Geoscience Reference
In-Depth Information
n=0
P
k
e
k
θ
k
P
3
e
3
θ
3
s
2
n
2
θ
2
P
2
e
2
N
h2
, N
w2
s
1
z
n
1
e
1
=
θ
1
N
h1
, N
w1
P
1
η
3
η
2
r
0
y
Fig. 7
Geometry of a 1D ray-tracing method, for a receiver located at
P
1
and the upper limit of the
troposphere at
P
k
. Points
P
2
and
P
3
show two sample points of the ray path. The y- and z-axis of
the Cartesian coordinate system are parallel to horizon and zenith direction at the site, respectively.
S
2
=
P
3
−
P
2
is the distance between two successive points along the path
layers in each intersection point of the trajectory. At the first point (receiver) these
two are same, i.e.
e
1
=
θ
1
.
In this coordinate system, the
z
and
y
components are equal to
r
1
and zero, respec-
tively. Following the geometrical relation in Fig.
7
we find
r
i
+
1
−
r
i
S
i
=
cos
θ
i
−
r
i
sin
θ
i
,
(109)
z
i
+
1
=
z
i
+
S
i
sin
e
i
,
(110)
y
i
+
1
=
y
i
+
S
i
cos
e
i
,
(111)
arctan
y
i
+
1
η
i
+
1
=
z
i
+
1
,
(112)
δ
i
+
1
=
η
i
+
1
−
η
i
,
(113)
10
−
6
1
+
η
i
×
θ
i
+
1
=
arccos
(
10
−
6
cos
(θ
i
+
δ
i
+
1
)),
(114)
1
+
η
i
+
1
×
e
i
+
1
=
θ
i
+
1
−
η
i
+
1
.
(115)
