Transmission loss measurements and geoacoustic sensitivity modeling at $1.2kHz$

The sensitivity of acoustic propagation to uncertain or variable environmental conditions, and the effect of this sensitivity on sonar performance predictions, has been the subject of much theoretical and experimental study.^1–4 During the Shallow Water Acoustics Experiment 2006 (SW06), a large-scale multilateral trial extending through July, August, and September of 2006, an examination of propagation sensitivity was undertaken in the context of rapid environmental assessment (REA), the salient questions being what the key sensitivity parameters are, and at what resolution they are required. The experiment took place at the Strataform East site, a natural laboratory established by the Office of Naval Research, off the coast of New Jersey.⁵ A previous sensitivity study³ in this area determined uncertainty in propagation loss due to internal waves as about $2dB$ at $4kHz$⁠. In this paper, one-way transmission loss measurements along several paths at a frequency of $1.2kHz$ are shown, along with a characterization of the environment made using several REA techniques. This environmental information is used to examine the sensitivity of propagation in the experimental area to uncertainty or variability in environmental parameters, using a recently published full-field stochastic sensitivity measure.⁶ This sensitivity is used to model mean expected transmission loss with error bounds on the model. The model results are then compared to the measured transmission loss along a line of approximately constant bathymetry parallel to the shelf break.

The transmission loss experiment was performed August 1, 2006. The goal of the experiment was to measure acoustic propagation perpendicular to the continental shelf and parallel to the continental shelf along tracks for which the seabed and water column properties are accurately and contemporaneously measured. The research vessel CFAV Quest towed a dual-free-flooding ring acoustic projector along two tracks, at a speed of approximately $5knots$⁠. Track 1 was parallel to the shelf, along the line from 39.02° N, 73.033° W to 39.223° N, 72.906° W. The water depth was nearly constant, at approximately $81m$⁠. Track 2 was upslope, perpendicular to the first track. The projector was at a depth of approximately $50m$⁠. The Track 1 data presented here is from $0.5s$ linear frequency modulated pings (LFMs) with a center frequency of $1.2kHz$⁠, with $200Hz$ bandwidth, and with a $20s$ repeat interval. The pings were transmitted with a source level of $200dB$ re $1μPa@1m$⁠. These pings were recorded on the underwater acoustic target (UAT), a moored recorder with eight hydrophones, at depths of approximately 22, 24, 31, 35, 39, 43, 48, and $52m$⁠. Data were also recorded on a bottom-moored single hydrophone recording unit (SHRU) operated by the Woods Hole Oceanographic Institute. The experimental configuration for Track 1 is shown in Fig. 1 (left).

Considering environmental uncertainty or variability as a set of normally distributed model parameters, an ensemble of acoustic fields can be modeled by randomly perturbing these parameters. A stochastic sensitivity measure can then be defined by⁶ 

where $p$ is an acoustic pressure field, $δp$ the modeled perturbed field and ⟨.⟩ represents an ensemble average over the set of acoustic fields. This sensitivity measure can be calculated for a given propagation and environmental model to obtain a full range-depth sensitivity field.

In order to calculate this sensitivity, a set of environmental model parameters and a forward propagation model are required. The environmental model used for this sensitivity analysis is shown in Fig. 1 (right). Thirteen expendable sound velocity probes were dropped during the course of the experiment. Nine representative sound speed profile (SSP) depths were selected, and the mean and standard deviations of the sound speed at these points was determined. The value of $80.7±1.9m$ for the water depth is the mean and standard deviation measured using an echo sounder along the transmission loss run. The mean values and standard deviations for sediment layer and basement compressional sound speed, density, and compressional attenuation, and for sediment layer thickness, were determined using a genetic algorithm inversion routine,⁷ using the OASES transmission loss (OAST)⁸ wave number integration transmission loss model as the forward model. The sea bottom was assumed to be a fluid sediment layer atop a fluid basement, and the mean sound speed profile and depth were used. The inversion inputs were sets of transmission loss data from the continuous wave transmissions at $1.2kHz$⁠, for the bottom six receivers of the UAT. The values found for the parameters are consistent with previous measurements in the area.⁹ The parameters were also compared to the results obtained from “pseudo cores” made using a free-falling cone penetrometer (FFCPt).¹⁰ Here, dynamic pore pressure and acceleration are measured as a function of penetration into the seabed. These values are used to calculate shear strength, which is then translated into a sediment type using the method of Robertson.¹¹ Figure 2 shows the results of the FFCPt drops together with sound speed profiles measured along the transmission loss run. The upper part of the sediment layer is primarily sand and gravelly sand, with some sand-silt mixtures. Wind speed averaged approximately $12knots$ through the course of the experiment, and was held constant in the model. The PECan parabolic equation model¹² was used as the forward propagation model.

Full-field sensitivity measures for the acoustic pressure field [Eq. (1)] were generated by randomly perturbing the following sets of parameters: The total water column SSP (all nine points perturbed independently); each of the seven geoacoustic parameters; the water depth; and the set of all model parameters. Five hundred perturbed fields were generated for each of these ten cases. In general, sensitivity is greatest for SSP, followed by water depth, and then sediment attenuation, sound speed, and density. The acoustic field at $1.2kHz$ was insensitive to perturbations in sediment thickness and the properties of the basement; in essence, the sediment layer acted as a half space. Three examples are shown in Fig. 3, sensitivity to perturbations of: sediment compressional sound speed; SSP; and all model parameters. The sensitivity is both range and depth dependent. Note that the increased sensitivity to the sediment layer properties (all of which behave in a similar manner to the sound speed) at shallower depths at long ranges is due to the propagation path—the downward refracting profile forces interaction with seabed. Sensitivity to the water column SSP is greatest near 30 and $50m$⁠. Fluctuations in the SSP near the minimum can cause an acoustic duct to form around $30m$⁠, or create a nearly isovelocity profile below the thermocline, leaving more acoustic energy at the source depth. The overall sensitivity shows the impact of fluctuations in water depth, with thin bands of higher sensitivity above and below the black line that denotes the seabed.

The transmission loss (TL) along Track 1, measured for two of the eight UAT receiver depths (22 and $52m$⁠) and for the SHRU 3 receiver, is shown in Fig. 4. TL was calculated for the matched filter output of the $1.2kHz$ LFM pings, using a replica that was Doppler shifted to correct for tow speed. The modeled coherent TL at these depths using the environmental model mean values is also shown in the top row, while the top and middle rows show the mean of the perturbed model runs with $±1σ$ values. The mean and standard deviation for the modeled transmission loss is calculated using the sensitivity ensembles previously described, but with the mean and standard deviation calculations done on the transmission loss in dB, to describe the statistics of the model output rather than the acoustic field. The top row shows model outputs where all parameters are perturbed, while the middle row shows those with only the sound speed profile in the water column perturbed. The sensitivities to the sediment parameters, water depth, and sound speed profile with respect to range are shown in the bottom row. The sensitivity to sediment attenuation was higher than expected, due to the high standard deviation on the value, i.e., the typical perturbation used in modeling was large relative to the value of the parameter. Improved estimates of the geoacoustic parameters will most likely result in a decreased sensitivity measure with respect to those parameters. The model results are averaged over $100m$ in range, or 20 grid points.

The one-sigma model results with all parameters perturbed bracket between 86.9% and 96.5% of the measured transmission loss points. This indicates that the specified uncertainty on the model parameters is too large. The sensitivity values in Fig. 3 show that the model variability is driven primarily by SSP and sediment attenuation for the upper- and mid-level receivers, and by water depth for the bottom receiver. Constraining the perturbations to the SSP has little to no impact on the model variability at $52m$ depth (and on the other receivers between 30 and $50m$⁠). The variability at $22m$ is reduced somewhat, decreasing the included measured points from 91.6% to 87.8%. The model variability at the bottom is considerably reduced by constraining the perturbed variables to just the SSP, although over 95% of the data points are still bracketed. Even with this constraint, the uncertainty in modeled propagation is between 10 and $12dB$ for ranges from $2to20km$⁠, considerably greater than that found previously.³ As the propagation variability is in general driven by the variability in the sound speed profile, improved measurements of the sediment layer properties would not necessarily result in improvements in accuracy of propagation modeling.

The sensitivity of the acoustic field along a track parallel to the shelf slope at the SW06 experimental site was modeled at $1.2kHz$⁠, and was found to depend on sound speed profile and then sediment attenuation, sound speed, and density, with water depth playing a greater role for areas near the bottom. Little dependence was found on either sediment thickness or basement properties. A comparison of these results with measured transmission loss data suggests that the environmental variability measured sufficed to explain the variability in transmission loss data, and resulted in model variability beyond that observed in the measured data. In fact, the variability in sound speed profile alone was able to explain observed transmission loss variability, therefore further constraints on the bottom would not greatly improve model prediction capabilities unless water column observations are also improved.

We wish to acknowledge Arthur Newhall and the Woods Hole Oceanographic Institute for the provision of SHRU data used in the analysis, and the Office of Naval Research for their support in organizing the Shallow Water Acoustics Experiment 2006.