Pavel Novák

Spatial and Spectral Analysis of Refined Gravity Data for Modelling the Crust–Mantle Interface and Mantle-Lithosphere Structure

We analyse spatial and spectral characteristics of various refined gravity data used for modelling and gravimetric interpretation of the crust–mantle interface and the mantle-lithosphere structure. Depending on the purpose of the study, refined gravity data have either a strong or weak correlation with the Moho depths (Moho geometry). The compilation of the refined gravity data is purely based on available information on the crustal density structure obtained from seismic surveys without adopting any isostatic hypothesis. We demonstrate that the crust-stripped relative-to-mantle gravity data have a weak correlation with the CRUST2.0 Moho depths of about 0.02. Since gravitational signals due to the crustal density structure and the Moho geometry are subtracted from gravity field, these refined gravity data comprise mainly the information on the mantle lithosphere and sub-lithospheric mantle. On the other hand, the consolidated crust-stripped gravity data, obtained from the gravity field after applying the crust density contrast stripping corrections, comprise mainly the gravitational signal of the Moho geometry, although they also contain the gravitational signal due to anomalous mass density structures within the mantle. In the absence of global models of the mantle structure, the best possible option of computing refined gravity data, suitable for the recovery/refinement of the Moho interface, is to subtract the complete crust-corrected gravity data from the consolidated crust-stripped gravity data. These refined gravity data, that is, the homogenous crust gravity data, have a strong absolute correlation of about 0.99 with the CRUST2.0 Moho depths due to removing a gravitational signal of inhomogeneous density structures within the crust and mantle. Results of the spectral signal decomposition and the subsequent correlation analysis reveal that the correlation of the homogenous crust gravity data with the Moho depths is larger than 0.9 over the investigated harmonic spectrum up to harmonic degree 90. The crust-stripped relative-to-mantle gravity data correlate substantially with the Moho depths above harmonic degree 50 where the correlation exceeds 0.5.

Developments in Hydraulic Engineering

Four detailed review chapters by different authors cover low-head hydropower utilization, intake design for ice conditions, the interface between estuaries and seas, and polders.

Glacial isostatic adjustment in the static gravity field of Fennoscandia

In the central part of Fennoscandia, the crust is currently rising, because of the delayed response of the viscous mantle to melting of the Late Pleistocene ice sheet. This process, called Glacial Isostatic Adjustment (GIA), causes a negative anomaly in the present-day static gravity field as isostatic equilibrium has not been reached yet. Several studies have tried to use this anomaly as a constraint on models of GIA, but the uncertainty in crustal and upper mantle structures has not been fully taken into account. Therefore, our aim is to revisit this using improved crustal models and compensation techniques. We find that in contrast with other studies, the effect of crustal anomalies on the gravity field cannot be effectively removed, because of uncertainties in the crustal and upper mantle density models. Our second aim is to estimate the effects on geophysical models, which assume isostatic equilibrium, after correcting the observed gravity field with numerical models for GIA. We show that correcting for GIA in geophysical modelling can give changes of several kilometer in the thickness of structural layers of modeled lithosphere, which is a small but significant correction. Correcting the gravity field for GIA prior to assuming isostatic equilibrium and inferring density anomalies might be relevant in other areas with ongoing postglacial rebound such as North America and the polar regions.

Integral formulas for computing a third-order gravitational tensor from volumetric mass density, disturbing gravitational potential, gravity anomaly and gravity disturbance

A new mathematical model for evaluation of the third-order (disturbing) gravitational tensor is formulated in this article. Firstly, we construct corresponding differential operators for the components of the third-order (disturbing) gravitational tensor in a spherical local north-oriented frame. We show that the differential operators may efficiently be decomposed into an azimuthal and an isotropic part. The differential operators are even more simplified for a certain class of isotropic kernels. Secondly, the differential operators are applied to the well-known integrals of Newton, Abel-Poisson, Pizzetti and Hotine. In this way, 40 new integral formulas are derived. The new integral formulas allow for evaluation of the components of the third-order (disturbing) gravitational tensor from density distribution, disturbing gravitational potential, gravity anomalies and gravity disturbances. Thirdly, we investigate the behaviour of the corresponding integral kernels in the spatial domain. The new mathematical formulas extend the theoretical apparatus of geodesy, i.e. the well-known Meissl scheme, and reveal important properties of the third-order gravitational tensor. They may be exploited in geophysical studies, continuation of gravitational field quantities and analysing the gradiometric-geodynamic boundary value problem.

Satellite gravity gradient grids for geophysics

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite aimed at determining the Earth’s mean gravity field. GOCE delivered gravity gradients containing directional information, which are complicated to use because of their error characteristics and because they are given in a rotating instrument frame indirectly related to the Earth. We compute gravity gradients in grids at 225 km and 255 km altitude above the reference ellipsoid corresponding to the GOCE nominal and lower orbit phases respectively, and find that the grids may contain additional high-frequency content compared with GOCE-based global models. We discuss the gradient sensitivity for crustal depth slices using a 3D lithospheric model of the North-East Atlantic region, which shows that the depth sensitivity differs from gradient to gradient. In addition, the relative signal power for the individual gradient component changes comparing the 225 km and 255 km grids, implying that using all components at different heights reduces parameter uncertainties in geophysical modelling. Furthermore, since gravity gradients contain complementary information to gravity, we foresee the use of the grids in a wide range of applications from lithospheric modelling to studies on dynamic topography, and glacial isostatic adjustment, to bedrock geometry determination under ice sheets.

Contribution of mass density heterogeneities to the quasigeoid-to-geoid separation

The geoid-to-quasigeoid separation is often computed only approximately as a function of the simple planar Bouguer gravity anomaly and the height of the computation point while disregarding the contributions of terrain geometry and anomalous topographic density as well as the sub-geoid masses. In this study we demonstrate that these contributions are significant and, therefore, should be taken into consideration when investigating the relation between the normal and orthometric heights particularly in the mountainous, polar and geologically complex regions. These contributions are evaluated by applying the spectral expressions for gravimetric forward modelling and using the EIGEN-6C4 gravity model, the Earth2014 datasets of terrain, ice thickness and inland bathymetry and the CRUST1.0 sediment and (consolidated) crustal density data. Since the global crustal density models currently available (e.g. CRUST1.0) have a limited accuracy and resolution, the comparison of individual density contributions is—for consistency—realized with a limited spectral resolution up to a spherical harmonic degree 360 (or 180). The results reveal that the topographic contribution globally varies between

Derivation of the Topographic Potential from Global DEM Models

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Numerical Studies on the Harmonic Downward Continuation of Band-Limited Airborne Gravity

-0.33 and 0.57 m, with maxima in Himalaya and Tibet. The contribution of ice considerably modifies the geoid-to-quasigeoid separation over large parts of Antarctica and Greenland, where it reaches