Forma normal de la bifurcaci´ on de Hopf

Changing temperature, salinity and pressure in the water column create a variable sound speed environment for acoustic propagation. Sound speeds change with location, season and local weather conditions. Sound speed profiles are primarily calculated by measuring a vertical profile of Conductivity and Temperature with Depth (CTD cast). CTD casts taken in the Antarctic are examined in this work to provide a picture of sound speed profiles that might be found on an AUV mission under sea ice. Casts measured during SIPEX 2007, V1 2010 and SIPEX2 2012 have been processed to provide sound velocity profiles, transmission loss estimates and ray trace modelling for a source at a depth of 20 m. The locations of the CTD casts for the three cruises are shown in Fig. 5.3 and the top 600 m of the sound speed profiles are shown collectively in Fig. 5.4. These cruises were all in early spring primarily in the sea ice zone, with some stations on SIPEX 2007 entering the fast ice zone. These locations and seasonality are of key interest for future AUV work. In the sound speed profiles shown in Fig. 5.4 the sound speed transitions from

Figure 5.3: Map of CTD locations for SIPEX 2007, V1 2010 and SIPEX2 2012 with Western Australia to the north for reference. Sound speed profiles and transmission loss model outputs for these CTD casts are shown in App. 8. Background colour bathymetry map from ETOP01.

below 1445 m/s to above 1455 m/s when moving between water masses. The thickness of the pycnocline is given by the change in depth over which the transition occurs. The profiles in Fig. 5.4 mostly show a sharp transition between the layers. The depth of the pycnocline varies from 60 m to 500 m, suggesting some traverse the SP and some the

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PP. Also visible in the sound speed profiles is the mixing or eddying that occurs at the water mass transition with some profiles moving back and forth before settling to the new water mass regime. Figure 5.4 shows some unrealistic values close to the surface the

Figure 5.4: Top 600 m of sound speed profiles calculated using Medwin’s formula for sound speed based with the CTD data of the three cruises SIPEX 2007, V1 2010 and SIPEX2 2012.

possible causes of which will now be discussed. Listed are several possible reasons for these abnormalities some that are discussed in Rosenberg [113] and others found through field experience:

• if the CTD has not been soaked before being cast this could be instrumentation error until the instrument stabilises

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• if the CTD cast has been taken through a hole in the ice this can be caused by strange mixing in the ice hole

• if the cast is made from the ship then the ship movement would cause mixing close to the surface

Because of these potential uncertainties in the surface data and to simplify input pro- cessing for BELLHOP, the casts have been processed using the following method:

• up cast data was selected as it showed less abnormalities in the near surface data

• data was aggregated in 1 m depth bins and the mean sound speed and depth measurement used to represent each group

• data containing any large changes in value in the top 3 m was removed and replaced by a linear regression of the twenty data points previous to extrapolate the data to the surface

For each cast processed using this technique the resulting full depth sound speed profile and ray trace and top 50 m incoherent transmission loss results, for both a flat ice surface and a completely unreflective surface, are shown in App. 8.

Modelling using a completely unreflective surface and bottom produces what is called the direct path. The direct path is made up of the combination of any signals that propagate between the source and receiver without interacting with the surface or bottom.

The propagation paths of acoustic signals are influenced by the shape of the sound speed profile. In Fig. 5.4 all sound speed profiles show an increase in sound speed with depth. The influence of this increase is the refraction of the sound back to the surface creating an area strongly insonified by direct path signals close to the surface and increased surface interaction. Sharp transitions in the sound speed profile influences the homogeneity in the direct path received sound field estimated by modelling. Variations from a linearly increasing sound speed profile, such as those produced by water mass transitions and mixing, create areas of signal focussing and defocussing.

Two sound speed profiles with their resulting top 400 m incoherent transmission loss and ray diagrams for a direct path only scenario are shown in Fig. 5.5. The sound speed profile in Fig. 5.5a has a shallower mixed layer and a sharper transition between water masses at 100 m depth than the sound speed profile shown in Fig. 5.5b which transitions over a greater depth range. This translates to a faster increase in transmission loss with

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range and greater focusing and defocusing of the signal, as shown in the transmission loss and ray diagrams.

(a)

(b)

Figure 5.5: This figure shows two sets of sound speed profiles (2012-10-05, 2012-10-14) with corresponding direct path only ray diagram and top 400 m incoherent transmission loss results for a 20 m deep source. This sound speed profile in (a) has a shallower mixed layer and a sharper transition at 100 m depth which translates to a faster increase in transmission loss with range and greater focusing and defocusing of the signal than the ray and transmission loss produced from the sound speed shown in (b).

Modelling the same scenario using a perfectly reflecting flat ice surface, presented as Fig. 5.6, shows that inclusion of reflected paths homogenises the transmission loss field compared to that found using only the direct path (Fig. 5.5). This reduces but does not remove the impact of the shape of the sound speed profile on the homogeneity of the

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predicted transmission loss. Inclusion of the flat ice surface reflected paths also reduces transmission loss with range compared to a direct path only scenario.

(a)

(b)

Figure 5.6: This figure shows two sets of sound speed profiles (2012-10-05, 2012-10-14) with corresponding flat ice surface ray diagram and top 400 m incoherent transmission loss results for a 20 m deep source. The flat ice layer uses ice properties given by [57] and shown in Tab. 5.1. The difference in the ray and transmission loss diagrams for the two profiles seen in Fig. 5.5 is no longer visible. The reflection of signal from the flat ice surface adds to the direct path signal increasing the homogeneity of the field.

The influence of a mixed layer on propagation paths and transmission loss can be seen in Fig. 5.7. Figure 5.7a shows strong mixing between 100-120 m and a decreased trans- mission loss compared to the second cast taken the next day, shown as Fig. 5.7b, which does not have this mixing. As can be seen in the ray diagram, the mixing event changes the way the sound refracts, decreasing the distance before the deeper paths return to the

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surface and hence increasing shallow insonfication in the first 5 km. A similar result to that noted for the previous sound speed profiles was found with the inclusion of a flat ice surface. That of an increased homogeneity in the transmission loss in the top 100 m and decreased transmission loss with range.

(a)

(b)

Figure 5.7: This figure shows two sets of sound speed profiles (2010-11-08, 2010-11-09) with corresponding direct path only ray diagram and top 400 m incoherent transmission loss results for a 20 m deep source. This figure highlights the influence of water mixing on transmission loss with strong mixing visible in the sound speed profile at approximately 100 m depth in (a). This mixing creates an area of stronger insonification visible in both the ray and transmission loss plots in the top 100 m for the first 5 km than the case shown in (b) with a similar sound speed but no mixing.

The variation in the sound speed profiles and their influence on propagation varies sig- nificantly in the data set reviewed here. These results highlight the importance of using

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either a range of sound speed profiles or a profile measured at the location and time being specifically considered, to model acoustic propagation in Antarctica.