The -4.6 seconds ray is also converted from a potentially very steep ray to a much less steep ray by reflections at the source. If a reflection coefficient of 0.8to 0.95 at low frequencies (and low angles of incidence) is assumed, the final ray amplitude would still be 0.2 to 0.8 times the amplitude before reflection. Since there are many of these reflected rays and their amplitudes may add, the final amplitude may be sufficient to have considerable effect.
Searching for eigenrays with the Bowlin model shows that the number of eigenrays increases sharply with increasing search resolution. Over 200 eigenrays were found for positive launch angles only during the first search and it seems likely that the totalnumber of eigenrays may be one or two magnitudes larger. This would mean that the number of reflected rays is far greater than the number of direct rays in the 3500 metre flat sea-floor comparison.
Comparison of arrival times of direct and reflected rays
Figure 9 summarises some results from the Bowlin ray tracing model. It shows the maximum turning point depth versus arrival time for both the flat ocean floor (continuous line) and the sea floor with ridges (points). The results for the ridged floor initially follow those of the flat floor for the slowest rays (only a sparse selection of these points is shown, so as not to obscure the line), but then deviate in both depth and arrival time. For the reflected rays, there is no simple relationship between arrival time and the maximum depth of the turning points. Figure 9 shows the end points of many rays that have been retarded or accelerated, just as Figures 6 to 8 showed particular retarded or accelerated rays. Reflected rays have at least two different turning point depths, while the average speed of the ray is normally related to a single intermediate turning point depth by interpreting the wavefront.
Figure 9. Wavefront results for direct and reflected rays.
