An
Opportunity for Improved Observation of Ocean Currents in the Coastal Zone
Oleg A. Godin
School of Earth and Ocean Sciences, University of Victoria, P.O.Box 1700,
Victoria, British Columbia V8W 2Y2 , Canada
Dmitry Yu. Mikhin
P. P. Shirshov Oceanography Institute of the Russian Academy of Sciences,
Moscow 117851, Russia
Abstract

We present a new lowfrequency acoustic technique for three dimensional current
monitoring which is based on an innovative use of reciprocal acoustic
transmission and matchedfield processing. Robustness and accuracy of the
inversion in the presence of acoustic ambient noise and uncertainties in
knowledge of the ocean bottom topography, sound velocity field in water, and
other environmental parameters as well as in positions of acoustic transceivers
are addressed via numerical simulations. Amount of the input data required for
the successful MNT inversion is evaluated in terms of the number of acoustic
transceivers comprising the monitoring system and of their signal's parameters.
[1]
I. INTRODUCTION
Realtime,
noninvasive measurements of flow velocity field in three dimensions over
horizontal scales large compared to the ocean depth would be perhaps the most
important contribution of acoustics to coastal oceanography. Such observations
are certainly beyond the reach of direct
in situ
measurements as well as of currently available highfrequency acoustic methods.
There is, however, a long list of compelling reasons for such observations.
Knowledge of the current field contributes to an understanding of the dynamics
of ocean circulation and upwelling and is necessary for estimating vorticity,
heat transfer, and other important characteristics of an ocean region. Current
measurements can be used to verify general circulation models and the
assumptions made in their derivation. There are situations where current
remote sensing in the coastal zone can contribute to global climate studies
through monitoring of major current systems in narrow, coastal straits. An
example is estimating the heat flux associated with the Gulf Stream system by
monitoring the flow in the Strait of Florida where the system is confined
between Florida and the Bahama Banks. Monitoring the flow further downstream
would be logistically more difficult.
There
are also a number of societal concerns that can be addressed through coastal
current monitoring. Realtime current measurements over horizontal scales
large compared to the ocean depth are of value to shipping and fishing
interests, in tracking potential pollutants, and in search and rescue
operations. They can be used to regulate the discharge of potential pollutants
and can support the design of new discharge systems.
Significance
of lowfrequency acoustics for flow velocity field measurement in shallow water
has been recognized long ago. An effort was made to apply traveltime acoustic
tomography, developed by Munk and Wunsch [1] for the deep ocean, in the Strait
of Florida [2]. The deepocean approach proved to be inapplicable to current
measurements in shallow water because of an inability to resolve and identify
bottominteracting acoustic rays, which translates into a lack of vertical
resolution in flow velocity measurements.
A
new fullfield acoustic technique for current monitoring was recently put
forward [3]. It is based on an innovative use of reciprocal acoustic
transmission and matchedfield processing. This Matched Nonreciprocity
Tomography (MNT) technique does not rely on rays or normal modes but uses
nonreciprocity of the full acoustic field, measured as a function of frequency
or position, as input data for the current velocity inversion. (Nonreciprocity
of an acoustic quantity, by definition, is a difference in the quantity value
for sound waves propagating in opposite directions between two given points in
space.) Further research has revealed [4, 5] that nonreciprocity of various
acoustic quantities (amplitude, phase and complex amplitude of a CW, etc.)
possess quite different sensitivity to variations of transceiver positions,
flow velocity, sound speed, and other environmental parameters. Acoustic phase
nonreciprocity was identified as the most promising quantity to be used as
input data for the fullfield current inversion.
In
this paper, performance of the MNTbased current inversion in the presence of
various mismatches is evaluated via numerical simulations for an environmental
scenario of particular interest.
II.
A
PPROACH
Our
environmental scenario is chosen to represent conditions met in the Strait of
Florida in summer during the shallowwater tomography experiment described in
[2]. Flow velocity and sound speed in water
_{}
are assumed to be rangeindependent. Vertical profiles of
_{}
and of current velocity horizontal component
_{}
in the vertical section containing source and receiver are shown in Fig. 1.
These profiles are obtained from data presented in [2, 6]. Note a welldefined
nearbottom sound channel which causes downward refraction and multiple bottom
interactions of acoustic signals. The ocean bottom was modeled as a
homogeneous fluid halfspace. As surfacescattered signals were not observed in
the experiment [2], we chose to represent the ocean surface by a
pressurerelease horizontal boundary.
FIGURE
1
Sound
speed and current velocity profiles used for numerical simulations in two cases
considered
The
numerical simulations consist of modeling sound propagation in a vertical plane
between a moored transceiver and a vertical transceiver array. The propagation
model [3] is based on a finitedifference solution of the parabolic wave
equation for sound in a moving fluid. The assumed geometry of the numerical
experiment provides for remote sensing of a single component of the current
velocity, namely,
_{}.
Monitoring of both horizontal components of the current, not considered in
this paper, requires an additional point transceiver. As with other tomography
techniques [1, Sec. 6.9], observations in many vertical planes crossing the
ocean region under study are necessary to get resolution in the horizontal
plane. Collecting such a data set for the MNT inversion would require two or
three arrays and a number of point transceivers. Hence, resources for a
threedimensional current velocity MNT inversion are not dramatically different
from those for the inversion in a single vertical plane.
To
find the current velocity through MNT, one should minimize a cost function,
which is a measure of similarity between measured and predicted nonreciprocity
in acoustic phase. We used one of two cost functions, either the RMS
difference between the simulated phase nonreciprocity for a "true" environment
and that for a "trial" environment, or the averaged sum of discrepancies
squared of sines and of cosines of the two phase nonreciprocities. During
averaging over the array transceivers, higher weights were given to those with
higher acoustic intensities. In the process of inversion, experimental
geometry and environmental parameters other than current velocity field were
assumed to be known (exactly or approximately). Unless stated to the contrary,
we looked for the solution to the inverse problem in a twodimensional
parametric space defined by the magnitude of the barotropic current component
and the magnitude of the baroclinic current component with linear depth
dependence. This was done by calculating a cost function at grid nodes in this
space. The current profile corresponding to the node having the minimal cost
function was taken to be the solution to the inverse problem.
Ambient
noise and inevitable uncertainties in our knowledge of system and environmental
parameters contribute to discrepancies between measured and simulated acoustic
fields and affect the inversion results. The mismatches we considered include
discrepancies in horizontal transceiver separation, array tilt, bottom
geoacoustic parameters, bathymetry, as well as acoustic noise and random and
systematic errors in the sound speed. In addition, the effect of number of
transceivers in the array on quality of the inversion was considered.
III.
N
UMERICAL
RESULTS
A.
Monochromatic Sound, RangeIndependent Environment
Consider
first a rangeindependent problem. Let a moored transceiver be situated at the
depth of 360 m and 40 m above the ocean bottom. Horizontal separation between
the moored transceiver and a vertical transceiver array is 20 km, sound
frequency
_{}
Hz. Relevant sound speed and current velocity profiles are shown at Fig. 1a.
There exist 10 normal modes with phase velocity below sound speed at the ocean
surface. With a grid in parametric space chosen, two adjacent nodes correspond
to 10 cm/s difference in the barotropic component of the current velocity or
5.77 cm/s RMS difference in the baroclinic component. In an ideal case, when
there no mismatches and the array consists of
_{}
equidistant transceivers spanning the whole water column, the cost function has
a sharp global minimum (Fig. 2a). The minimum occurs in the node which is the
closest one to the point in the parametric space corresponding to the best fit
(in the RMS sense) of the given profile of current velocity by a linear
function of depth.
FIGURE
2
Inverse
MNT cost function
_{}
vs. the model parameters in nomismatch case (a) and under the presence of 6
different mismatches (b) (all details are given in the text)
To
study the effect of mismatch in horizontal separation of transceivers,
"experimental" data were calculated for various values of the separation,
whereas in the process of inversion the separation was fixed at a nominal value
of 20 km. With the mismatch increasing, the minimum value of the cost function
increases and position of the minimum shifts. We consider inversion successful
if shift of the global minimum is not greater than to an adjacent node in the
parametric space and there are no qualitative changes in the cost function
relief in the vicinity of the minimum. This analysis show that mismatches up
to 100 m in the horizontal separation are admissible, which are well above
routinely achievable navigation accuracy. When the system mismatch consists of
an unknown array tilt, no significant variations of the cost function have been
found, provided the tilt is within 20 dg. of vertical.
When
a random, uncorrelated acoustic noise is added to the "experimental" value of
pressure at each hydrophone, a SNR of 10 to 12 dB has been found necessary for
a successful inversion. For a narrowband signal such a limitation does not
seem restrictive.
The
relation between amount of acoustic data available and the quality of the MNT
inversion has been considered by inverting data from arrays of various length,
position, and with various numbers of equidistant elements. Not surprisingly,
it turns out that robust inversion requires a sufficient number of array
elements located in the lower part of water column where in case of a
nearbottom sound source the major part of acoustic energy propagates. This
requirement being met, 16 element arrays spanning 30 to 40 per cent of water
column are found sufficient for a successful inversion in the case considered.
We therefore believe that MNT technique requirements for array positioning and
number of elements are not as demanding as those of normal mode approaches
requiring moderesolving arrays.
Acoustic
phase at oneway propagation is quite sensitive to sound speed variations. To
simulate the effect of uncertainty in knowledge of the sound speed on the MNT
inversion, "experimental" data have been simulated in a medium with systematic
or quasirandom rangeindependent variation from the reference state assumed
for calculation of the acoustic field replicas. Systematic error in
_{}
is taken as varying linearly from its maximum value at the ocean surface to
zero at the bottom. Amplitude of the random error has its maximum values at 9
prescribed horizons, sign of the error being opposite at any two adjacent
horizons, and varies linearly between them. The horizons chosen are those at
which values of the unperturbed sound speed are given. It is found that the
current velocity inversion is successful when amplitudes of the sound speed
variations are up to 0.50.7 m/s with systematic variations having more
pronounced effects that random ones. It is expected that for rangedependent
environments the above limit represents restriction of rangeaveraged
uncertainty in the sound speed.
Figure
2b illustrates the cumulative effect on the inversion of all the mismatches
considered above. In this case the vertical array consists of 16 equidistant
elements at depths from 250 to 400 m. Mismatch in horizontal separation of the
transceivers is 50 m, SNR equals 10 dB, the array tilt is 10 dg., and the
amplitudes of random and systematic errors in the sound speed are 0.5 and 0.25
m/s, respectively. In spite of all the mismatches and the limited amount of
data available, the cost function still has a single minimum in the domain of
the parametric space considered. Although the minimum is not as deep as in the
ideal case of Fig. 2a and somewhat smeared, it is sufficiently welldefined and
amplitudes of both barotropic and baroclinic components of current velocity are
determined correctly by the inversion within a spacing of the computational
grid. This translates into depthaveraged RMS accuracy of the current velocity
inversion within 10 cm/s.
B.
E
ffect
of Bathymetric Variations
Under
conditions of downward refraction and multiple interaction of acoustic energy
with the ocean bottom, uncertainty in the knowledge of bathymetry is likely to
be the factor of main concern as to applicability of fullfield inversions,
including the MNT technique. To obtain a quantitative estimate of bathymetric
accuracy required for the MNTbased current velocity inversion, "experimental"
input data were simulated in a number of rangedependent environments with
piecewise linear bathymetric variations of two kinds using the sound speed and
current velocity profiles shown at Fig. 1b, whereas replica fields were
calculated assuming a flat bottom at the nominal depth of 570 m. Bathymetric
variations of the first kind are periodic functions of range with zero mean
characterized by their spatial period
_{}
ranging from 0.6 to 5.0 km and amplitude
_{}
ranging from 0 to 30 m. Bathymetric variations of the second kind represent a
single bathymetric hill (or, at negative values of its height
_{},
an ocean bottom depression). In the numerical simulations
_{}
varied from 20 m to 20 m. It is assumed that in the vertical plane
considered, the bathymetry consists of 3 horizontal segments and two sloping
ones. Horizontal separation between a point transceiver and the array equals
36 km. The horizontal segments occupy ranges from 0 to 3 km, 6 km to 30 km,
and 33 km to 36 km, respectively. The two short horizontal segments have a
nominal depth, whereas that of the long segment differs by
_{}.
All other mismatches are neglected. In particular, the transceiver array
consists of 114 elements equally spaced between the surface and the bottom.
The
bathymetric variations considered caused sizable perturbations of acoustic
fields propagating upstream and downstream. Although suppressed in phase
nonreciprocity, the perturbations are still significant for the MNT inversion.
Influence of the unknown bathymetry on solution of the inverse problem is
illustrated by Fig. 3, where an error in the inversion for the amplitude of the
baroclinic current component is shown as a function of the bathymetric hill
height and the depression depth. In these simulations, the barotropic
component of the current velocity was assumed to be known. The simulation
results show that the inversion error depends strongly on acoustic wave
frequency and depth of the point transceiver. Rate of the error increase with
_{}
is different for the hill and the depression. In most cases considered, to
determine the current velocity from the MNTbased inversion with accuracy of 10
cm/s RMS one has to know bathymetry within 5 to 15 m, depending on sound
frequency.
Effects
of periodic variations in ocean depth on the ocean current inversion turn out
to be as pronounced as those of a single hill (depression), but more
complicated because of their non monotonous dependence on
_{}
and
_{}
as well as on frequency. This is likely to be related to resonance phenomena
in acoustic normal mode coupling. In most cases considered, for the current
velocity to be determined within 10 cm/s RMS, the amplitude of the depth
variation has to be less than 2.5  5 m. Hence, for both kinds of bathymetric
variations 0.5 to 3 per cent accuracy in ocean depth measurements is required.
This accuracy is well within reach of commercially available bathymetric
mapping systems.
C.
Parametric space of high dimensionality
As
true current velocity profiles in the examples considered above are not linear
functions of depth, there is a discrepancy between the true profile and any
inversion result obtained using the twodimensional parametric space we have
assumed so far. With a sufficient amount of input data available, accuracy of
the MNT inversion may be increased by using a parametric space of high
dimension. We have verified this via numerical simulations involving current
velocity inversions in three and fourdimensional parametric spaces. Second
and third order polynomials of depth were used as additional basis functions to
represent current velocity in acoustic field replica calculations. It was
found that simultaneously with improved inversion accuracy, parametric spaces
of high dimension give rise to progressively more complicated landscapes of the
cost function. Efficient navigating of such landscapes possessing numerous
local extrema requires application of advanced global search strategies, as are
needed in other applications of matchedfield processing [7; 1, Sects. 6.8,
6.10].
D.
Multifrequency probing signals
FIGURE
3



The
error in the reconstructed amplitude of the baroclinic current component vs.
the hill height (depression depth)



a)
CW sound source is at 530 m depth. The signal frequencies are 100 Hz (solid
line with crosses), 50 Hz (long dashes with squares) and 25 Hz (short dashes
with triangles). The other details of modeling are given in the text.


b)
The same as (a) for two frequencies (50 and 25 Hz) and the source depth of 490 m.

Although
current velocity inversion is possible with CW sound, one can increase the
amount of input data available by using broadband or multifrequency signals.
We recently considered [8] the possibility of exploiting frequency dependence
of phase nonreciprocity instead of or in addition to its depth dependence.
Numerical simulations show that phase nonreciprocity is a distinct and
nondegenerate function of frequency. An orderofmagnitude estimate of the
rate of variation of the phase nonreciprocity with frequency is
_{}
where
_{}
is the range,
_{}
is the average Mach number, and
_{}
is the average sound speed. This gives 510 degrees per Hertz for the
environmental parameters we are using. This rate implies that phase
nonreciprocity can be resolved at several dozen frequencies with existing
transceivers for moderate values for the SNR.
Numerical
experiments were carried out [8] under environmental conditions similar to that
described above and for four types of probing signals: a CW sound field with
frequency of 50 Hz, and fields at 3, 11, and 41 frequencies, equally spaced
between 40 and 60 Hz. In the process of inversion, input data at different
frequencies were processed incoherently by averaging a cost function over
frequency. It was shown, that data on depth and frequencydependence of phase
nonreciprocity can be efficiently combined for current inversions with the MNT
method. Just as in the singlefrequency case, the threefrequency case
required detailed information on the depth dependence for a robust inversion.
With data at 11 or 41 frequencies, the inversion results were accurate and
robust with as little as 2 or 3 transceivers in the array. At a SNR of 20 dB,
with mismatches of 50 m in horizontal separation of transceivers, 25 per cent
and 30 m/s mismatches in the ocean bottom density and sound speed,
respectively, no significant effect on the inversion was found.
IV.
D
ISCUSSION
The
new approach to acoustic remote sensing of ocean currents in coastal ocean,
MNT, considered in this paper, is based on a remarkable property of longrange
underwater sound propagation, namely, that nonreciprocity of acoustic phase
does not depend, to first order, on variations of sound speed, ocean bottom
geoacoustic parameters, bathymetry or horizontal transceiver separation. As
previously discussed [4, 5, 7], the phase nonreciprocity possesses a distinct
dependence on current velocity profile as well as on transceiver depth and
sound frequency. Therefore, as demonstrated in the present research through
numerical simulations under environmental conditions representative of that in
the Straits of Florida, the MNTbased inversion of phasenonreciprocity depth
dependence gives rise to good results in spite of significant uncertainty in
knowledge of system and environmental parameters and at considerable noise
levels. The benign restrictions on accuracy of the array element positioning
for the MNT inversions suggest the possibility of using a synthesized aperture
instead of a true transceiver array for shortterm experiments. The
synthesized aperture could be created with a vesselsuspended transceiver or
with an underwater winch, by varying the depth during the measurement cycle.
There
are a number of ways to further improve quality of MNTbased inversion. For
the sake of simplicity, inversion results described above were obtained with a
primitive algorithm to search for position of the cost function minima in a
lowdimensional parametric space. Application of an advanced search algorithm
and/or flowvelocity model of higher dimension, although more computationally
demanding, would result in better resolution of the inversion. Simultaneous
tomographic inversion of the nonreciprocal component of acoustic field for
current velocity and of the reciprocal field component for transceiver
positions and/or the ocean bottom geoacoustic parameters, sound speed in water,
etc., can further increase the range of admissible system and environmental
mismatches, when necessary. Improvements in both resolution and robustness may
be achieved by using oceanographically meaningful basis functions to model the
flow velocity field. Such basis functions could be obtained from a
hydrodynamic model describing ocean circulation in the region under
consideration. Using such a basis is particularly valuable to enhance
resolution in the horizontal plane.
Theoretical
studies suggest that in a coastal ocean, including straits, MNT has a number of
important advantages over the traditional raytraveltime tomography and normal
mode tomography, including applicability to a much wider range of propagation
conditions and higher robustness with respect to system and environmental
mismatches. If the theoretically predicted properties of the MNT technique are
confirmed experimentally, this approach would provide a basis for longterm
monitoring of ocean dynamics in coastal regions. It seems essential and timely
to have the MNT concept validated in an atsea experiment.
ACKNOWLEDGMENT
The
authors gratefully acknowledge many helpful discussions with Dr. D. R. Palmer,
NOAA/AOML, of the MNT technique and its possible role in remote sensing of the
coastal ocean.
REFERENCES
[1] W.
Munk, P. Worcester, and C. Wunsch, Ocean Acoustic Tomography.
Cambridge:
Cambridge University Press, 1995.
[2] D.
S. Ko, H. A. DeFerrari, and P. MalanotteRizzoli, "Acoustic
tomography
in the Florida Strait: temperature, current and vorticity
measurements,"
J. Geophys. Res., vol. 94 , pp. 61976211, 1989.
[3] O.
A. Godin and A. V. Mokhov, "Parabolic equation modeling of ocean
currents
influence on acoustic field," in European Conference on
Underwater
Acoustics, M. Weydert, Ed. Amsterdam: Elsevier Applied
Science,
1992., pp. 280283.
[4] O.
A. Godin, D. Yu. Mikhin, and A. V. Mokhov, "A full field inversion
method
for acoustic tomography of oceanic currents," in "Full Field
Inversion
Methods in Ocean and SeismoAcoustics," O. Diachock,
A.
Caiti, P. Gerstoft, H. Schmidt, Eds. Dordrecht: Kluwer Academic
Publishers,
1995, pp. 261266.
[5] O.
A. Godin and D. Yu. Mikhin, "A fullfield approach to acoustic
tomography
of oceanic currents," J. Acoust. Soc. Amer., vol. 97, p.
3264
(A),1995.
[6] C.
L. Monjo and H. A. DeFerrari, "Analysis of pulse propagation in a
bottomlimited
sound channel with a surface duct," J. Acoust. Soc.
Amer.,
vol. 95, pp. 31293148, 1994.
[7] C.
E. Lindsay and N. R. Chapman, "Matched field inversion for
geoacoustic
model parameters using adaptive simulated annealing," IEEE
J.
Ocean Eng., vol. 18, pp. 224238, 1993.
[8] O.
A. Godin and D. Yu. Mikhin, "Numerical simulations of acoustic
tomography
of ocean currents in coastal regions," in Third European
Conference
on Underwater Acoustics, Ed. FORTHIACM, Heraklion,
Crete,
1996, pp. 785790.
[W]ork
supported in part by RFBR, project 960218538a, and NSERC Research
Partnerships program grant at the University of Victoria, Victoria, B. C.,
Canada.