**Reconstruction of vertical distributions of sound and flow velocities at strong
oceanic currents via inversion of acoustic travel times.**

O.A.Godin, D.Yu.Mikhin, S.Ya.Molchanov

P.P.Shirshov Institute of Oceanology, the USSR Academy of Sciences, Moscow 117218,
USSR.

Effect of strong ocean currents on sound propagation is simulated numerically in framework of ray acoustics. For acoustic remote sensing of sound speed and flow velocity a nonperturbative approach is proposed and implemented. Under environmental conditions typical to the Gulf Stream applicability of this approach is demonstrated.

L'influence du courant oceanique fort a la propagation du son est
reproduite numeriquement par l'approximation de l'acoustique rayonnante.
Pour le sentiment acoustique éloigné de la vitesse sonoree et de
la rapidité du flot l'approche nonperturbatrice est proposé et
realisee. Sous les conditionis de l'environnement typiquees pour Gulf
Stream l'applicabilité de cette approche est demonstree.

Tomographic mapping of ocean currents seems to be one of the most
promising tools to study dynamics of the ocean [1-3]. This paper is a part
of theoretical study of possibilities of acoustic monitoring of powerful
oceanic flows from moving ships. Effect of strong current such as the
Gulf Stream on acoustic signals propagating in opposite directions is
estimated by numerical simulation in the framework of ray acoustic.
Reconstruction of vertical distributions of sound and horizontal flow
velocities by nonperturbative inversion of acoustic travel times is
considered. Some properties of this solution are studied using simulated
data. Environmental conditions close to that of the Gulf Stream are
implied in all these calculations.

The influence of currents on the propagation of acoustic signals depends upon many factors and first of all upon the flow velocity , which is typical for medium in hand. The most pronounced azimuth variations of acoustic fields appear to take place in the regions of powerful flows, like the Gulf Stream or the Kuroshio. Such a currents have sufficiently high flow velocity at the surface and intervening the ocean up to a large depth. To simulate all the effects induced by ocean currents one should certainly use computer code which makes it possible to calculate acoustic field in range-dependent moving media. However, if the source-receiver separation is not too large, adequate estimates can be obtained in the framework of the layered model of the ocean.

Departing from explicit integral expressions for eikonal, pressure amplitude at a ray and for its trajectory, an efficient computer code was developed by the authors to simulate high-frequency acoustic field in stratified moving media [4]. This code was applied to study a shift of convergence zone's boundaries induced by currents as well as differences in transmission loss and acoustic travel times in reciprocal transmission. For more details the reader is referred to [4].

The powerful currents turns out to exert an evident influence on the parameters of acoustic signals in the deep ocean, which is large enough to be measured using the modern experimental equipment. The vertical displacement of shadow zone's boundary

at fixed distance from the source mounts to 100-150 meters. The
relative changes in the horizontal distance *D* from source to the
beginning of first convergence zone approximately equals
,
where
and
are variations of sound and flow
velocities respectively. For typical values
m/s,
m/s and *D* = 50 km in accordance with this
estimate the shift of convergence zone proved to be
km.
Due to this reason considerably acoustic reciprocity breaking may occur in
the vicinity of shadow zone's boundaries. The difference in transmission
loss with and against the current exceeds 15 dB in the frequency domain
about 500 Hz. In the reciprocal tomography experiments data set consists
of differential travel times .
The flow velocity usually reaches
its maximum values near the ocean surface. That's why the shadow turning
rays have greater magnitudes of
about 15-20 ms per cycle of
ray.

Some of these results are illustrated by graphs of sound field intensifies
versus depth (Fig. 1), calculated for signals propagating
downstream (solid curve) and upstream (dashed curve). Profiles of sound
speed *c* and flow velocity *u*, used in this simulation, are shown at
Fig. 1a. They correspond to CTD measurements during the survey of
the Gulf Stream meander [5]. The point monopole source with frequency
*f*=500 Hz is situated at depth *z*_{s}=500 m. The horizontal separation
from the source equals *R*=58 km. The absorption of sound was not taken
into account. Surface and bottom assumed to be flat and perfectly
reflecting. In this example the shadow zone's boundary passes at depth
*z*_{p}=290 m and *z*_{m}=220 m for rays, propagating with and against the
current. It results in large differences in acoustic intensity between
these horizons, which mounts to 15 dB. These deviations are clearly
observable in spite of presence of bottom reflected and surface reflected
rays.

To simulate propagation of acoustic signals in moving ocean some
approximate methods are widely used, which are based on substitution of
real medium by a stationary one with some effective sound speed (ESS)
depending on flow velocity [6-9]. Conditions of validity of such
approximation were addressed in paper [4] using analytical comparison of
exact and approximate solutions as well as numerical simulation. ESS was
taken to be
,
where
is the projection of
on the vertical plane containing both source and
receiver. It is shown that under conditions of guided propagation the
main error in transmission loss is caused by errors in phases of separate
eigenrays
,
accumulating with distance. Here *R* is source-receiver
separation, *f* is the signal frequency and
is the grazing angle of
the ray involved. Bar denotes the average value along the ray path. The
error grows with frequency *f* and distance *R*. This conclusion is in a
good agreement with computer simulations. Let us consider Fig. 2
for example. The vertical dependence of acoustic field intensity at the
distance *R*=280 km downstream was calculated with *f*=1 kHz
(Fig. 2a) and *f*=5 kHz (Fig. 2b). Other conditions
being equal to those of Fig. 1. Solid curve and squares
represent the acoustic pressure amplitude obtained via exact formulas of
ray acoustic of moving media and within ESS approximation respectively.
Discrepancies between these two graphs rises rapidly with frequency
increase.

Determining sound speed *c* and current velocity
by
means of ocean acoustic tomography implies solution of an inverse problem.
This paper treats a kinematic inverse problem (KIP), where acoustic travel
times *T* for various source-receiver separations are considered as input
data.

If currents are slow, the inverse problem may be addressed via linear
inversion [2]. However, linearization with respect to
isn't usually permissible, when sound propagates through powerful currents
such as the Gulf Stream. Another approach, which was developed in paper
[10], consists in generalizations of some results, obtained earlier using
Abel's transformation for media at rest, on moving media. The main
advantage of our methods is their nonperturbative nature. That is, any
reference profiles of *c* and
are not used during the
inversion.

The inversion formulas mentioned above involves continuous data. It is of
great importance for practical implementation, what amount of input
information is really needed to find *c*(*z*) and
.
This question is addressed at Fig. 3. Original profiles *c* and
*u* are just the same as on Fig. 1a. Source and receiver are both
at depth *z*_{s}=680 m. The problem consists in determining *c*(*z*) and
*u*(*z*) above this horizon.

Input data (i.e. times of flight of all eigenrays) were calculated for
source-receiver separations
*x*=*iX*_{max}/*N*, where
*X*_{max}=15 km is the
distance from source to the boundary of shadow zone,
and
*N* is the number of points of measurements. Light circles, stars and
squares stand for the difference between estimated and original profiles
with *N*=7, *N*=15 and *N*=20 respectively. It turns out, that
satisfactory accuracy of the inversion is presented even when the travel
times between only 7 points are given. In practice, it is expedient to use
the nonperturbative methods of inversion to obtain some initial estimate
of *c* and
vertical dependence, which can be
refined, including determining *c* and
variability
in horizontal plane, via standard linear inversion.

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[10] GODIN,O.A, MIKHIN,D.YU., MOLCHANOV,S.YA, Izv. Acad. Sci. USSR Atmos. Ocean Phys. 27 (1991) 139