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 60

based on the assumption of a variable compensation density (Pratt 1855 ; Hayford
1909 ; Hayford and Bowie 1912 ), while a variable compensation depth is considered
in the Airy-Heiskanen isostatic model (Airy 1855 ; Heiskanen and Vening Meinesz
1958 ). Vening Meinesz ( 1931 ) modified the Airy-Heiskanen theory by introducing
a regional isostatic compensation based on a thin plate lithospheric flexure model
(cf. Watts 2001 ). The regional compensation model was later adopted in the Parker-
Oldenburg isostatic method (Oldenburg 1974 ). Moritz ( 1990 ) utilized the Vening
Meinesz inverse problem of isostasy for the Moho depth estimation. Sjöberg ( 2009 )
reformulated Moritz's problem, called herein the Vening Meinesz-Moritz (VMM)
problem of isostasy, as that of solving a nonlinear Fredholm integral equation of the
first kind. Sjöberg and Bagherbandi ( 2011 ) developed and applied a least-squares
approach, which combined seismic and gravity data in the VMM isostatic inverse
scheme for a simultaneous estimation of the Moho depth and density contrast. They
also presented and applied the non-isostatic correction to model for discrepancies
between isostatic and seismic models (cf. Bagherbandi and Sjöberg 2012 ).
In this study, we present a numerical scheme of the Moho depth determination
using gravity and crustal density structure models. This numerical scheme utilizes
expressions for the gravimetric forward and inverse modeling in a frequency
domain. The functional model for the gravimetric inverse problem (in terms of
a nonlinear Fredholm integral equation of the first kind) is established based on
the assumption that the refined gravity disturbances have a maximum correlation
with the Moho geometry. This maximum correlation can be attained by applying
the topographic and crust components stripping gravity corrections to gravity dis-
turbances, yielding the consolidated crust-stripped gravity disturbances. However,
these gravity data still comprise a long-wavelength signal from unmodeled mantle
heterogeneities and uncertainties of a crustal structure model. A linearization of
the Fredholm integral equation of the first kind is applied, which incorporates the
isostatic compensation scheme based on minimizing the correlation between the
isostatic gravity and (a priori) Moho depth data. The resulting complete crust-
stripped isostatic gravity disturbances are then used to solve the gravimetric inverse
problem for finding the Moho depths. These input gravity data are computed by
applying the gravimetric forward modeling.

4.2 Gravimetric Forward Modeling

The consolidated crust-stripped gravity disturbances ı g cs are obtained from the cor-
responding gravity disturbances ı g after applying the topographic and crust density
contrasts stripping gravity corrections. The computation is realized according to the
following scheme (Tenzer et al. 2012a ):

ıg cs D ıg g t g b g i g s g c ; (4.1)