Geoscience Reference
In-Depth Information
Table 9.1. Estimated values of the covariance
function for free-air anomalies [unit mgal
2
]
ψ
(
ψ
)
ψC
(
ψ
)
ψ
(
ψ
)
0
.
0
◦
8
◦
27
◦
+1201
+124
+18
0
.
5
◦
9
◦
29
◦
751
104
+6
1
.
0
◦
10
◦
31
◦
468
82
+8
1
.
5
◦
11
◦
33
◦
356
76
+5
2
.
0
◦
13
◦
35
◦
332
54
−
8
2
.
5
◦
15
◦
40
◦
306
47
−
12
3
.
0
◦
17
◦
50
◦
296
45
−
20
4
.
0
◦
19
◦
60
◦
272
34
−
30
5
.
0
◦
21
◦
90
◦
246
35
−
4
6
.
0
◦
23
◦
120
◦
214
10
+12
7
.
0
◦
25
◦
150
◦
−
174
20
21
where
C
0
= 337 mgal
2
,
d
=40km
.
(9-11)
This function is valid for
s<
100 km.
In the meantime it has been recognized that a proper determination of
global and local covariance functions is a central practical problem in this
context.
The Tscherning-Rapp covariance model and the COVAXN sub-
routine
The fundamental covariance model by Tscherning and Rapp (1974) and the
subroutine COVAXN (Tscherning 1976) are still very much up to date, as
the following quotation from Kuhtreiber (2002 b) shows:
“The global covariance function of the gravity anomalies
C
g
(
P, Q
)given
by Tscherning and Rapp (1974, p. 29) is written as
C
g
(
P, Q
)=
A
∞
n
−
1
2)(
n
+
B
)
s
n
+2
P
n
(cos
ψ
)
,
(9-12)
(
n
−
n
=3
where
P
n
(cos
ψ
) denotes the Legendre polynomial of degree
n
;
ψ
is the spher-
ical distance between
P
and
Q
;and
A, B
and
s
are the model parameters.
A closed expression for (9-12) is available in (ibid., p. 45).
