**ACOUSTICAL IMPACTS AND INVERSION SCHEME**

**OF INTERNAL SOLITARY WAVES**

**E. C. Shang, Y. Y. Wang and L. Ostrovsky**

CIRES, University of Colorado/NOAA/ETL, Boulder, Colorado,USA

###
**Abstract**

Based on the internal solitary waves (ISWs) data obtained during the COPE
experiment conducted from September-October, 1995 in the Oregon coastal
area, numerical simulation on acoustic propagation has been performed.
Frequency dependency of transmission loss (TL) is analyzed in range of
50 - 1000 Hz. It has been found that for lower frequencies (< 100 Hz)
the propagation is *adiabatic*, whereas for higher frequencies (>
200 Hz) significant mode-coupling takes place which causes a 5~10 db loss
increase as compared with the background case (without ISW) , but no strong
*resonant
*loss
appears in this case.
The tomographic inversion scheme based on modal phase tomography is
proposed; the ISW parameter that can be retrieved in this scheme is the*
integral depression (ID) *of the ISW.

###
**1. Introduction**

The nonlinear internal waves in the ocean have been known for over a century
and extensive investigations have been made by the oceanographic community
in the recent years [1,2]. The increased interest to this phenomenon in
the ocean acoustic community during the 1990s, was stimulated by Zhou's
paper, which considered the ISWs as possible candidates to explain the
strong frequency-selected transmission loss observed in the shallow water
of the Yellow Sea [3].
In this paper, the numerical simulation is performed based on the ISW
data obtained in the "Coastal Probing Experiment" (**COPE**) which was
conducted by NOAA/ETL in Sept-Oct 1995 in the Oregon coastal area [4].
Trains of extremely nonlinear tide-generated solitary waves (thermocline
depressions up to 30 m on the background of 5-8 m depth thermocline) were
observed. They seem to approach critical magnitudes when the Richardson
number is close to 0.25, and particle velocities are close to wave velocities
so that most usable models (**KdV**, Benjamin-Ono, Joseph) are inapplicable.
Both the forward problem (acoustic propagation) and the inverse problem
(parameter retrieval) are studied.

###
**2. Forward Problem**

The acoustic propagation through the ISW is calculated by using a PE code.
The TL of a point source at depth z_{s}=50 m, and receiver at depth
50m (water depth is 150 m) are calculated in frequency range of 50 - 1000
Hz for the distance R=32 km (covered the whole ISW at the normal direction).
It is found that for lower frequencies ( < 100 Hz), the TL only suffered
a phase shift and there is no interference pattern change compared with
the background case showing that the propagation is *adiabatic
*in
this case*.* However, for higher frequencies (> 200 Hz), the pattern
of TL changed significantly and an extra 5-10 dB loss is found that shows
that a significant mode-coupling takes place. The *adiabaticity* is
also verified by mode repopulation by exciting a single mode as the starting
field. The azimuthal dependency of the adiabatic modal phase is also investigated.

###
**3. Tomographic Inverse Scheme**

The modal phase tomography based on adiabatic mode theory has been suggested
previously [5]. If we take the constant depth of the thermocline, h_{0}
= 5 m, as the background , then the perturbed modal phase shift by the
ISW is given by

_{m} = [ k_{m}(r) - k_{m}^{b} ] dr
= [ k_{m}^{Ave} - k_{m}^{b} ] L()
(1)

where k_{m}^{Ave} is the range-averaged modal wavenumber
over the effective length L(), and k_{m}^{b} is the modal
wavenumber corresponding to the background. By replacing the averaged modal
wavenumber with an "*effective*" modal wavenumber k_{m}^{eff}
which corresponds to the effective perturbation with a constant thermocline
depression h^{eff} in the same length L(), we have

_{m} () = [ k_{m} (h^{eff}) - k_{m}^{b}
] L()
(2)

In equation (2) , there are only two unknown parameters : h^{eff}
and L(). By measuring one more modal phase perturbation, we can eliminate
the parameter L() and get

{_{m} / _{n} } = { [k_{m}(h^{eff})
- k_{m}^{b}] / [k_{n}(h^{eff}) - k_{n}^{b}]
}
(3)

The parameter h^{eff} can be uniquely determined by Eq.(3). After
that, the parameter L can be calculated from Eq.(2). Finally, the "*integral
depression*" (ID) of the thermocline caused by ISW (which is roughly
related to the total energy storaged in ISW) can be estimated. The real
ID is

(ID)^{real} = [ h(r) - h_{0} ] dr
(4)

and the effective (ID)^{eff} is

(ID)^{eff} = [ h^{eff} - h_{0} ] L
(5)

Our numerical result shows that (ID)^{eff} = 1.4 10^{5}
m^{2 }, that is pretty close to the real value of the depression
area (ID)^{real} = 1.5 10^{5} m^{2} .
The retrieved parameter (ID) combined with the soliton width data obtained
independently by radar measurement or SAR measurement can be used for amplitude
estimation.

**Acknowledgment: ** This work was supported by the Office of
Naval Research (ONR) and NOAA.

###
**References**

[1]. L.Ostrovsky and Y. Stepanyants, "Do internal solitons exist in the
ocean ?", *Rev. Geophys.* 27, pp.293-310, 1989.
[2]. J.R. Apel, L. Ostrovsky and Y. Stepanyants, "Internal solitons
in the ocean," Applied Physics Lab.. Johns Hopkins University, 1997.

[3]. Jin-Xun Zhou, Xue-zhen Zhang and P. Rogers, "Resonant interaction
of sound wave with internal solitons in coastal zone," *J.Acoust.Soc.Am*.,90,
pp.2042-2054, 1991.

[4]. R. Kropfli, L. Ostrovski, T. Stanton, E. Skirta, A. Keane and V.
Irosov, "Relationship between strong internal waves in the coastal zone
and their radar and radiometric signatures" (accepted by *J. Geophy.
Res.*)

[5]. E.C. Shang, "Ocean acoustic tomography based on adiabatic mode
theory, " *J. Acoust. Soc. Am*., 85, pp.1531-1537, 1989.