Temporal Fluctuations of the Sound Speed Field and How They Affect Acoustic Mode Structures and Coherence

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In an idealized shallow water propagation channel with smooth boundaries and range independent sound speed profiles, normal modes can accurately describe the entire sound field which can be predicted using normal mode models.

We also know that fluctuations in the sound field can be caused by fluctuations in the sound speed profile or by source/receiver motion. These phenomena are deterministic and can be simulated by changes in the mode shape or by a combination of the motion of modes past the receiver. If the fluctuations are small then small changes will occur in the mode  shape  or in the mode positions, hence the phase response will be approximately linear and our propagation is “phase coherent” relative to the background noise. Furthermore, spatial and temporal averaging is possible, which enhances the signal-to-noise ratio (SNR). But random  fluctuations of the sound speed caused by multipath interactions with the boundaries can  totally distort the acoustic modes reducing and sometimes annihilating phase coherence.

The research community seeks to understand the effects of internal waves on temporal coherence and a considerable number of experiments using fixed system to observe both oceanographic and acoustic fluctuations has been conducted.

On the other hand, the applied Navy is more concerned with mobile platforms and underwater  communications in which spatial coherence is measured instantaneously. Thus, the long term temporal coherence observed by basic research has little interest to mobile platforms.

In this work we seek to understand coherence in terms of the normal acoustic mode structure. This structure can be randomized by fluctuations of the sound field and fluctuations of the  boundaries. The research proposed here emphasizes the temporal fluctuations of the sound speed profile and how they affect acoustic mode structures and coherence. To achieve that, the MMPE (Monterey-Miami Parabolic Equation) model will be used to predict the mode shapes in a range dependent channel and random fluctuations will be introduced to observe how the modes are distorted in space and time. In turn, we can use these mode structures to estimate the temporal and spatial coherence of the mode arrivals allowing us to compare predictions of  coherence for individual acoustic modes with observations.


The Oceanographic Acoustic Environment:

The data for the first experiment used in this thesis were collected in the summer of 2006 during a large  multi-disciplinary experiment, the New Jersey Shelf Shallow Water 2006 (SW06) experiment. This work was conducted on the Mid-Atlantic Bight continental shelf at a location  about 160 Km east of the New Jersey coast and about 80 Km southwest of the Hudson Canyon. The moorings were deployed in a “T” geometry creating an along-shelf track following an  approximate 80 m isobath line and a cross-shelf track with depths from 50 m to 500 m.

Sw06 Chart With Moorings and Locations. Reprinted From Woods Hole Oceanog. Inst. Tech. Rept., Whoi-2007-04.

Sw06 Chart With Moorings and Locations. Reprinted From Woods Hole Oceanog. Inst. Tech. Rept., Whoi-2007-04.

Monterrey-miami Parabolic Equation Model:

The basic premise of the work is to relate coherence and mode structure. Earlier studies have  found that coherence begins to deteriorate when mode structures break up beginning with  higher-order modes. In this work the aim is to predict and calculate the temporal coherence for the individual modes. To predict the temporal coherence we will use time histories of the  fluctuation for each mode arrival, which are going to be the result of the variation of the  Sound Speed Profile (SSP) due to the passage of internal waves. The hope is to find new parameters to describe the coherence calculation.

SW06 Data:

The SSP acquired during the SW06 experiment will be used as the primary model input. This data is a statistical merging of data sources used to estimate the full water-column during  the experiment (Y.-T. Lin et al 2006).  An empirical orthogonal function (EOF) was used to  merge overlapping profile data sets into a single time series of profiles. The data merged  are from the WHOI VLA array, an air-sea interaction spar (ASIS) buoy and a nearby environmental mooring (ENV#30). The ENV#30 provided the temperature and salinity measurements used in the sound-speed conversion.

SW06 Shark Sound Speed Profiles – Window Selection.

SW06 Shark Sound Speed Profiles – Window Selection.


The data analysis is divided in the following four sections in order to provide clarity to  the individual problems addressed. The first section discusses the Solitary Internal Waves (SIW) that are long regular wave trains with energy concentrated around a specific frequency. These are energized at regular intervals by tidal currents spilling over the edge of the  shelf and then propagate shoreward over the propagation site. The second section addresses  the raw data after some averaging.

Solitary Internal Wave:

This section analyzes the influence of the slow temperature variation due to the passage of internal waves. In order to study this slow variation we first selected a window from the original data. This window represents a period of time in which strong Solitary Internal  Wave (SIW) activity is seen.

 400 Hz Modeled Temporal Coherence for 4 hours of Input Data.

400 Hz Modeled Temporal Coherence for 4 hours of Input Data.

Raw Data After Averaging:

Another calculation that was made used the full water column SSP after using a 8 hour
running average filter on the data. This value was chosen because it kept the internal wave  signal while avoiding the background noise.

The Background Internal Wave Field:

So far an ideal model regarding the internal wave setup has been used, as range dependence of the IW wasn’t taken into account. In the following section the contribution of range  dependence on the coherence will be investigated. It presents the moorings that will be used for this modeling.

Sw06 Chart With Moorings and Locations. Reprinted From Woods Hole Oceanog. Inst. Tech. Rept., Whoi-2007-04

Sw06 Chart with Moorings and Locations. Reprinted From Woods Hole Oceanog. Inst. Tech. Rept., Whoi-2007-04.

Model Predictions for Acoustic Mode Coherence:

In this section the effect of frequency filters on the acoustic mode coherence will be shown, with data from the Shark mooring used as input. As mentioned in previous sections, the data  were demeaned and filtered using different frequencies as a basis for our experiment and time series from a thermistor located at mid-depth (41m) was used.


For many years, the research communities have focused on the effects of internal waves on temporal coherence; whereas, Navy applied programs are more concerned with the randomizing effect of the combination of bottom bathymetry variations and platform motion on array (spatial) coherence. It seems unlikely that it is possible to isolate these two causes in the shallow ocean.

In the deep ocean and for propagation by refracted paths,  one need only consider the effects of internal waves to understand coherence. But in shallow oceans, propagation is generally by reflected paths and bottom variability can and does affect coherence and often is more randomizing than internal waves. We have found that for very low  frequencies the bottom appears flat and internal waves alone determine coherence. At very  high frequencies we observed that the slightest sound speed variations randomize and de-correlate the signal even without internal waves.

Source: University of Miami
Author: Felipe Lourenco

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