Geoscience Reference
In-Depth Information
For a specific volumetric layer, the mass density is either constant , laterally
varying (ǝ
0
), or - in the most general case - approximated by the laterally
distributed radial density variation model using the following polynomial function
(for each lateral column):
I
X
a
i
0
R
r
0
i
;
.r
0
;
0
/
D
.D
U
;
0
/
C
LJ.
0
/
(4.9)
iD1
for R
D
U
.
0
/
r
0
>R
D
L
.
0
/;
where a nominal value of the lateral density (
D
U
, ǝ
0
) is stipulated at the depth
D
U
.
This density distribution model describes the radial density variation by means of the
coefficients
f
Ǜ :
i
D
1, 2, :::,
I
g
and LJ within a volumetric mass layer at a location
0
. Alternatively, when modeling the gravitational field of anomalous mass density
structures, the density contrast .r
0
;
0
/ of a volumetric mass layer respective to
the reference crust density
c
is defined as
r
0
;
0
D
r
0
;
0
¡
c
I
X
D
D
U
;
0
C
LJ
0
a
i
0
R
r
0
i
;
iD1
for R
D
U
0
r
0
>R
D
L
0
;
(4.10)
where .D
U
;
0
/ is a nominal value of the lateral density contrast at the depth
D
U
.
The coefficients
L
n
,
m
and
U
n
,
m
combine the information on the geometry and
density (or density contrast) distribution of a volumetric layer. These coefficients
are generated to a certain degree of spherical harmonics using discrete data of the
spatial density distribution (i.e., typically provided by means of density, depth, and
thickness data) of a particular structural component of the Earth's interior.
From Eqs. (
4.1
)and(
4.3
), the spectral representation of the consolidated crust-
stripped gravity disturbance ı
g
cs
is written as
R
r
nC2
n
n
X
X
GM
R
2
ıg
cs
.r;/
D
.n
C
1/T
cs
n;m
Y
n;m
./;
(4.11)
m
D
n
nD0
where the potential coefficients
T
c
n
,
m
consist of the following components:
T
cs
n;m
D
T
n;m
V
n;m
V
n;m
V
n;m
V
n;m
V
n;m
:
(4.12)
Tenzer et al. (
2009a
,
b
) and Tenzer et al. (
2012b
) demonstrated that the consolidated
crust-stripped gravity disturbances ı
g
cs
have a maximum correlation with the
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