuation is significant near the resonant frequencies, observed as a depression in $|R|$ around the minima. The extent of this depression is determined by the intrinsic attenuation of the sediment layer; if the sediment were lossless, true zeros and poles of Eq. (1) exist and the minimum becomes a point.

Unlike its effect on the magnitude of $|R|$, attenuation has less of an effect on the phase of *R* [see Fig. 2(b)]. Resonances occur along contours of the zero-phase at grazing angles less than the critical angle (<5° in the example). The zero-phase contours of the reflection coefficient identify a set of interference patterns, generally understood as the constructive interference of rays rattling within the thin layer, i.e., modes of the layer. The exception is the lowest-frequency zero-phase contour, which emerges at the critical angle. This feature is caused by the downward refraction from the low-speed surficial layer, and we deem this feature a quasi-resonance because there is no associated trapped mode in the surficial layer at these low frequencies. Still, this quasi-resonance has a significant effect on the reflected waveform.

The resonant effect on the bottom reflection is apparent in synthetic waveforms based on Eq. (1). The total signal is constructed as a superposition of the direct and bottom reflected fields generated by the source. Each contribution is based on the source spectrum, $S\u0302(f)$, representing the first 2 ms of the measured SUS explosions (see Fig. 1). Both are modified by a respective propagation delay and geometrical spreading term, determined by the source-receiver geometry, and the bottom reflection is further modified by the reflection coefficient evaluated at the grazing angle. The complex spectrum of the total signal, *S*(*f*), is the sum

The first term is the direct field with slant range, $r1=x2+(zr\u2212zs)2$, where *x* is the distance between the source and receiver along the surface of the ocean, *z _{s}* is the depth of the source, and

*z*is the depth of the receiver. The second term is the reflected arrival with slant range, $r2=x2+(2H\u2212zr\u2212zs)2$, where

_{r}*H*is the depth of the water column. The reflection is modified by the time delay, $\Delta t=(r2\u2212r1)/cw$, and reflection coefficient, $R(\theta g,f)$, as given by Eq. (1) and evaluated at the grazing angle, $\theta g=cos\u22121(x/r2)$. Fourier synthesis is then employed to generate a time domain signal for a given source-receiver geometry.

The reconstructed signal can be parsed into three components: the direct arrival, the initial reflection from the water–mud interface, and an additional arrival of energy that was first transmitted across the water–mud interface. Figure 3(a) is the waveform of the direct arrival, normalized to a peak amplitude of unity. Figure 3(b) is the reflection from the water–mud interface, constructed from the plane wave reflection coefficient in Eq. (2). The waveform appears inverted from the direct arrival, which is typical of near horizontal reflection from an interface. Figure 3(c) shows the remaining resonant arrival, the result of subtracting the reflection of the water–mud interface [Fig. 3(b)] from the total reflection as represented by Eq. (1). This arrival appears as a signal consisting of two relatively narrowband wave packets, i.e., resonant frequencies that correspond to the intercept of the zero-phase contours of the reflection coefficient at the incident angle (see Fig. 2). The characteristics of this arrival depend explicitly on the geoacoustic properties of the layer (and halfspace).

Figure 3(d) shows the total signal from the plane-wave ray model (thin solid line) and a waveform constructed from PE simulations of the field (dashed-dotted line). The waveforms from these methods match closely. For this PE simulation, the environmental grid replaces the sea surface with a perfectly matched layer to remove the effect of the sea surface. Additionally, the environment grid includes a higher speed halfspace (1650 m/s) below the 10 m mud interval, representative of the mud-to-sand transition of the NEMP. Due to the critical angle within the mud interval and low propagation angle, the bottom reflection is unaffected by the deeper, higher speed halfspace.

Before comparing models of the total signal to the data (Fig. 1) to infer the geoacoustic profile of the upper mud sediments, it is worth considering the reflection from deeper sand layers. We conducted detailed numerical modeling that includes a sandy basement about 9 m below the surface. We found that the sandy basement has no impact on the portion of data under study. When the mud-interval exhibits a critical angle greater than the incident grazing angle, sound does not reach the basement. Conversely, if the sound speed over the extent of the mud-interval were lower than the overlaying water (*n *<* *1), a reflection from the sand basement will arrive; however, owing to the lower propagation speed of the mud, the sub-bottom reflection is delayed. As an example, given the 1.3 km range and a 10 m mud interval with *n *=* *1, the basement reflection arrives 0.75 ms after the water-mud reflection. Given a lower mud speed (*n *<* *1), this basement arrival is even further delayed. These effects are demonstrated with simulation at the end of Sec. IV using candidate geoacoustic profiles of the NEMP.

## IV. RESULTS AND DISCUSSION

We now examine the sensitivity of the reflection to the geoacoustic profile with emphasis on matching the complicated arrival structure after the arrival of the initial narrow pulse. Implementing the model developed in Sec. III, we compare 1.5 ms of the measured waveform at 1.3 km (see Fig. 1, spanning time is 0.3–1.2 ms) to parameterized synthetic waveforms to estimate the most probable profile. The model parameter space is a uniformly sampled grid of sound speed and density for the surface layer and halfspace, the surface layer thickness, and overall mud attenuation, totalling six search parameters (Table I).

Parameter . | Search bounds . | Units . | MAP(6) . | 95% CI(6) . | MAP(4)^{a}
. | 95% CI(4)^{a}
. |
---|---|---|---|---|---|---|

L | [0.05–1.0] | m | 0.47 | 0.28–0.56 | 0.42 | 0.29–0.49 |

$nLcL/cw$ | [0.955–1.02] | — | 0.987 | 0.955–0.988 | 0.977 | 0.960–0.982 |

$nH=cH/cw$ | [0.955–1.02] | — | 1.008 | 1.003–1.010 | 1.005 | 1.004–1.008 |

ρ _{L} | [1.0–2.0] | g/cm^{3} | 1.0 | 1.0–2.0 | 1.4 | — |

ρ _{H} | [1.0–2.0] | g/cm^{3} | 2.0 | 1.0–2.0 | 1.6 | — |

α _{H} | [0.0–0.06] | dB/λ | 0.02 | 0.0–0.05 | 0.01 | 0.0–0.05 |

Parameter . | Search bounds . | Units . | MAP(6) . | 95% CI(6) . | MAP(4)^{a}
. | 95% CI(4)^{a}
. |
---|---|---|---|---|---|---|

L | [0.05–1.0] | m | 0.47 | 0.28–0.56 | 0.42 | 0.29–0.49 |

$nLcL/cw$ | [0.955–1.02] | — | 0.987 | 0.955–0.988 | 0.977 | 0.960–0.982 |

$nH=cH/cw$ | [0.955–1.02] | — | 1.008 | 1.003–1.010 | 1.005 | 1.004–1.008 |

ρ _{L} | [1.0–2.0] | g/cm^{3} | 1.0 | 1.0–2.0 | 1.4 | — |

ρ _{H} | [1.0–2.0] | g/cm^{3} | 2.0 | 1.0–2.0 | 1.6 | — |

α _{H} | [0.0–0.06] | dB/λ | 0.02 | 0.0–0.05 | 0.01 | 0.0–0.05 |

^{a}

MAP(4) and CI(4) are based on four variables with the density parameters fixed.

The inversion is placed within a Bayesian framework, leading to a probably density function *P*(*m*|*d*) having one-dimensional (1D) marginal probability density functions for the six unknown geoacoustic variables. The key steps follow closely Eqs. (19)–(21) from Holland *et al.*,^{13} where the model-data mismatch column vector $r=d\u2212d(m)$ represents the error between the data and parameterized synthetic waveforms. Marginal probabilities of the unknown parameters are estimated from the data misfit function, $E(m)=(N/2)\u2009ln\u2009\u2009rTr$, i.e., the natural logarithm of the mean squared error normalized by the model variance. Assuming that the waveform can exhibit a rapid fluctuation, the model variance is estimated here with *N* = 37, i.e., the number of data samples in the 1.5 ms analysis window given the 25-kHz sample rate. This yields *P*(*m*|*d*), which is integrated over the model space to produce 1D marginal probably density functions for the six parameters.

Figure 4 summarizes the 1D marginal probabilities for the six parameters: layer thickness, *L*, attenuation, *α*, sound speed ratio, *n*, and density, *ρ*, in the layer and halfspace. The corresponding maximum *a posteriori* (MAP) parameter estimates (Table I) fall within the 95% percentile of the 1D marginal probabilities but are not quite aligned (Fig. 4, vertical lines) with the peak of the marginal probabilities. The MAP estimates of density in the layer and halfspace occur at the minimum and maximum of the search bounds, respectively. These values for density are well outside of the measured values from coring data;^{4} however, if densities are set *a priori*, the MAP estimates for sound speeds and layer thickness then align with the peak of their respective distributions (see the dotted lines in Fig. 4).

The most relevant finding from this inversion is that the sound speed within the surficial layer has an index of refraction of $n<$ 1 and transitions to $n>$ 1 within the top meter of sediment. It is important to note here that a more complex profile representing a smooth transition provides an equally acceptable fit to the data but still predicts a transition from *n *<* *1 to *n *>* *1 at a depth near the layer thickness estimated from the uniform surface layer model. Another important finding is that the mid-frequency ($\u223c8$ kHz) resonance requires that the surficial layer have low attenuation that is no greater than 0.025 dB/*λ*. This “low-level” attenuation agrees with the aggregate studies of attenuation in mud sediments,^{14} noting that greater attenuation would excessively dampen resonances in the bottom reflection.

As suggested by fixing the density *a priori*, additional constraints on the model parameters improve the inversion. In part, this is due to the coupling between parameters, which can be assessed by inspection of the two-dimensional (2D) marginal probability densities. Figure 5(a) shows the 2D distribution for the layer sound speed and thickness. A ridge of high probability shows that an increase in layer thickness corresponds to a faster speed within the layer. We can understand this coupling satisfying an arrival with equal travel time, which is necessary to align the direct and bottom reflected data. Figure 5(b) shows the 2D distribution of the layer sound speed and density, which shows an increase in the sound speed corresponding to a decrease in the density. This correlation maintains an impedance contrast across the water–mud interface, which suggests that the data are sensitive to an angle of intromission, which could be included as a further constraint in the inversion. The blue dotted line in Fig. 5(b) corresponds to parameters satisfying an 8 deg angle of intromission as measured in Ref. 9 three weeks after the SUS data at a site roughly 7 km southeast.

As a check on the model/data comparison, it is worth plotting the modeled waveforms relative to the measured data. The red ellipses in Figs. 5(a) and 5(b) identify a set of parameters that provide a best fit to the data, falling within the 3-dB point of the peak in the distribution. Figure 5(c) shows the measured waveform (black line) and best-fit model waveforms (red lines) for a source located 57 m above the seafloor at a range 1.3 km and a hydrophone 1.1 m above the seafloor. Finally, as a check to the success of the inversion, the optimized model parameters at a 1.3 km range are applied to data at 2.27 km [Fig. 5(d)]. Again, the model agrees with the measured data, providing validation to the result. Although the single layer model does not fit the data perfectly, the gross features (e.g., resonant frequencies) are reproduced.

The model (and its more general form^{15}) can also be used to qualify other more complex mud profiles. We proceed, here, to demonstrate the importance of the *n *<* *1 to *n *>* *1 transition near the water–mud interface with the goal to resolve some ambiguity in the inverted mud profiles. To be complete, the following results implement a profile extending 11 m below the water–mud interface with a faster basement representative of the transition to sand and denser sediments. These deep layers, however, do not affect the first 1.2 ms of the waveforms. As an aside, there is a low-frequency (<100 Hz) ground-wave and precursor component in these SUS data (see Fig. 1 in Ref. 10), but these contributions are significantly lower in amplitude (>30 dB) and have little affect on the overall waveform.

Figure 6 presents a comparison of the data (black lines) to synthetic waveforms based on four different geoacoustic profiles, two extrapolated from this study and two published profiles.

The first comparison [see Fig. 6(a)] is to the synthetic waveform using the MAP estimate with *a priori* mud densities 1.4 g/cm^{3} and 1.6 g/cm^{3} in the layer and halfspace, respectively (see Table I for a list of properties). The geoacoustic profile includes a higher speed basement below the mud interval to be complete, although due to the critical angle within the mud, this additional basement layer has no effect on the waveform. While this waveform matches the extent of the positive and negative excursions and has a similar resonant frequency, the fit to the data is not perfect. This is likely the result of a bias in the one-layer model, suggesting that the true geoacoustic profile is more complex.

The second comparison [see Fig. 6(b)] is to the synthetic waveform of the profile from Ref. 16, inverted from higher-angle bottom reflection measurements. This profile contains a significant amount of structure at the bottom of the mud interval and has a lower speed surficial layer. However, the sound speed ratio throughout the mud interval is less than one, i.e., there is no critical angle within the mud interval. The waveform is missing the resonant arrival, and the resulting fit to the shallow-angle reflection data is poor. Although outside of this analysis window, this synthetic waveform does contain the sub-bottom arrival at ∼2 ms.

The third comparison [see Fig. 6(c)] is to the synthetic waveform of the profile from Ref. 17, inverted from the complete waveform of the SUS data in the band 25–275 Hz. This profile contains a 9.5 s^{−1} gradient in the sound speed over the mud interval with a depth dependent critical angle that exceeds 3 deg at about 7 m depth. The presence of a critical angle within the mud profile does establish a resonance, corresponding to the rise at 0.7 ms is followed by a similar dip at 1.4 ms. The resonant frequency is lower than observed due to an insufficiently steep sound speed gradient within the lutocline, and the fit to the shallow-angle reflection data is poor.

Finally, a more complex geoacoustic profile is considered that includes three layers and allows a gradient within the surface layer [Fig. 6(d)]. This result is meant to temper the inversion results of the simple model and emphasize that the inversion here does not require an iso-velocity surficial layer. A profile defined by a 0.6 m surficial layer with a 70 s^{−1} gradient, continuing as an iso-speed layer with *n* = 1.0008–3.5 m and then increasing to 1.028 until the basement at 10 m, provides a better match to the resonant features as compared to the single iso-speed layer model [Fig. 6(a)]. This more complex profile maintains a critical angle less than the propagation angle down to 3.5 m below from the water–mud interface.

These comparisons suggest that broadband signal features are only reproduced when the profile includes the transition to $n\u22731$ within the top meter of sediments. One consideration in future studies is how stable the resonant frequencies are given that they depend explicitly on the index of refraction at the water–mud interface. An influx of warmer or colder water may change *n*, causing the resonant frequencies to shift or even disappear. This is especially important when the profile has a region where the index of refraction is close to unity [e.g., Fig. 6(d)]. Another implication of the surficial layer is the isolation of low-angle energy paths from interaction with deeper sediment layers, thus, a potential reduction in both transmission loss and reverberation. It is an intriguing question to examine the effect of this surficial layer on long-range propagation on the NEMP for all frequencies, where low-angle energy (which is most sensitive to layer resonances) becomes increasingly dominant with increasing range due to mode stripping.

## V. SUMMARY

The focus of this investigation is to understand broadband sound reflection at low grazing angles from a muddy seabed. Broadband data enable results that refine the crucial details of the sediment structure that are important to mid-frequency sound propagation. The key finding is that the NEMP has a thin, low-speed surficial layer (lutocline) that forms a sound duct. Using these findings as an inversion tool to estimate muddy sediment structure, the current work proves effective in inverting surficial sediment sound speed and attenuation properties. The data also serve as a tool to qualify candidate geoacoustic profiles.

While mostly consistent with previous investigations of the NEMP mud,^{8} replicating the data requires that the sound speed below the low-speed surficial layer exceed the speed of sound in the overlaying seawater. Based on comparison to a signal layer model, we estimate that the geoacoustic profile of the NEMP mud consists of a 30–60 cm thick surficial layer with a sound speed ratio of $0.97>n>0.99$, resting on top of higher speed mud with a sound speed ratio of $1.004>n>1.01$. This model/data comparison provides a close but not perfect fit to the resonant features observed in the 10 Hz–10 kHz band. A more complex three-layer model, including a gradient in the surficial layer, improves the fit slightly but still requires a thin surface layer with *n *<* *1 and a rapid increase to *n *>* *1 within the topmost meter of mud.

Further efforts to establish a physics-based geoacoustic profile of the NEMP mud should consider sedimentation modeling, where processes such as particle suspension, settling, and consolidation will better constrain the geoacoustic parameters. Such understanding, in turn, can improve modeling of long-range mid-frequency propagation in shallow waters where sound interacts with the seafloor repeatedly.

Finally, the sedimentation and settling processes that created the surficial layer of mud on the NEMP are not unique. The existence of a sound duct within the lutocline could be universal to a general muddy seafloor. It is interesting to speculate the impact that resonant features in bottom reflections may have on sonar operations. As discussed, the layer acts as a filter at low angles and will cause spectral modulation of bottom reflected signals. We also suspect that in long-range propagation, the layer will produce a noticeable effect on transmission loss and reverberation at the resonant frequencies.

## ACKNOWLEDGMENTS

This research was supported by the Office of Naval Research (ONR Code 32) Ocean Acoustics Program.