VARIABILITY, COHERENCE AND PREDICTABILITY
OF SHALLOW WATER ACOUSTIC PROPAGATION
IN THE STRAITS OF FLORIDA
H.A. DEFERRARI, N.J. WILLIAMS AND H.B. NGUYEN
RSMAS – University of Miami, 4600 Rickenbacker Cswy, Miami FL 33149, USA
E-mail: hdeferrari@rsmas.miami.edu
Results of two shallow water propagation experiments are analyzed and compared with
model predictions using observed environmental parameters as model inputs. The site
of the experiments is off the coast of South Florida near Ft. Lauderdale nearby the future
location of the planned Acoustic Observatory. Unique to the Florida Straits Propagation
Experiments (FSPE) is an autonomous source that transmits broad band pulse-like
signals at each of six center frequencies from 100 to 3200 Hz in octave steps. The
transmissions last for 28 days and are received with a 32 element vertical array that is
connected to shore by fiber-optic cable. Pulse arrivals along water born paths are
identified by comparison with PE and normal mode model predictions. Three mode/ray
groups of arrivals are identified: 1) RBR arrivals, which refract in the water column and
interact with the bottom below the critical angle. These modes have low loss and nearly
identical group velocities so that they coalesce to form a very intense focused arrival, 2)
SRBR arrivals, that are spread in time and have increasing bottom angle with mode
number and 3) numerous and mysterious late arrivals that couple with deep layers of the
bottom and rapidly attenuate with higher frequency. The ocean environment, near the
edge of the Florida Current, is highly variable with a saturated GM internal wave field
and relatively large sub-inertial fluctuations from eddies and stream meanders. Sound
speed fluctuations are generally 1 to 2 orders of magnitude larger than observed in the
deep ocean. The bottom is composed of unconsolidated carbonate granules that have the
density of sand and attenuation of fine sediment. Fluctuation statistics and coherence are
computed and modeled in a parameter space of range, depth and frequency. The
acoustic propagation, like the environment, is highly variable and complicated and many
new interesting dependencies are revealed.
1
Introduction
The acoustic measurements reported here are from a 10-km propagation experiment
conducted in Dec/Jan of year 1999–2000. The system installation and general features of
the range site are described in a previous paper. The source and receiver arrays were
situated along a nearly constant depth contour of 145 m as shown in Fig. 1. Two
thermistor arrays were located symmetrically at ranges of 2.5 and 7.5 km from the source.
The source is a multi-frequency and autonomous broadband transmitter that is moored
and transmits for a period of one month under battery power. Several sets of transducers
transmit m-sequence coded pulse trains at each of 6 carrier frequencies, f c = 100, 200,
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N.G. Pace and F.B. Jensen (eds.), Impact of Littoral Environmental Variability on Acoustic Predictions and
Sonar Performance, 245-254.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
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400, 800, 1600 and 3200 Hz with a .25x f c bandwidth. Each frequency was transmitted
continuously for 1 h and then cycling to repeat sequence every six hours.
Data were processed following the SHARP methods of Birdsall and Metzger. The
result is one pulse response per minute. The duration of sequence period is very nearly
2.55 s for each frequency and sample resolution is 1 / f c seconds. Once the data are
averaged and pulse compressed they are stored on a server that can be access in either
MATLAB of FORTRAN. The hourly pulse responses are readily access by specifying
the transmission number (time), the frequency of the transmission and the hydrophone
number (depth). For some of the time history of pulse response plots that follow the
hourly samples are run together ignoring the five-hour gaps between samples.
Environmental Arrays
145 m
Acoustic Projector
Mooring (5 Octaves
from 100 - 3200 Hz)
(12 temperature recorders, 1 temp.-cond.,
1 Temp.-press. per mooring)
Hydrophone Array
(3-D Cartesian Layout
32 channels per leg
500 m long horizontal legs)
10 km
Figure 1. Experimental geometry of the 10-km Florida Straits propagation experiment.
Very energetic oceanography fluctuations and a highly variable sound speed field
characterize the acoustic environment along the coast of south Florida. The mean sound
speed profile is strongly downward refracting. The profile is typical of shelf areas
shoreward of western boundary currents and comes about from the quasi-geostrophic
balance of the current field. Sub-inertial fluctuations, with periods longer than the local
inertial period of 25.6 h, result from meanders and eddies of the edges of the Florida
current as well as coastal up- and down-welling produce very large variations in sound
speed at inshore locations. Likewise internal waves and tides are energetic so that the
overall sound speed variations are typically an order of magnitude greater than observed
in the deep ocean.
The temperature data, Fig. 2, were collected during the acoustic experiment
conducted Dec/1999 – Jan/2000 and are referenced to “experimental time”. The
computed sound speed profile is below. The 28-day long time series exhibits large slow
fluctuations with roughly a fortnightly period. The temperature profile varies from an
ACOUSTIC VARIABILITY IN THE STRAITS OF FLORIDA
247
exceptionally strong thermocline to a nearly isothermal profile over the period. The cause
is dynamical effects from the edges of the Florida Current (i.e. meanders and eddies).
Perturbations to the temperature profile are evident over the internal wave band of
frequencies although solitons are rare.
The total variability < ∆c / c > including the sub-inertial fluctuations, is a factor of
10 greater the typical internal wave fluctuations of Flatté for the deep ocean (Fig. 3).
Comparing variations over the same IW band and including internal tidal contributions
the Florida Straits site exhibits about twice the magnitude of the deep ocean.
The internal wave variability is hardly stationary. A burst of coherent wave trains,
possibly a soliton, occurs around hour 200 and persists for two days with several 5–6 h.
cycles. Likewise, the internal wave energy is greater during the time periods before and
after the large changes in the mean profile. This observation is confirmed by the
calculation of η 2 (Fig. 4) which approximates the internal wave potential energy
η ' = T ' / dT / dz ,
(1)
where T ' is the temperature perturbation over the internal waveband and dT/dz is the
vertical temperature gradient. η is related to the potential energy of the internal waves
by,
(2)
PE = ( ρ / 2)N 2η 2 ,
where ρ is the density and N is the Vaisala frequency.
Geo-acoustic properties of the bottom at the site of the experiments are not
completely understood. The bottom sediment is thought to consist of unconsolidated
carbonate covered with a veneer of finer sediment. The density of the carbonate is about
the same as sand and the attenuation nearly that of fine sediment. Sound speed in the
bottom is upward refracting but little is known about the sub-strata and sub-bottom at this
site of these experiments. Further to the north, cores have been analyzed and bottom
properties described by Monjo siting four studies as follows; “The sediment is 25 to 100
m thick composed of partially lithified sand or silty sand, made up of approximately 85%
carbonate material.”
The geo-acoustic model constructed by Monjo, when used with PE and normal mode
propagation models predicted channel pulse responses in good agreement with
measurements for previous experiments. A similar bottom and sediment model is used for
the predictions that follow (Table 1).
Table 1. Geoacoustic model.
Velocity
(m/s)
1550
Gradient
(1/s)
1.4
Density
1.85
Loss
(dB/km/Hz)
0.30
Shear
(m/s)
300
Shear Loss
(dB/km/Hz)
3.30
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H.A. DEFERRARI ET AL.
Figure 2. Temperature observations and the computed sound speed profiles.
Figure 3. Averaged normalized sound speed variations over various frequency bands.
ACOUSTIC VARIABILITY IN THE STRAITS OF FLORIDA
249
Figure 4. η 2 vs depth and time.
2
Analysis
The objective of the experiments is to study fluctuations, coherence and predictability in
a parameter space of frequency, range of transmission and receiver depth. The computed
measures are straightforward.
The coherency is computed as an averaged lagged product in space or time. The
temporal coherence has three time variables: 1) T - the arrival time along the pulse, 2) t the arrival time of the pulse in 1min intervals and 3) τ - the pulse to pulse lag time also in
minutes.
COH (T , t ,τ ) = < p(T , t ) * p (T , t + τ ) >2 / < p (T , t ) > 2 < p (T , t + τ ) > 2 .
(3)
In this way we compute a coherency for every cycle of the received pulse response. For
fluctuations we time gate arrivals, and compute intensity distributions and scintillation
index SI is given by
SI = < I 2 > / < I >2 −1 .
(4)
The scintillation index can be computed for a particular arrival at several depths.
Predictability is studied by comparing measured pulse responses to the predicted
pulse responses using propagation models with measured sound speed profiles as inputs.
The models used are:
1.
PROSIM Broadband Normal Mode Model , F. Bini-Verona, P.L. Nielsen and
F.B. Jensen, SACLANTCEN SM-358 (based on ORCA model by E. Westwood
et al).
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2.
SNAP: Saclantcen Normal mode Acoustic Propagation model, F.B. Jensen and
M.C. Ferla (with SUPERSNAP solution engine by M.B. Porter and E.L. Reiss).
3. MMPE: Monterey-Miami Parabolic Equation model, K.B. Smith and F.D.
Tappert.
3
Identifying arrival groups
We report on data collected during the first 14 days of the 10 km experiment. The sound
speed profile varies from strongly downward refracting during the first few days to nearly
isothermal profile during the two day. (Hrs 104 through 140, Fig. 2.) Figure 5 displays 6
1-hour long samples of the 800 Hz pulse reception. The blue gap between hourly records
is 5 h in duration. Persistent arrivals result from two types of water borne paths, surface
reflected – bottom reflected (SRBR) modes, comprising the early arrivals, and refracted –
bottom reflected BRB modes that focus in time to form the single intense late arrival.
This is consistent feature of the 200, 400 and 800 Hz pulse responses.
Both PE and normal mode models predict similar pulse responses at all frequencies.
A PE prediction of the pulse response vs. range (Fig. 6) shows the SRBR arrivals fanning
out in time with increasing range while the BRB group remains focused. Normal mode
calculations of the group velocity (Fig. 7) show that the group velocity of the first 10
RBR modes is very nearly constant thus explaining the focusing. Figure 8 shows the 200
Hz pulse response for 14 days. The focused arrival persists until the sound speed
gradient weakens during day 12.
Surface coupled mode groups
Refracted mode groups
Figure 5. Pulse responses for the 800 Hz transmission showing SRBR and BRB mode groupings.
ACOUSTIC VARIABILITY IN THE STRAITS OF FLORIDA
Figure 6. PE prediction of 800 Hz pulse vs. range.
251
Figure 7. Group velocity for 800 Hz modes.
Figure 8. Pulse response for the 200 Hz. data fore 14 days. The BRB mode group focused arrival
persists until the gradient weakens during hour 375.
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Frequency dependence of intensity and coherence
Pulse response arrival patterns have been analyzed for an 11-day period during which
time the sound speed profile remained strongly downward refracting. Beyond 11 days
the profile became nearly iso-velocity and it was no longer possible to identify the same
sets of arrivals. The discussion and conclusions that follow are based on some 44 plots
like the example shown in Fig. 9. For five consecutive hours, pulse responses measured
every minute and coherency as computed by Eq. (3) are shown for center frequencies of
200, 400, 800, 1600 and 3200 Hz. Some of the conclusions that follow are not clearly
exemplified with this figure and the example is presented as a guide for discussion and
not as proof. It is not practical to present all the data.
For all frequencies the waterborne paths (discussed above) arrive during the time
interval of 1–1.2 s. The later arrivals that are more intense at lower frequencies are not
yet identified. We suspect they come about from modes that travel deep into the bottom
perhaps as much as 100 to 200 m. In fact, we can simulate the observed arrivals with
normal mode models by admitting some layers deep in the sub-bottom. More
information about the geo-acoustic properties is needed to resolve the issue.
The later arrivals are remarkably coherent and stable in time as one might expect if a
significant portion of the propagation path is through the bottom. In the example, the
arrival at time 1.45 s, for the 200 Hz pulse, is less intense but more coherent than any of
the water born paths.
The late modes strip away with increasing frequency and are barely detectable for the
800 Hz signal. At first look, the mode stripping continues through the waterborne paths
with the late arrivals attenuating more rapidly with increasing frequency. Mode stripping
usually results from the higher order mode incurring more bottom loss because of steeper
bottom angles. But here, the late arriving refracted modes have lower bottom angles than
the earlier surface reflected modes.
Another loss mechanism may be at play. At 200 Hz the reception is dominated by
the focused refracted arrival which is on average 15 dB higher than the individual SRBR
arrivals. Likewise at 400 Hz. But the focused late arrival at 1600 Hz is about the same
level as the SRBR’s. Further, the RBR mode arrivals are always much less coherent in
time generally decorrelating in less that half the time of SRBR mode arrivals that have
nearly the same arrival time and bottom angle. The essential difference in the two mode
types in that the BRB modes interact with stratified density fluctuations with near zero
grazing. We suspect that there is a substantial loss associated with volume scattering near
turning points. The lower the frequency the more lossless is the refraction. Model that
use smooth sound speed profiles miss this effect and over predict the intensity of the
focused BRB group.
Statistics of intensity fluctuations were computed for several receiver depth below
and above the source depth. The RBR mode arrivals were time gated for these
calculations. Results are summarized in Fig. 10. As the receiver depth approaches the
source depth the intensity distribution looks more nearly Rayleigh; further away either
above or below the distributions become more log–normal with increasing SI.
ACOUSTIC VARIABILITY IN THE STRAITS OF FLORIDA
253
Figure 9. Left column: Pulse intensity (dB//up) vs arrival time for 200, 400, 800, 1600 and 3200
Hz transmission – 58 1min samples. Right column: Coherency for the corresponding pulse
history.
Near the source depth all of the BRB modes have about equal amplitude and
multipath interference dominates and hence saturated Rayleigh statistics. Further above
or below one or two modes dominate and the distributions are more log–normal in
appearance. We suspect, but have not yet been able to establish, that the distributions of
fluctuation of the intensity of single modes will be log–normal.
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Figure 10. SI versus depth for BRB mode group arrival.
5
Summary
Low frequency pulse propagation is dominated by a single arrival consisting of several
unresolved RBR modes – about 3 modes for the 200 Hz signals, 6 for the 400 and 12 for
the 800. As much energy is carried in an SRBR group, they fan out in time and are
readily resolved for the higher frequency measurements. In fact, arrivals associated
individual modes are resolvable, stable and persistent for many hours even for the 3200
Hz signals. SRBR modes are generally more coherent and stable for all frequencies.
There is a large observed transmission loss (10dB+) for RBR modes at higher
frequencies that is not consistent with bottom loss. Models don’t predict the loss and
SBRB modes are immune. We hypothesize the loss results from volume scattering at low
grazing near turning depths.