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In geophysical and geodetic studies, gravity inversion is typically performed such that observed gravity values are first continued downward onto a regular (planar, spherical or spheroidal) surface by solving an inverse integral transform, which originates from a classical solution to the first boundary-value problem in potential theory. A typical example is continuing gravity observed at the topographic surface down to the mean sea level (geoid). Nowadays, gravity-dedicated satellite missions and aerial gravimetry provide gravity data above the topographic surface in addition to classical terrestrial gravity observations. For specific purposes (such as gravity data combination and validation, or quasigeoid determination), satellite and aerial gravity observations have to be continued to the irregular topographic surface. In this study, we address this issue by formulating a functional model for a spectral downward continuation of selected gravitational field quantities to an irregular topographic surface. Moreover, we generalize this functional model to allow for transformation between different types of gravitational field quantities. In particular, we derive spectral weights for estimation of the disturbing potential or disturbing/anomalous gravity at the Earth's surface by combining the first-, second- and third-order radial gradients of the disturbing potential (disturbing gradients). The correctness of the developed combined spectral estimator is verified in a closed-loop test based on synthetic satellite disturbing gradients. The combined spectral estimator is applied to simulated satellite disturbing gradients polluted by a realistic Gaussian noise. Results of the numerical experiments show that the combined spectral estimator puts the highest importance on the least polluted disturbing gradient, while the contribution of the least accurate disturbing gradient is negligible. An important advantage of this spectral combination method is that no matrix inversion with numerical instabilities requiring regularization is needed. [ABSTRACT FROM AUTHOR]

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]

In geophysical studies investigating the lithosphere structure, the gravitational field generated by the ocean density contrast (i.e., bathymetry-generated gravitational field) represents a significant amount of the signal to be modelled and subsequently removed from the Earth's gravity field. The ocean density contrast is typically calculated as the difference between the mean density values of the Earth's crust and seawater. The approximation of the actual seawater density distribution by its mean value yields relative errors up to about 2% in computed quantities of the gravitational field. To reduce these errors, a more realistic model of the seawater density distribution is utilized based on the analysis of existing oceanographic data of salinity, temperature, and pressure (depth). We study the accuracy of the bathymetry-generated gravitational field quantities formulated for a depth-dependent model of the seawater density distribution. This density distribution approximates the seawater density variations due to an increasing pressure with depth, whereas smaller lateral density variations caused by salinity, temperature, and other oceanographic factors are not taken into consideration. The error analysis reveals that the approximation of the seawater density by the depth-dependent density model reduces the maximum errors to less than 0.6%. The corresponding depth-averaged errors are below 0.1%. The depth-dependent seawater density model is further facilitated in expressions for computing the bathymetry-generated gravitational field quantities by means of the spherical bathymetric (ocean bottom depth) functions. The numerical realization reveals large differences in the results obtained with and without consideration of the depth-dependent seawater density distribution. The maxima of absolute differences reach 201 m/s and 16.5 mGal in computed values of the potential and attraction, respectively. The application of the depth-dependent seawater density model thus significantly improves the accuracy in the forward modelling of the bathymetric gravitational field quantities. [ABSTRACT FROM AUTHOR]

In the last few decades, satellites have acquired various potential data sets hundreds of kilometers above the Earth's surface. Conventionally, these global magnetic and gravitational data sets are approximated by using spherical harmonics that allow straightforward work with both fields outside the Earth's mass. In this article, we present an alternative approach for working with potential data in mass-free space given over a regular coordinate grid on a spherical surface. The algorithm is based on an iterative scheme and the Poisson integral equation for the sphere. With help from the Fourier transform, global potential (magnetic or gravitational) data can efficiently be continued from a mean orbital sphere down to a reference surface without using the spherical harmonics. This is illustrated both with simulated magnetic field data and with real data from the satellite gradiometry mission GOCE. In the case of simulated magnetic data and the downward continuation for 450 km, we have achieved a root mean square at the level of 0.05 nT, while it was <1 E (eotvos) for real GOCE data continued for 250 km. The crucial point is to apply the algorithm twice as a large part of noise can be removed from the input data. [ABSTRACT FROM AUTHOR]

The global crustal model CRUST1.0 (refined using additional global datasets of the solid topography, polar ice sheets and geoid) is used in this study to estimate the average densities of major crustal structures. We further use this refined model to compile the gravity field quantities generated by the Earth's crustal structures and to investigate their spatial and spectral characteristics and their correlation with the crustal geometry in context of the gravimetric Moho determination. The analysis shows that the average crustal density is 2,830 kg/m, while it decreases to 2,490 kg/m when including the seawater. The average density of the oceanic crust (without the seawater) is 2,860 kg/m, and the average continental crustal density (including the continental shelves) is 2,790 kg/m. The correlation analysis reveals that the gravity field corrected for major known anomalous crustal density structures has a maximum (absolute) correlation with the Moho geometry. The Moho signature in these gravity data is seen mainly at the long-to-medium wavelengths. At higher frequencies, the Moho signature is weakening due to a noise in gravity data, which is mainly attributed to crustal model uncertainties. The Moho determination thus requires a combination of gravity and seismic data. In global studies, gravimetric methods can help improving seismic results, because (1) large parts of the world are not yet sufficiently covered by seismic surveys and (2) global gravity models have a relatively high accuracy and resolution. In regional and local studies, the gravimetric Moho determination requires either a detailed crustal density model or seismic data (for a combined gravity and seismic data inversion). We also demonstrate that the Earth's long-wavelength gravity spectrum comprises not only the gravitational signal of deep mantle heterogeneities (including the core-mantle boundary zone), but also shallow crustal structures. Consequently, the application of spectral filtering in the gravimetric Moho determination will remove not only the gravitational signal of (unknown) mantle heterogeneities, but also the Moho signature at the long-wavelength gravity spectrum. [ABSTRACT FROM AUTHOR]