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Gayana (Concepción)

versión impresa ISSN 0717-652Xversión On-line ISSN 0717-6538

Gayana (Concepc.) v.68 n.2 supl.TIIProc Concepción  2004 

  Gayana 68(2): 385-388, 2004



Marta. E. de Milou, Silvia R. Salvadores & Silvia Blanc

Naval Service of Research and Development (SENID), 327 Libertador Ave., 1638, Vicente López, Argentina.,,


Up and down slope acoustic propagation measurements were conducted in 1989 [Milou et al., 1990] over the Argentinean continental slope leading to experimental values of Transmission Losses (TL) for the 100 - 400 Hz frequency band. This enabled comparisons between the obtained data and the parabolic equation (PE) model predictions. With the aim of examining the effects of using updated PE codes [Collins, 1993] including their corresponding physical and computational improvements, on the already obtained results, predicted TL values are recomputed. An analysis of these new comparisons are presented here.


An excellent analysis of works dealing with the application of the parabolic wave equations to underwater sound has been reported in Computational Ocean Acoustic (Jensen et al., 1994).

It provides not only historical references but also enables understanding of the steps followed by researchers in this wave-theory technique since early 1970 (Hardin et al., 1973) for solving range-dependent propagation problems including different improvements achieved through many years up to 1994. Some further new PE codes have been developed till nowadays.

In this work up-dated versions of Range-dependent Acoustic Model, RAM vers. 1.5 (Collins, 1993); Range-dependent Seism-ocean Acoustic Model RAMS vers. 0.6s (considering the ocean overlying an elastic bottom) (Collins, 1989, 1459-1464; Collins, 1993), both with the possibility of multiple horizontal sediment layers and one version of RAM with multiple sediment layers parallel to the bathymetry called RAMGEO vers. 2.0g (Collins, 1993) to calculate coherent Transmission Loss, were analysed for their eventual application. To this purpose, the above mentioned codes were adapted to get output files that could be easily used to illustrate the results. Matlab codes were developed to enable their graphical visualisation.

These codes use the Padé series for numerical implementation of the wide-angle parabolic equation which enables to achieve a combination of accuracy and stability in the obtained theoretical results.

The current knowledge about the bottom characteristics in the studied area1 proves the advantage of choosing RAMS vers. 0.6s, among the three selected codes, to compute the sound field.

RAMS vers. 0.6s takes into account shear velocities and attenuation coefficients which may characterise the typical unconsolidated sediments in the selected zone, having enough rigidity to transmit acoustic shear waves. The previous PE code used in the referenced article (Milou et al., 1994) had not considered the possibility of introducing shear waves in the TL computation.

A better fitting between experimental data and theoretical results is even reasonable to be expected due to the improvement in the seabed geoacustic representation.


According to the description of the down-slope experiment (Milou et al., 1990), the calibrate passive sonobuoy was deployed in deep waters with the receiver at a depth of approximately 18 m while explosive charges (sources) were dropped from different positions along a 50 km track between the stations A (37° 16' S, 55° 08' W) and B (38° 02' S, 54°22' W). The average explosion depth was about 20 m. The experiment area seabed mainly consisted of fine sand. No data could be gathered neither for source- receiver distances less than 40 m nor for distances longer than 90 km because it was previously checked that charges dropped into those regions (up to ranges of 40 km) caused saturation of the hydrophone pre-amplifier receiver while charges dropped outside (at ranges larger than 90 km), were below the signal/noise threshold. All oceanographic and environmental data were provided by the Ocabalda Oceanographic Vessel from the Argentinean Navy.

In the already mentioned article (Milou et al., 1994), the theoretical TL reported values were computed by running the PE code for each source position.

Calculus is simplified here using the Reciprocity Principle valid for parabolic wave equations (Nghiem-Phu, 1977). Accordingly, source and receiver positions can be exchanged and a receiver moving away from a fixed source is considered, thereby avoiding the necessity for re-computing the field for each different source position.

A Padé number 5 is used as input data for running RAMS vers. 0.6s, since Collins (Collins, 1989, 1097-1102) has shown that most ocean­acoustic problems can be adequately handled by less than 5 terms in the Padé series expansion. This choice agrees with an already reported remark (Jensen et al., 1994) -The best PE approximation is clearly the Padé (5) equation, which has small phase errors for angles within ± 60° of the main propagation direction.-

A shear wave velocity, cs, of 400 m/s and shear attenuation of 1.5 dB/l were estimated (Blanc et al., 1987) from in situ porosity (F»45.2 % ) and granulometry (medium grain diameter, d 0. 3 mm.) measurements1, respectively. Non laboratory measurements of cs were used since they might be unreliable values because the coring process frequently disturbs the sediment structure.

For down-slope acoustic propagation, computed range dependent coherent TL values, using RAMS vers. 0.6s as well as the theoretical fitting curve from the previous work (Milou et al., 1994), are compared with the corresponding measurements held in selected 1/3 octave frequency bands between 100 Hz and 400 Hz.

RAMS vers. 0.6s code's facility of providing 2-D Transmission Loss contours over depth and range that give information on the spatial intensity distribution in a vertical slice through the ocean is also used.


Coherent TL, here computed through RAMS Vers. 0.6 code, as well as already reported experimental data and a logarithmic regression curve for coherent TL computed with the previous code (Milou et al., 1994) are graphically shown in FIGS. 1 and 2 (a) for seven central frequencies within the 100 Hz-400 Hz band. A representation of the sound field as 2-D TL contour lines plotting using RAMS vers. 0.6s for 400 Hz and a 20 m source depth is shown in Fig. 2(b).

Figure 1: Transmission Losses vs. range for the band 100-317 Hz: · Measurements; _ Up-dated code; _ Previous code.

Comparison of experimental data and theoretical predictions leads to conclude that recent computed values with the up-dated code, provide a better fitting for all frequencies in the studied interval.

This result could be explained by the combination of two factors: (i) several significant improvements incorporated in the updated code, and (ii) a modified geoacoustic bottom description instead of the one originally used.

Figure 2: Transmission Losses for f = 400 Hz: (a) TL vs. range: · Measurements; _ Up-dated code; _ Previous code. (b) 2-D contours over depth and range.

Regarding the first factor (i), it is currently well known by the scientific community that the PE method has undergone extensive development along the two last decades since it was first introduced in the field of underwater sound (Tappert, 1977). Since the PE solutions are approximations, interest in their accuracy has permanently given rise to different attempts to improve it. On the other hand, the efficiency problems associated to numerical solutions of PE techniques cannot be neglected when range-dependent ocean environments have to be handled. Precisely the PE updated code used in this work differs from the previous one since it includes a higher-order energy-conservation correction at vertical interfaces that is accurate for problems involving large ocean bottom slopes, large depth and range variations in sound speed; very wide propagation angles and piece-wise continuous density variations (Collins et al., 1991); a split-step Padé accurate and efficient solution that enables very wide propagation angles, large depth variations in the properties of the waveguide and elastic ocean bottoms capable of supporting shear waves (Collins, 1993); and a self-starter approach for the initial condition of the PE, jointly with some other fine corrections such as one that tends to eliminate overflow problems or to improve stability problems. All these improvements might undoubtedly contribute to achieve the obtained better fitting here presented.

Concerning the second factor (ii), inclusion of shear waves propagating into unconsolidated marine sediments layers overlying a solid substrate with their corresponding estimated phase velocity and absorption coefficient, might also contribute to increase the agreement between current computations and experimental data.


The authors acknowledge Dr M. Collins and Dr L. Fielkowski's valuable discussions on RAM vers. 1.5, RAMS vers. 0.6s and RAMGEO vers. 2.0g updated codes during a visit to the Naval Research Laboratory on 2002 (ONRIFO-VSP4063-2002). They also thank Dr G. Parker with the Marine Geological Dept. - Argentinean Hydrographic Service1 for providing seabed features in the studied area.



Blanc, S. & Novarini, J. C., 1987, Dependencia con la frecuencia del coeficiente de reflexión de las ondas acústicas en el lecho marino, Revista Latinoamericana de Acústica, 1, 22-28. [1]

Collins, M. D., 1989, A higher-order parabolic equation for wave propagation in an ocean overlying an elastic bottom, Journal of the Acoustical Society of America, 86, 1459-1464. [2]

Collins, M. D., 1989, Applications and time-domain solution of higher-order parabolic equations in underwater acoustics, Journal of the Acoustical Society of America, 86, 1097-1102. [3]

Collins, M.D., 1993, A split-step Padé solution for the parabolic equation method, Journal of the Acoustical Society of America, 93, 1736-1742. [4]

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Jensen, Finn B., Kuperman, William A., Porter Michel B. & Schmidt Henrik, 1994, Computational Ocean Acoustic, American Institute of Physics, New York, 343-412. [6]

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Tappert, F. D., 1977, The parabolic approximation method, in Wave Propagation in Underwater Acoustic, J. B. Keller & J. S. Papadakis, Springer-Verlog, New York, 224 - 287. [10]


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