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d X
d t
k x
k x + k y
= c
,
(5.11)
d Y
d t
k y
k x + k y
= c
,
(5.12)
k x + k y ,
d k x
d t
c
=
(5.13)
x
k x + k y ,
d k y
d t
c
=
(5.14)
y
where x and y are the coordinates of ray points, k x and k y are components of
the wave vector and t represents time. The ray equations written in this form, per-
mit not only to easily calculate the course of the wave ray, but also the evolution of
the wave front. For computing the ray evolution the set of equations (5.11)-(5.14)
must be supplemented by initial conditions consisting in determination of the initial
coordinates and direction. It is not difficult to note that in the case of a fixed basin
depth ( c = const) the rays will be straight lines.
Figure 5.7 presents two examples of the computation of ray behaviour, performed
with the aid of formulae (5.11)-(5.14). The model bottom relief in the first case
(Fig. 5.7a) imitates a mountain ridge in the middle of the ocean. Part of the rays
emitted by a point-like source turn out to be captured, these rays further propagate
(a)
(b)
Fig. 5.7 Examples of influence of bottom relief on the course of wave rays emitted by a pointlike
source: capture of rays by an underwater ridge (a); refraction and capture of waves in the shelf
zone (b)
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