Gravity effect of Alpine slab segments based on geophysical and petrological modelling

In this study, we present an estimate of the gravity signal of the slabs beneath the Alpine mountain belt. Estimates of the gravity effect of the subducting slabs are often omitted or simplified in crustal-scale models. The related signal is calculated here for alternative slab configurations at near-surface height and at a satellite altitude of 225 km. We apply three different modelling approaches in order to estimate the gravity signal from the subducting slab segments: (i) direct conversion of upper mantle seismic velocities to density distribution, which are then forward calculated to obtain the gravity signal; (ii) definition of slab geometries based on seismic crustal thickness and high-resolution upper mantle tomography for two competing slab configurations – the geometries are then forward calculated by assigning a constant density contrast and slab thickness; (iii) accounting for compositional and thermal variations with depth within the predefined slab geometry. Forward calculations predict a gravity signal of up to 40 mGal for the Alpine slab configuration. Significant differences in the gravity anomaly patterns are visible for different slab geometries in the near-surface gravity field. However, different contributing slab segments are not easily separated, especially at satellite altitude. Our results demonstrate that future studies addressing the lithospheric structure of the Alps should have to account for the subducting slabs in order to provide a meaningful representation of the geodynamic complex Alpine area.

Altitude dependence of geomagnetic external fields using Swarm and ground observatories data

<p>The separation of different sources  in the geomagnetic field signal measured at satellite altitude is still an open issue. One approach to tackle this problem may be non-parametric statistical methods, such as the Principal Component Analysis (PCA). Here, PCA is applied to Virtual Observatories (VO) geomagnetic time series, computed from an enlarged Swarm dataset  covering all local times and geomagnetic activity levels, from January 2014 to December 2019. For each 30-days time window, an Equivalent Source Dipole mathematical model is fitted to the data to reduce a cloud of satellite data points inside a cylinder to one single 'observation' at its axis and 500 km altitude. A VO mesh is constructed with 3394 VOs, with 2 degrees radius each and 3.5 degrees apart in latitude. We study the distribution of satellite data among the cylinders to test if any spatial or temporal sampling asymmetries can be present in the VO dataset and propagate to the PCA results. We also compare observed time series at ground level with VO time series at satellite altitude for the same latitude and longitude. After subtracting a main field model to both series, comparison of the residuals can give further insight on the dependence of external fields with altitude, with a 30-day time resolution.</p>

Validation of calibrated GOCE gravity gradients GRD_SPW_2 by least-squares spectral weighting

<p>The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first mission which carried a novel instrument, gradiometer, which allowed to measure the second-order directional derivatives of the gravitational potential or gravitational gradients with uniform quality and a near-global coverage. More than three years of the outstanding measurements resulted in two levels of data products (Level 1b and Level 2), six releases of global gravitational models (GGMs), and several grids of gravitational gradients (see, e.g., ESA-funded GOCE+ GeoExplore project or Space-wise GOCE products). The grids of gravitational gradients represent a step between gravitational gradients measured directly along the GOCE orbit and data directly from GGMs. One could use grids of gravitational gradients for geodetic as well as for geophysical applications. In this contribution, we are going to validate the official Level 2 product GRD_SPW_2 by terrestrial gravity disturbances and GNSS/levelling over two test areas located in Europe, namely in Norway and former Czechoslovakia (now Czechia and Slovakia). GRD_SPW_2 product contains all six gravity gradients at satellite altitude from the space-wise approach computed only from GOCE data for the available time span (r-2, r-4, and r-5) and provided on a 0.2 degree grid. A mathematical model based on a least-squares spectral weighting will be developed and the corresponding spectral weights will be presented for the validation of gravitational gradients grids. This model allows us to continue downward gravitational gradients grids to an irregular topographic surface (not to a mean sphere) and transform them into gravity disturbances and/or geoidal heights in one step. Before we compared results obtained by spectral downward continuation, we had to remove the high-frequency part of the gravitational signal from terrestrial data because in gravitational gradients measured at GOCE satellite altitude is attenuated. To do so we employ EGM2008 up to d/o 2160 and the residual terrain model correction (RTC) has been a) interpolated from ERTM2160 gravity model, b) synthesised from dV_ELL_Earth2014_5480_plusGRS80, c) calculated from a residual topographic model by forward modelling in the space domain.  </p>

Estimation of gravitational curvature through a deterministic approach and spectral combination of space-borne second-order gravitational potential derivatives

SUMMARY Second- and third-order gravitational potential derivatives can be employed for the determination of the medium- and high-frequency parts of the Earth's gravity field. Due to the Gravity field and steady-state Ocean Circulation Explorer mission, second-order derivatives (SOD) in particular, express currently observed functionals of high accuracy and global coverage. Third-order derivatives (TOD), or gravitational curvature data, provide significant gravity field information when applied regionally. The absence of directly observed TOD data underlines the importance of investigating the relationship between SOD and TOD. This paper discusses the combination of simulated SOD in order to obtain TOD at satellite altitude by applying the spectral combination method. For the determination of TOD integral equations are developed that utilize SOD data at satellite altitude, thus extending the well-known Meissl spectral scheme. The performance of the derived mathematical models is investigated numerically for the test area of Himalayas and the Tibet region. Two different TOD computational strategies are examined. First, we define a deterministic approach that recovers TOD data from noise-free simulated SOD data. Results show that retrieved TOD data at satellite level reach an agreement of the level of 1 × 10−17 m−1s−2 when compared with the true TOD data. Secondly, we propose a new mathematical model based on the spectral combination of integral relations and noisy SOD data with Gaussian noise for recovering TOD. Integral estimators of biased and unbiased types are examined in the cases of SOD data at satellite altitude. The used vertical SOD components show differences between the recovered and true vertical TOD components in the order of 1 × 10−17 m−1s−2 in magnitude, proving the vertical–vertical component of SOD as the best for validating purposes.

Application of Spherical Cap Harmonic Analysis on CHAMP satellite data to develop a lithospheric magnetic field model over southern Africa at satellite altitude

We apply a Spherical Cap Harmonic Analysis technique on CHAMP satellite data recorded over southern Africa between 2007.0 and 2009.0 epochs, and develop a Southern African Lithospheric Magnetic Model (SALMM) at satellite altitude. The comparative evaluation of the SALMM with the global model MF7 shows a good agreement in the Y and Z field components that are not much contaminated by external field contributions. We use the Z lithospheric field map to confirm the prominent long-wavelength anomalies over the southern African region and its surrounding ocean areas, discussing the underlying geological and tectonic structures of the identified crustal anomalies.