Mid-frequency $(1\u201310kHz)$ sound propagation was measured at ranges $1\u20139km$ in shallow water in order to investigate intensity statistics. Warm water near the bottom results in a sound speed minimum. Environmental measurements include sediment sound speed and water sound speed and density from a towed conductivity-temperature-depth chain. Ambient internal waves contribute to acoustic fluctuations. A simple model involving modes with random phases predicts the mean transmission loss to within a few dB. Quantitative ray theory fails due to near axial focusing. Fluctuations of the intensity field are dominated by water column variability.

## I. Introduction

One of the major goals in ocean acoustics is to understand transmission loss (TL). This includes the mean intensity and the fluctuation of intensity. In shallow water, most work has been in the low-frequency band $(<1kHz)$.^{1–3} Narrowband low-frequency intensity fluctuations due to water column variability have been investigated.^{4,5} Mid-frequency $(1\u201310kHz)$ propagation has received much less attention either theoretically or experimentally. Ewart and Reynolds^{6} measured specifically mid-frequency intensity fluctuations in the deep ocean, and quantified the intensity scintillation index.^{7} In shallow waters, there is a dearth of measurement data in the mid-frequency range, especially those which measure intensity versus time at fixed ranges, necessary for statistical analysis.

During the Shallow Water '06 experiment (SW06), on August 11, 2006, a mid-frequency acoustic propagation experiment was performed in the frequency band of $2\u201310kHz$ and at ranges $1\u20139km$. First, a $1-km$ propagation experiment, accompanied by detailed two-dimensional (2D) sound speed measurements from a towed CTD chain (conductivity, temperature, and depth) along the anticipated nonlinear internal wave travel direction was conducted. Then, propagation paths were chosen along the $80-m$ isobath for $1,2,\u2026,9km$ ranges. At each of these stations, 100 identical acoustic transmissions were made in order to study the mean and fluctuations of the intensity. This paper will provide details of the experiment setup and environmental measurements supporting the acoustics, and will also present the results on mean sound intensity over range and frequency. A companion paper will address the issue of intensity fluctuations.

## II. Experiment description

At the experiment site, a typical strong summer thermocline existed, and in addition, warm, salty slope water underlay the colder mid-depth water. Thus, there was a sound speed minimum at $\u223c32m$ depth, forming a sound channel. This day was very unusual for SW06 because there were very few nonlinear internal waves. The combination of the sound channel and ambient internal waves had a large impact on mid-frequency sound propagation.

The mid-frequency sound source, an ITC-2015 transducer, was deployed off the stern of the R/V KNORR at $30m$ depth, close to the sound axis to emphasize the propagation of energy trapped in the channel. The waveform transmitted consisted of two signals separated by $100ms$. The leading signal is a $10-ms$ multitone with nine frequencies, spanning 2–10 times the base frequency of $1011Hz$. The trailing signal is a $20-ms$ linear frequency-modulated chirp, which spanned the $1.5\u201310.5-kHz$ frequency band with a Hann window and 10% taper. Transmissions were repeated about every $20s$.

The signals were recorded on a moored receiving array system,^{8} which was moored throughout the experiment at 39.0245 N, 73.0377 W. The system had two four-element vertical subarrays with the top four elements at depths 25.0, 25.2, 25.5, and $26.4m$, and the bottom four at 50.0, 50.2, 50.5, and $51.4m$. The data were stored at the array.

Both water column and bottom environmental data were collected to support modeling of the acoustics. Surfacial sediment sound speed was measured to be $1610\u20131620m\u2215s$ in the experiment area using a system called SAMS.^{9} In addition to regular CTD casts, 2D sound speed profiles in the water column were measured by a towed CTD chain deployed from the R/V ENDEAVOR for a set of acoustic measurements at the $1-km$ range. An example of the 2D sound speed profile is given in Fig. 1, where the channel is clearly shown. In addition, it is evident that heterogeneity in sound speed exists as a function of range. The towed CTD chain data are available for several hours. After minor corrections, they will be used to simulate sound transmission through heterogeneities to statistically model the acoustic data.

The propagation experiment was divided into two segments. The first was at $1-km$ range over an extended period of time, lasting over $6h$ and including 1500 ping repetitions. This provides ample data for statistical analysis of field fluctuations. It was during this segment that the accompanying towed CTD chain data were available. The second segment was at ten stations along the $80-m$ isobath at ranges $1,2,\u2026,10km$. At each station, 100 pings were transmitted [except at the $10-km$ station (see Table I), where a failure to communicate with the receiver limited the data to only eight pings].

Acoustic source locations and number of transmissions. . | ||||
---|---|---|---|---|

Station . | Lat (N) . | Lon (W) . | Pings . | Compassbearing . |

$1km$ | 39.0203 | 73.0277 | 1500 | 300° |

$1km$ | 39.0325 | 73.0316 | 100 | 30° |

$2km$ | 39.0404 | 73.0259 | 100 | 30° |

$3km$ | 39.0482 | 73.0201 | 100 | 30° |

$4km$ | 39.0559 | 73.0143 | 100 | 30° |

$5km$ | 39.0637 | 73.0085 | 100 | 30° |

$6km$ | 39.0715 | 73.0028 | 100 | 30° |

$7km$ | 39.0776 | 72.9983 | 100 | 30° |

$8km$ | 39.0871 | 72.9912 | 100 | 30° |

$9km$ | 39.0948 | 72.9853 | 100 | 30° |

$10km$ | 39.1021 | 72.9794 | 8 | 30° |

Acoustic source locations and number of transmissions. . | ||||
---|---|---|---|---|

Station . | Lat (N) . | Lon (W) . | Pings . | Compassbearing . |

$1km$ | 39.0203 | 73.0277 | 1500 | 300° |

$1km$ | 39.0325 | 73.0316 | 100 | 30° |

$2km$ | 39.0404 | 73.0259 | 100 | 30° |

$3km$ | 39.0482 | 73.0201 | 100 | 30° |

$4km$ | 39.0559 | 73.0143 | 100 | 30° |

$5km$ | 39.0637 | 73.0085 | 100 | 30° |

$6km$ | 39.0715 | 73.0028 | 100 | 30° |

$7km$ | 39.0776 | 72.9983 | 100 | 30° |

$8km$ | 39.0871 | 72.9912 | 100 | 30° |

$9km$ | 39.0948 | 72.9853 | 100 | 30° |

$10km$ | 39.1021 | 72.9794 | 8 | 30° |

## III. Results

Ray tracing normally applies to medium frequencies. In Fig. 2, a fan of rays is calculated to a range of $2km$ based on the range-independent sound speed profile shown on the right of the figure from a CTD cast. In this figure, the sound source is at $30m$ depth, and rays span $\xb123\xb0$, corresponding to all rays with bottom grazing angle smaller than the critical angle (22°). For the receiver depth near the sound axis, shallow angle rays dominate. At about $1km$ a strong focus can be seen near $30m$ depth, and a similar one near $2km$, close to ranges used in the experiment. The multiple caustics in the focusing regions imply that that mid-frequency sound intensity levels cannot be accurately calculated from ray theory. Thus, it is more appropriate to think in terms of modes.

Examples of received intensities at the $1-km$ range are shown in Fig. 3. The received signals shown are the result of pulse compressing the FM transmissions. Two characteristics of these signals are evident: Each individual arrival in a ping has more structure than the transmitted waveform, and there are strong ping-to-ping fluctuations in each arrival. The sidelobes of the transmitted pulse are 180° out of phase with the main lobe, which causes the individual arrivals to have structure of the same time extent as the transmitted pulse, as checked by simulations. The first arrival has most of the total received sound energy. This arrival corresponds to rays that remain in the water column with all initial angles between $\xb16\xb0$. Other arrivals correspond to rays that encounter the bottom, which ray tracing predicts will arrive later by a few milliseconds. Therefore, the fluctuations of total received sound are dominated by the variations in the water column. The depth uncertainty of the sound source was estimated to be within $0.5m$. To estimate the impact of such uncertainty on intensity fluctuations, we correlated the integrated intensity between two receivers vertically separated by $0.9m$. The correlation coefficient is found to be 0.95, thus source vertical motion was ruled out as having substantial impact on intensity fluctuations. There is nothing in our environmental measurements that would deterministically distinguish one pulse from another, so the pulses must be treated as random. The first statistic to consider is the mean intensity. Because the geometrical spreading loss and loss due to seawater absorption are well understood, the term reduced transmission loss will be used for this paper, which is defined as the transmission loss with the cylindrical spreading and seawater absorption removed.

The measured variation in transmission loss (TL) for individual pulses at a fixed range was large and assumed caused by scattering from sound speed variations in the water column. If one considers a sound channel where there is no range-dependent sound speed variation in the water column, so there is no scattering, then the TLs measured at two receivers separated by a small range difference would have similarly large variations as the measurement. The variation in this range-independent case over short distances is due to interference between the modes. However, the measured reduced mean TL is much more constant among all ranges than the individual ping TLs at a fixed range. Thus we infer that the ocean-induced ping-to-ping variability is indicative of random phase addition of multiple modes. This suggests a model in which the mean intensity is the incoherent sum of mode intensities. To complete the model, it is assumed that the mode intensities are, on the average, the same as the range-independent mode intensities. The Dozier and Tappert^{5} transport theory makes a similar random phase approximation, but is designed to calculate the mode intensities more accurately.

Sound speed variations measured by the towed chain (such as shown in Fig. 1) were used to quantitatively examine the modal phase changes. The difference between the sound speed fields of two almost coincident tracks from the towed chain is calculated. This difference is integrated, at each depth, over the $1-km$ segment closest to the acoustic path. The resulting depth variation is then projected onto all 15 modes that remain in the water column at $2kHz$. This simulates the first arrival in Fig. 3. This projection simulates the phase difference for each mode between the two times of the towed chain measurements. These calculations give a standard deviation of $7.4rads$. This value supports the validity of the random phase assumption. The phase difference will increase linearly with increasing frequency and in an undetermined manner with range depending on the correlation of the sound speed fluctuation. This level of fluctuation makes the coherent field small, and supports the assumption that the incoherent mode intensity sum should be used.

The incoherent mode intensity sums at ranges $1\u20139km$ and for center frequencies $2,3,\u2026,9kHz$ were calculated using KRAKEN.^{10} The sound speed profile used in the model was from a CTD cast from the R/V KNORR during the $1-km$ range measurements and is given in Fig. 2. For the small amount of sound energy interacting with the bottom, the bottom is modeled to be a fluid half space with sound speed $1610m\u2215s$,^{9} bulk density $1800kg\u2215m3$, and attenuation coefficient $0.2dB\u2215m\u2215kHz$. The last two numbers were decided through iterative fitting. The attenuation in the water column is included in the model. The model transmission losses are compared to those from data in Fig. 4. The reduced TL for all ranges and frequencies is near a constant value of $20dB$. Initially, the wave field spreads spherically, and then transitions to cylindrical spreading. The reduced TL has only cylindrical spreading subtracted, and the spherical spreading leads to extra TL. The range at which the transition from spherical to cylindrical spreading occurs can be estimated from the vertical spacing between nearby rays. This spacing turns out to be $100m$ times the initial angular separation of the rays, indicating that the transition occurs at about $100m$, giving an initial $20dB$ extra TL.

The model predicts the mean intensity for all ranges and frequencies considered to within a few dB. Because the reduced TL is nearly a constant for all ranges, the acoustic energy is trapped in the sound channel. Error bars were not calculated because successive pings are correlated, and the number of degrees of freedom is yet to be evaluated. Instead, the 100 pings at each station were split into the first and last 50-ping groups and the difference is found to be less than the difference between the model and data. Thus, the data are sufficient to show small inaccuracies of the model assumptions. There are a few places where the model is off by more than $3dB$, for example at $8kHz$ and $5km$.

## IV. Summary and discussion

Mid-frequency sound propagation in shallow water was measured at multiple ranges along with extensive environmental measurements, especially 2D CTD measurements using a towed chain. These measurements provided the opportunity to quantify the statistics of transmission loss. This paper concentrated on estimating the mean intensity, and a companion paper will address the issue of intensity fluctuations. It was found that most of the sound is trapped in the sound channel where water column variability dominated the acoustics field fluctuations. Because of the presence of closely packed caustics at convergence regions, ray theory cannot be used to accurately calculate sound intensity levels. The intensity was estimated from data and compared to an incoherent mode sum model. The comparison indicated that the mean intensity can be modeled to within 2 dB for most of the ranges and frequencies studied, but there were exceptions where the difference between model and data exceeded $4dB$. Although the differences between the model and data are small, they are statistically significant.

Sufficient towed chain data were taken to allow a more detailed statistical model of the internal waves. We expect that Monte Carlo propagation calculations using this statistical model will more accurately describe the data than the simple model presented. The data will also be used to check the validity of the transport theory,^{11} where certain approximations are made. While such a theory, when applicable, can be used to predict the statistics of the intensity, simulations based on the Parabolic Equation method are potentially a more reliable and general way to study mid-frequency acoustics propagation in complex environments.

An important quantity for scientific understanding and applications is the coherent field, where phase coherence over time is measured. However, because the relative positions of the source and receivers were not known to sufficient precision during SW06, field coherence was not studied, but should be a high priority for a future field experiment.

## Acknowledgments

This work was supported by the Office of Naval Research. The authors thank the crews of the R/V KNORR and R/V ENDEAVOR for their professional support.