Geoscience Reference
In-Depth Information
ıg
m
.r;/
Š
G¡
c=m
“
T
r; ;D
0
0
ıD
0
d
0
;
(4.17)
0
2dž
where
T
is the integral kernel. They gave the solution of Eq. (
4.17
) in the following
spectral form:
R
r
nC2
X
n
X
n
GM
R
2
ıg
m
.r;/
D
F
ıD
.n
C
1/
n;m
Y
n;m
./;
(4.18)
n
D
0
mDn
where the numerical coefficients F
ıD
n;m
read
n
C
2
k
.
1/
k
R
kC1
ıD
.k/
n
C
2
X
¡
c=m
¡
Earth
3
2n
C
1
F
ıD
n;m
D
n;m
:
(4.19)
k
D
0
The inverse solution to the system of linearized observation equations (in Eq.
(
4.19
)) yields the Moho depth correction coefficients ıD
.k/
n;m
. These coefficients are
converted into the Moho depth corrections ı
D
0
using the following expression:
“
2n
C
1
4
D
0
0
P
n
.t/ıD
0
d
0
ıD
.k
n
./
D
0
2
dž
X
n
ıD
.k/
D
n;m
Y
n;m
./ .k
D
1;2;3;4;:::/:
(4.20)
mDn
4.4
Numerical Realization and Results
The gravity disturbances were generated using the GOCO03S coefficients (Mayer-
Guerr et al.
2012
) with a spectral resolution complete to degree 180 of spherical
harmonics. The spherical harmonic terms of the normal gravity field were computed
according to the parameters of GRS-80 (Moritz
2000
). The same spectral resolution
was used to compute the topographic and bathymetric (ocean density contrast)
stripping gravity corrections. These two gravity corrections were computed from the
DTM2006.0 coefficients of the solid topography (Pavlis et al.
2007
). The average
density of the upper continental crust 2,670 kg m
3
(cf. Hinze
2003
) was adopted for
defining the topographic and reference crustal densities. The bathymetric stripping
gravity correction was computed using the depth-dependent seawater density model
(see Tenzer et al.
2012c
). For the reference crustal density of 2,670 kg m
3
and the surface seawater density of 1,027.91 kg m
3
(cf. Gladkikh and Tenzer
2011
), the nominal ocean density contrast (at zero depth) equals 1642.09 kg m
3
.
Search WWH ::
Custom Search