ALBERT

Description: Robustness analysis in forward modelling gravity data in crustal/lithospheric studies The robustness of the gravimetric forward modelling is investigated by applying the harmonic inversion procedure at the input which is the difference of the calculated and measured surface gravity. The gravity data are taken from two profiles in the Carpathian-Pannonian Basin region. The result of the inversion are density models obtained from the original two-layer models with various horizontal boundary depth and density contrast. The deformation of the originally planar boundary is the measure of the mismatch between calculated and measured data. The calculated deformation has reached up to tens of kilometers and thus the uncertainties in determining the geometry of disturbing bodies by the forward modelling are substantial.

Description: Predicted values of the vertical gradient of gravity (VGG) on benchmarks of Etna’s monitoring system, based on calculation of the topographic contribution to the theoretical free-air gradient, are compared with VGG values observed in situ. The verification campaign indicated that improvements are required when predicting the VGGs at such networks. Our work identified the following factors to be resolved: (a) accuracy of the benchmark position; (b) gravitational effect of buildings and roadside walls adjacent to benchmarks; (c) accuracy of the digital elevation model (DEM) in the proximity of benchmarks. Benchmark positions were refined using precise geodetic methods. The gravitational effects of the benchmark-adjacent walls and buildings were modeled and accounted for in the prediction. New high-resolution DEMs were produced in the innermost zone at some benchmarks based on drone-flown photogrammetry to improve the VGG prediction at those benchmarks. The three described refinements in the VGG prediction improved the match between predicted and in situ observed VGGs at the network considerably. The standard deviation of differences between the measured and predicted VGG values decreased from 36 to 13 μGal/m.

Description: The spherical harmonic representation of the gravitational field quantities generated by the ice density contrastWe derive the expressions for computing the ice density contrast stripping corrections to the topography corrected gravity field quantities by means of the spherical harmonics. The expressions in the spectral representation utilize two types of the spherical functions, namely the spherical height functions and the newly introduced lower-bound ice functions. The spherical height functions describe the global geometry of the upper topographic bound. The spherical lower-bound ice functions combined with the spherical height functions describe the global thickness of the continental ice sheet. The newly derived formulas are utilized in the forward modelling of the gravitational field quantities generated by the ice density contrast. The 30×30 arc-sec global elevation data from GTOPO30 are used to generate the global elevation model (GEM) coefficients. The spatially averaged global elevation data from GTOPO30 and the 2×2 arc-deg ice-thickness data from the CRUST 2.0 global crustal model are used to generate the global lower-bound ice model (GIM) coefficients. The mean value of the ice density contrast 1753 kg/m3(i.e., difference of the reference constant density of the continental upper crust 2670 kg/m3and the density of glacial ice 917 kg/m3) is adopted. The numerical examples are given for the gravitational potential and attraction generated by the ice density contrast computed globally with a low-degree spectral resolution complete to degree and order 90 of the GEM and GIM coefficients.

Description: A mathematical model of the bathymetry-generated external gravitational field The currently available global geopotential models and the global elevation and bathymetry data allow modelling the topography-corrected and bathymetry stripped reference gravity field to a very high spectral resolution (up to degree 2160 of spherical harmonics) using methods for a spherical harmonic analysis and synthesis of the gravity field. When modelling the topography-corrected and crust-density-contrast stripped reference gravity field, additional stripping corrections are applied due to the ice, sediment and other major known density contrasts within the Earth's crust. The currently available data of global crustal density structures have, however, a very low resolution and accuracy. The compilation of the global crust density contrast stripped gravity field is thus limited to a low spectral resolution, typically up to degree 180 of spherical harmonics. In this study we derive the expressions used in forward modelling of the bathymetry-generated gravitational field quantities and the corresponding bathymetric stripping corrections to gravity field quantities by means of the spherical bathymetric (ocean bottom depth) functions. The expressions for the potential and its radial derivative are formulated for the adopted constant (average) ocean saltwater density contrast and for the spherical approximation of the geoid surface. These newly derived expressions are utilized in numerical examples to compute the gravitational potential and attraction generated by the ocean density contrast. The computation is realized globally on a 1 x 1 arc-deg geographical grid at the Earth's surface.

Description: We present a new interpretation of the Kolárovo gravity and magnetic anomalies in the Danube Basin based on an inversion methodology that comprises the following numerical procedures: removal of regional trend, depth-wise separation of signal of sources, approximation of multiple sources by 3D line segments, non-linear inversion based on local corrections resulting in found sources specified as 3D star-convex homogenous bodies and/or 3D contrasting structural contact surfaces. This inversion methodology produces several admissible solutions from the viewpoint of potential field data. These solutions are then studied in terms of their feasibility taking into consideration all available tectono-geological information. By this inversion methodology we interpret here the Kolárovo gravity and magnetic anomalies jointly. Our inversion generates several admissible solutions in terms of the shape, size and location of a basic intrusion into the upper crust, or the shape and depth of the upper/lower crust interface, or an intrusion into the crystalline crust above a rise of the mafic lower crust. Our intrusive bodies lie at depths between 5 and 12 km. Our lower crust elevation rises to 12 km with and 8 km without the accompanying intrusion into the upper crust, respectively. Our solutions are in reasonable agreement with various previous interpretations of the Kolárovo anomaly, but yield a better and more realistic geometrical resolution for the source bodies. These admissible solutions are next discussed in the context of geological and tectonic considerations, mainly in relation to the fault systems.

Description: Results from a detailed gravity survey realized along the planned highway tunnel in the karstic area of Slovak Karst in the eastern Slovakia are presented. Detailed gravity profiles crossed an area of rugged topography, therefore the terrain corrections played a crucial role in the gravity data processing. The airborne laser scanning technique (LiDAR) was used in order to compile a high-resolution digital terrain model (DTM) of the surrounding area and to calculate terrain corrections properly. The difference between the Bouguer anomalies calculated with an available nationwide DTM and those with new LiDAR-based model can be significant in some places as it is presented in the paper. A new method for Bouguer correction density analysis based on surface data is presented. Special underground gravity measurements in the existing nearby railway tunnel were also conducted in order to determine the mean density of the topographic rocks. The Bouguer anomalies were used to interpret lithological contacts and tectonic/karstic discontinuities.

Description: We test here the feasibility of ground-penetrating radar (GPR) and microgravity methods in identifying underground voids, such as cellars, tunnels, abandoned mine-workings, etc., in complex urban conditions. For this purpose, we selected a cellar located under a private lot in a residential quarter of the town of Senec in Western Slovakia, which was discovered by chance when a small sinkhole developed on the yard just two meters away from the house. The size of our survey area was limited 1) by the presence of a technical room built at the back of the yard with a staircase leading to the garden, and 2) by the small width of the lot. Therefore the geophysical survey was carried out only in the backyard of the lot as we were not permitted to measure on neighbouring estates. The results from the GPR measurements obtained by the GSSI SIR-3000 system with 400 MHz antenna were visualized in the form of 2D radargrams with the corresponding transformed velocity model of studied cross-sections. Only the profiles running over the pavement next to the house yielded interpretable data because the local geological situation and the regular watering of the lawn covering prevailingly the backyard caused significant attenuation of the emitted GPR signal. The Bouguer gravity map is dominated by a distinctive negative anomaly indicating the presence of a shallow underground void. The quantitative interpretation by means of Euler deconvolution was utilized to validate the depth of the center and location of the cellar. Comparison with the gravitational effect of the cellar model calculated in the in-house program Polygrav shows a quite good correlation between the modelled and observed fields. Only a part of the aerial extent of the anomaly could be traced by the used geophysical methods due to accessibility issues. Nevertheless, the test cellar was successfully detected and interpreted by both methods, thus confirming their applicability in similar environmental and geotechnical applications, even in complex urban conditions.

Description: We review here the gravitational effects on the temporal (time-lapse) gravity changes induced by the surface deformation (vertical displacements). We focus on two terms, one induced by the displacement of the benchmark (gravity station) in the ambient gravity field, and the other imposed by the attraction of the masses within the topographic deformation rind. The first term, coined often the Free Air Effect (FAE), is the product of the vertical gradient of gravity (VGG) and the vertical displacement of the benchmark. We examine the use of the vertical gradient of normal gravity, typically called the theoretical or normal Free Air Gradient (normal FAG), as a replacement for the true VGG in the FAE, as well as the contribution of the topography to the VGG. We compute a topographic correction to the normal FAG, to offer a better approximation of the VGG, and evaluate its size and shape (spatial behavior) for a volcanic study area selected as the Central Volcanic Complex (CVC) on Tenerife, where this correction reaches 77% of the normal FAG and varies rapidly with terrain. The second term, imposed by the attraction of the vertically displaced topo-masses, referred to here as the Topographic Deformation Effect (TDE) must be computed by numerical evaluation of the Newton volumetric integral. As the effect wanes off quickly with distance, a high resolution DEM is required for its evaluation. In practice this effect is often approximated by the planar or spherical Bouguer deformation effect (BDE). By a synthetic simulation at the CVC of Tenerife we show the difference between the rigorously evaluated TDE and its approximation by the planar BDE. The complete effect, coined here the Deformation Induced Topographic Effect (DITE) is the sum of FAE and TDE. Next we compare by means of synthetic simulations the DITE with two approximations of DITE typically used in practice: one amounting only to the first term in which the VGG is approximated by normal FAG, the other adopting a Bouguer corrected normal FAG (BCFAG).

Description: A global correlation of the step-wise consolidated crust-stripped gravity field quantities with the topography, bathymetry, and the CRUST 2.0 Moho boundaryWe investigate globally the correlation of the step-wise consolidated cruststripped gravity field quantities with the topography, bathymetry, and the Moho boundary. Global correlations are quantified in terms of Pearson's correlation coefficient. The elevation and bathymetry data from the ETOPO5 are used to estimate the correlation of the gravity field quantities with the topography and bathymetry. The 2×2 arc-deg discrete data of the Moho depth from the global crustal model CRUST 2.0 are used to estimate the correlation of the gravity field quantities with the Moho boundary. The results reveal that the topographically corrected gravity field quantities have the highest absolute correlation with the topography. The negative correlation of the topographically corrected gravity disturbances with the topography over the continents reaches -0.97. The ocean, ice and sediment density contrasts stripped and topographically corrected gravity field quantities have the highest correlation with the bathymetry (ocean bottom relief). The correlation of the ocean, ice and sediment density contrasts stripped and topographically corrected gravity disturbances over the oceans reaches 0.93. The consolidated crust-stripped gravity field quantities have the highest absolute correlation with the Moho boundary. In particular, the global correlation of the consolidated crust-stripped gravity disturbances with the Moho boundary is found to be -0.92. Among all the investigated gravity field quantities, the consolidated crust-stripped gravity disturbances are thus the best suited for a refinement of the Moho density interface by means of the gravimetric modeling or inversion.