It can be seen that the first reflected rays occur at about 1.1 second, corresponding to a turning or reflection depth of about 1650 metres, which is the same depth as the highest peaks of Walvis Ridge. The deepest ray to get through without reflection has a turning point at 1850 metres, corresponding to a delay time of 2.3 seconds. In Figure 2 it Is at 1.5 seconds that the amplitude of the received signal deviates from the theoretical. This suggests that the energy of the reflected rays is mainly received between 1.5 to 6 seconds. The distribution of the scattered points in Figure 9 seems to agree with this - particularly those points that have been reflected 1 to 11 times and which should have the largest amplitudes.
The agreement between the results for reflected rays and the recorded signal sugagests that the reflected ray model is fairly similar to the actual process. Referring back to Figure 2, it seems that the gradual increase in slope above noise level of the recorded signal could be caused by the summation of many reflected rays with the number of reflections increasing for the faster rays. The way in which rays are reflected in the model, however, does have implications for ocean acoustic tomography.
Implications for ATOC
In a real ocean a low frequency, near-omni-directional ATOC source is bound to reflect some rays off the irregular ocean floor. These reflected rays will be deflected so that their arrival time is to, some extent, not representative of the depths the ray has sampled. If the reflected ray arrives concurrently with an eigenray used for tomography calculations, some error may be included in the average temperature calculated from that ray. It is also probable that the reflected rays will be less stable with changes in the environment than direct rays. This wili result in increased variability for the ATOC thermal signal. The rays with the deepest turning points (that is, the earliest arrivals) will be the most likely to be affected and the more irregular the sea-floor, the larger the likely effect. The results shown here represent an extreme case, insofar as the ridge is shallow and the total distance is large, resulting in many reflected eigenrays. In most ATOC Iines the effect may be small but possibly worthy of further investigation. In a 1966 paper on the analysis of the Pacific ATOC results (7), the comment is made that many unstable receptions are present and that stable arrivals have to be selected by a template that uses both travel time and arrival angale. It seems probable that at least some of the instability in those receptions is due to reflected rays, despite the relative flatness of the north-west Pacific basin.
To reduce these effects, the source or receiver or both would have to be directional, or made to be directional, by siting them behind suitable screening topography. This would result in discarding the deeper rays along with most of the interfering rays, so that less information would be available. Modelling the problem will probably give only a crude idea of the errors unless high resolution bathymetry is available.
References
1. David Palmer, ATOC-FACT arrival-time differences, ATOC Occasional Notes Number 17, March 1994.
2. G.B. Brundrit, L. Krige, D. Palmer, A. Forbes, K. Metzger, Acoustic thermometry of ocean climate: Feasibility, Ascension - Cape Town, 2nd European Conference on Underwater Acoustics,edited by L. Bjorno, 1994.
3. M. Porter and E. L. Reiss, A numerical method for ocean-acoustic normal modes, JASA 76(1), p. 244, July 1984.
4. Website http://biudc.nbi.ac.uk/bodc/gebco.html.
5. Walter Munk, Peter Worcester and Carl Wunsch, Ocean Acoustic Tomography, 1995.
6. Website http://njit.oalib.edu and ftp://njit.oalib.edu/pub/ray
7. Brian Dushaw, Bruce Howe, James A. Mercer, Robert C. Spindel and Kurt Metzger ATOC Occasional Notes Number 35, November 1996, Acoustic receptions at SOSUS arrays“k”and“I”of transmissions from Pioneer Seamount and Pacific Basin acoustic thermometry
