Realistic Simulation Studies of Acoustic Signal Coherence ...

Realistic Simulation Studies of Acoustic Signal Coherence
in the Presence of an Internal Soliton Wavepacket

Ching-Sang Chiu

Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943

Abstract: Based on moored Acoustic Doppler Current Profiler (ADCP) data obtained during the 1995 Shallow Water Acoustic Random Media Experiment (SWARM), the temporal and spatial fluctuations in the sound-speed field associated with the passage of an internal soliton wavepacket were synthesized. Using a coupled normal-mode sound propagation model and the synthesized sound-speed variations, the variability of sound pressure and of the acoustic modal amplitudes for a 224-Hz CW transmission were simulated. The auto and cross-correlations of sound pressure at different depths, and of the acoustic modal amplitudes at a fixed range, were computed for estimating the vertical and temporal scales of the fluctuating sound field. The results of the correlation analysis are presented and discussed. [The research is partially sponsored by the Office of Naval Research.]

1. Introduction

As part of the environmental monitoring network in the 1995 Shallow-Water Acoustic Random Media Experiment (SWARM), the Naval Postgraduate School (NPS) provided two self-contained Acoustic Doppler Current Profilers (ADCPs). They were moored 4 m above the seafloor, facing upward, at two separate locations, 16.5 km apart, along the experimental track. The resultant ADCP data set comprises a time series of depth profiles of three-dimensional current velocities with a sampling time interval of 90 s and a depth interval of 4 m over a three-week period. A detailed oceanographic analysis of the ADCP time-series has been performed by NPS, and the subsequent results were reported in Ref. 1 along with the initial acoustic findings obtained by the other SWARM investigators. The ADCP data analysis has provided a far-reaching physical understanding as well as a high-quality characterization of the medium fluctuations which were produced predominately by the large-amplitude, nonlinear, internal soliton wavepackets that propagated shoreward from the shelfbreak. The generation mechanism, vertical structure, evolution behaviors and spectral characteristics of these soliton wavepackets, as observed by the ADCPs, were discussed in Ref. 1.

Moving forward from the oceanographic findings, the focus of this paper is on estimating (or predicting) the properties of the fluctuating sound field. Our method of estimation uses the ADCP observations in conjunction with an acoustic model. Based on the analyzed ADCP results, the internal displacement structure of a soliton wavepacket was developed to realistically synthesize the temporal and spatial fluctuations in the sound-speed field. Using a coupled normal-mode model for sound propagation and the synthesized sound-speed variations, the variability of sound pressure and of the acoustic modal amplitudes along a SWARM acoustic transmission path were simulated. The auto and cross-correlations of sound pressure at different depths, and of the acoustic modal amplitudes at fixed ranges, were then computed for estimating the vertical and temporal scales of the fluctuating sound field. In this paper, we report the simulated acoustic variability as well as the results of the correlation analysis for a 224-Hz CW transmission.

2. Acoustic Modeling

The inferred displacements of the isotherms were used to empirically model the sound-speed perturbations. In Fig. 1, the inferred displacements of the first baroclinic mode of internal waves at JD (Julian day) 211.3 is shown, revealing the presence of a large-amplitude soliton wavepacket. (Hereafter, range is the distance toward the shelfbreak from a 224-Hz sound source and time is relative to JD 211.3.) These internal-wave modal displacements were derived from the ADCP data using an empirical orthogonal function analysis, a nonlinear relation between current and displacement, and a time-to-space mapping based on observed phase speeds of the wavepackets [Ref. 1]. The shape of the first baroclinic mode is shown in Fig. 2., which accounts for most of the observed temperature fluctuations.

The coupled normal-mode model of Chiu et al. [Ref. 2] was employed to calculate the fluctuating sound field for a 224-Hz CW sound source located at a depth of 50 m,. At the initial time, i.e., t = 0, the leading edge of the soliton wavepacket was approximately 2 km from the source. The movement of the wavepacket was simulated by translating the wavepacket with an observed phase speed of 0.8333 m/s. "Snap-shots" of the soliton wavepacket were taken at every 5 seconds to create the sound speed perturbations at those instances. The sound speed perturbations were simply the products of the displacements in first baroclinic internal-wave mode and the vertical sound speed gradients of the mean profile. With such an evolution model of the sound speeds, the fluctuating acoustic wavefield within a range of 10 km from the sound source was then calculated at a geophysical time-step of five seconds over a period of half an hour. This produced time series of sound pressure at various ranges and depths, as well as time series of the modal amplitudes at various ranges.

Figure 1. Soliton modal displacement (top) and the relative magnitudes
of the first five acoustic normal modes (bottom).

Figure 2. The 1st baroclinic
internal-wave mode.

3. Results and Discussion

Figure 3 shows the temporally and spatially varying transmission loss (TL) calculated by the coupled normal-mode model. Only the TL at every 90 seconds is displayed although it was calculated at a 5-second interval. Given the large displacements produced by the soliton wavepacket, the large fluctuations in the calculated transmission loss are expected. At ranges longer than 0.5 km, there are rampant abrupt variations in the TL of up to 20 dB over short distances of 50-100 m out to the 10-km range. These spatial changes, i.e., highs and lows, are due to the interference of the different acoustic normal modes. Of interest is the shifting of the locations of the highs and lows in the TL as the soliton wavepacket evolves in time. These shifts, or changes in the interference pattern, are due to small but different changes in the phases of the different normal modes. These shifts result in a temporal variability in the TL that has a time scale of approximately 10 minutes as displayed in Figure 3.

To illustrate the significance of mode coupling, the calculated magnitudes of the first five acoustic modes versus range at t = 0 are displayed in the bottom panel of Fig. 1. Note that the internal soliton displacements for the same time is shown on the top. Energy transfer between modes is evident. For example, Modes 1 and 2 as well as Modes 3 and 5 are easily seen to be tightly coupled. As energy in one mode increases, the energy in the other mode decreases. It can also be seen that mode coupling takes place as soon as the sound energy passes the leading edge of the soliton wavepacket, particularly in the vicinity of the local peaks in the wavepacket. Where the internal displacements are small, i.e., at the back of the leading portion of the wavepacket, the coupling between modes is mild. Active energy exchange between modes, thus largely occurs within the leading portion of the wavepacket. Figure 4 shows the variability of the magnitudes of Mode 1 and Mode 2 over the modeled duration of 30 min. Again, it is seen that the modal magnitudes change abruptly at the leading edge of the soliton wavepacket as the wavepacket propagates toward the sound source. The fluctuations in the modal amplitudes have the same time-scale as the TL, which is about 10 min.

Figure 3. Space-time variability of transmission loss.

Figure 4. Space-time variability of the relative magnitudes of Mode 1 (top) and Mode 2 (bottom).

To investigate the correlation (vertical) distance and time of the sound pressure field, the receptions by seven hydrophones representing a vertical line array (VLA) located at 10 km from the 224-Hz CW sound source were synthesized. The top phone is located at a depth of 10-m and the bottom phone at 70 m. These hydrophones are labeled as Phone 1 to 7 from top to bottom. The depth spacing between adjacent hydrophones is 10 m. Table 1 shows the auto and cross-correlation coefficients (at zero lag) of the synthesized time records of complex sound pressure perturbation at the seven depths. For all the cross-correlation functions computed, the peaks occur at zero lag. This indicates that the sound field is dominated by the low modes or the low grazing-angle acoustic energy. High correlations of the sound pressure perturbations over the entire VLA (or the entire water depth) are obtained. This outcome is expected because the large-amplitude soliton wavepacket affects a major portion of the shallow water column producing sound speed fluctuations that are in phase at all depths.

Table 2 shows the de-correlation times estimated from the auto-correlation functions of the sound pressure perturbation time series. The de-correlation time is taken to be the lag at which the correlation coefficient drops to a value of 0.3679, i.e., e-1.. A de-correlation time of 50-60 seconds is found at all the hydrophones. The sound pressure perturbations at the various depths along the VLA are likely to have similar structure again due to the shallow water depth and the large-amplitude and vertically in-phase sound-speed changes.

The de-correlation times of the various acoustic modes are tabulated in Table 3. A value of 0.3679 is again used to determine these modal de-correlation times. There are considerable variability in the de-correlation times of the various modes. Mode 1 has the longest de-correlation time. Given a negative sound speed profile in the SWARM site, the soliton wavepackets are expected to have a lesser impact on Mode 1, since the span of Mode 1 is well below the depths of maximal sound speed perturbation. Due to the larger vertical spans of the higher modes, they are likely to be more affected by the soliton wavepacket. Since the de-correlation times of the modal amplitudes are longer than the sound pressure observed by a single phone, the use of VLAs in shallow water can be more advantageous. A shorter de-correlation time in the single-phone measurements is due to the interference of the multi-modes.

Table 1: Cross-correlation coefficients of the sound pressure perturbations at the seven depths.

Phone	1	2	3	4	5	6	7
1	1
2	0.9310	1
3	0.9061	0.8432	1
4	0.9296	0.8535	0.9385	1
5	0.8934	0.8276	0.9773	0.9558	1
6	0.7599	0.6765	0.8229	0.8277	0.8436	1
7	0.8745	0.8387	0.9679	0.9030	0.9730	0.7720	1

Table 2: De-correlation times of the sound pressure perturbations at seven depths.

Phone	1	2	3	4	5	6	7
De-correlation time (s)	60	60	50	55	50	55	55

Table 3: De-correlation times of theamplitudes of acoustic normal modes.

Mode	1	2	3	4	5
De-correlation time (s)	300	75	112	90	83

4. Conclusions

From the modeling investigations carried out thus far, the following conclusions for a 224-Hz signal transmission can be drawn:

The modal magnitudes change abruptly at the leading edge of the soliton wavepacket as the wavepacket propagates toward the sound source. Coupling between the modes takes place immediately after their initial contact with the wavepacket. Active coupling occurs within the front portion (approximately the first half) of the wavepacket where the sound-speed perturbations are large. At the downstream of the wavepacket, the coupling of modes is significantly lessened. The time scale of the variability of both the modal magnitudes as well as transmission loss is approximately 10 minutes.

There is a high correlation between the sound pressure changes at different depths over the entire water column. This outcome is expected because the large-amplitude soliton wavepackets affect a major portion of the shallow-water column producing sound speed fluctuations that are in phase at all depths. The de-correlation times of sound pressure are about one minute, independent of depth.

There are large differences in the de-correlation times of various acoustic modes. Mode 1 has the longest de-correlation time of about 300 s. The higher modes have de-correlation times on the order of 100 s. With a negative sound-speed profile in the SWARM site, the effects of the soliton wavepacket on Mode 1 are minimized because the vertical span of Mode 1 is well below the depths of maximal sound speed perturbation. Higher modes are likely to be affected more by the soliton wavepacket due to their larger vertical spans.

References

SWARM Group (J. Apel, M. Badiey, C.-S. Chiu, R. Headrick, J. Kemp, J. Lynch, M. Orr, A. Turgot and S. Wolf), "An overview of the 1995 SWARM shallow water internal wave acoustic scattering experiment," IEEE Journal of Oceanic Engineering, July issue, 1997.

Chiu, C.-S., J. H. Miller and J. F. Lynch, "Forward coupled-mode propagation modeling for coastal acoustic tomography," J. Acoust. Soc. Am. 99(2), Feb. 1996.