Gravimetric Forward and Inverse Modeling Methods of the Crustal Density Structures and the Crust-Mantle Interface - Planetary Exploration and Science: Recent Results and Advances - page 64

CRUST2.0 Moho geometry. Tenzer and Chen ( 2014 ) proposed an isostatic com-
pensation scheme based on minimizing a spatial correlation between the isostatic
gravity disturbances and the Moho geometry. According to this scheme, the isostatic
compensation attraction g i defines the stripping gravity correction of a homogenous
crust layer (below the geoid surface) respective to the upper mantle density. For
the adopted constant densities of the reference crust and upper mantle, the stripping
density contrast is defined as a constant value of the Moho density contrast ¡ c=m .
The isostatic compensation attraction g i reads

R
r

nC2 n

X

n

X

GM
R 2

g i .r;/ D F n;m Y n;m ./; (4.13)

n D 0 mDn

where the numerical coefficients F n , m are given by

n C 3
k

. 1/ k
R kC1 D .k/

X

nC3

¡ c=m
¡ Earth

3
2n C 1

n C 1
n C 3

F n;m D

n;m :

(4.14)

kD1

f D ( k )

n , m : k D 2,

The Moho depth coefficients D n , m and their higher-order terms

3, 4, ::: g are computed from discrete values D 0 0

of the a priori Moho model using

the following expression:

“

2n C 1
4

D 0 0 P n .t/d 0

D .k n ./ D

0 2dž

n

X

D .k/

D

n;m Y n;m ./ .k D 1;2;3;4;:::/:

(4.15)

m D n

The complete crust-stripped isostatic gravity disturbance ı g m

is obtained from the

consolidated crust-stripped gravity disturbance ı g cs

after subtracting the isostatic

compensation attraction g i . Hence

ıg m .r;/ D ıg cs .r;/ g i .r;/: (4.16)

The values of ı g m are used as the input data to determine the Moho depths in the
gravimetric inverse scheme.

4.3 Gravimetric Inverse Problem

Tenzer and Chen ( 2014 ) formulated a relation between the complete crust-stripped
isostatic gravity disturbances ı g m and the Moho depth corrections ı D 0 by means of
a linearized Fredholm integral of the first kind: