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We derive expressions for computing the gravitational field (potential and its radial derivative) generated by an arbitrary homogeneous or laterally varying density contrast layer with a variable depth and thickness based on methods for a spherical harmonic analysis and synthesis of gravity field. The newly derived expressions are utilised in the gravimetric forward modelling of major known density structures within the Earth's crust (excluding the ocean density contrast) beneath the geoid surface. The gravitational field quantities due to the sediments and crust components density contrasts, shown in numerical examples, are computed using the 2 × 2 arc-deg discrete data from the global crustal model CRUST2.0. These density contrasts are defined relative to the adopted value of the reference crustal density of 2670 kgm. All computations are realised globally on a 1 × 1 arc-deg geographical grid at the Earth's surface. The maxima of the gravitational signal due to the sediments density contrast are mainly along continental shelf regions with the largest sedimentary deposits. The corresponding maxima due to the consolidated crust components density contrast are over areas of the largest continental crustal thickness with variable geological structure. [ABSTRACT FROM AUTHOR]

Recent applications in Earth sciences require geoid models to be determined with a sub-centimetre internal error. Regional models of the geoid are usually determined using discrete gravity values measured at and/or outside the Earth, and global models of the Earth gravity field and topographic surface. In this article, we review previous studies that (to some extent) discuss the estimation of the geoid internal error, and provide formulations and methodologies required for a comprehensive formal propagation of errors of gravity data and global models through a mathematical model used for regional geoid determination. The mathematical model is based on combining the inverse Poisson integral equation and the Hotine integral transform in the Helmert harmonic space; also called the one-step integration method. Calculations and tests are performed in one of the most challenging test areas ("the Colorado test area") using ground and airborne gravity observations, a global digital terrain model (DTM) for topographic effects on gravity and the geoid, and a global Earth gravitational model (EGM) for the long-wavelength components of gravity and the geoid. There are three main contributors to the total internal error of the geoid height, namely those associated with the EGM (for estimating the long-wavelength geoid height), DTM heights (for evaluation of the topographic effects on observed gravity and the geoid height), and gravity observations (for determining the short-wavelength components of the geoid height). The geoid errors stemming from the EGM formal variances of its spherical harmonic coefficients amount to 0.3 cm of the total internal error budget of the geoid. The mean value of the standard deviation of the geoid height stemming from the topographic effects (due to uncertainties of DTM heights) is 1.0 cm. The observation errors and spatial distribution (resolution) of regional ground and airborne gravity observations, i.e., the design of the project, are the dominant contributors to the internal error of the geoid height. The internal error estimate of the geoid model in the Colorado test area computed on a 1′ × 1′ grid is 2.7 cm which agrees with the differences between various geoid models that contributed to the Colorado 1-cm geoid experiment. Determining a regional geoid model with a sub-centimetre internal error in areas of rough topography, such as that of Colorado, requires high-accuracy and high-resolution gravity observations. To assess the accuracy of regional gravity measurements required for sub-centimetre geoid models, we simulate airborne gravity measurements in the Colorado test area at a practical lower flight altitude, and improve the spatial distribution of existing ground gravity observations by filling in gaps using synthetic (EGM-based) gravity disturbances. Results show that carrying out airborne gravity surveys with a gentle drape approach at an average flight altitude between 300 and 500 m above the Earth's surface provides airborne gravity measurements with a mean standard deviation of 0.75 mGal at 2.2 km spatial resolution. Thus, a sub-centimetre regional gravimetric geoid model in the Colorado test area would be achievable using the proposed configuration of the ground and airborne gravity observations and more accurate DTMs. [ABSTRACT FROM AUTHOR]

Abstract: In classical isostatic models for a gravimetric recovery of the Moho parameters (i.e., Moho depths and density contrast) the isostatic gravity anomalies are usually defined based on the assumption that the topographic mass surplus and the ocean mass deficiency are compensated within the Earth''s crust. As acquired in this study, this assumption yields large disagreements between isostatic and seismic Moho models. To assess the effects not accounted for in classical isostatic models, we conduct a number of numerical experiments using available global gravity and crustal structure models. First, we compute the gravitational contributions of mass density contrasts due to ice and sediments, and subsequently evaluate respective changes in the Moho geometry. Residual differences between the gravimetric and seismic Moho models are then used to predict a remaining non-isostatic gravity signal, which is mainly attributed to unmodeled density structures and other geophysical phenomena. We utilize three recently developed computational schemes in our numerical studies. The apparatus of spherical harmonic analysis and synthesis is applied in forward modeling of the isostatic gravity disturbances. The Moho depths are estimated globally on a 1 arc-deg equiangular grid by solving the Vening-Meinesz Moritz inverse problem of isostasy. The same estimation model is applied to evaluate the differences between the isostatic and seismic models. We demonstrate that the application of the ice and sediment density contrasts stripping gravity corrections is essential for a more accurate determination of the Moho geometry. We also show that the application of the additional non-isostatic correction further improves the agreement between the Moho models derived based on gravity and seismic data. Our conclusions are based on comparing the gravimetric results with the CRUST2.0 global crustal model compiled using results of seismic surveys. [Copyright &y& Elsevier]