Pavol Zahorec

Role of Near Topography and Building Effects in Vertical Gravity Gradients Approximation

Importance of precise vertical gradient of gravity (VGG) determination by means of relative gravity measurements is mainly connected with absolute gravity measurements and setting of global and local gravity reference networks. The gravitational effect of the topography and near building structures and their contribution on the vertical gradient of gravity (VGG) was studied. A strong impact of near topography on the VGG values was found in the case of the mountainous areas - deviations up to 88 percent of normal value were obtained by means of relative gravity measurements. Near building structures gravitational effect was estimated by means of simple polyhedrons - very specific nonlinear behaviour of VGG is demonstrated on two model examples. Synthetic tests for the estimation of determined VGG precision are also presented. The error of polynomial estimation of the VGG can be several times higher than the error within measured gravity. For a set of 29 real measurement points a relatively good coincidence between the measured and calculated VGG values was achieved. Application of predicted values of the VGG instead of the normal ones in cases of unknown actual values can lead to a quality improvement of gravimetric reference networks, as well as prospecting VGG measurements.

Inner zone terrain correction calculation using interpolated heights

Abstract The discrepancy between real heights of gravity points and the elevation model has a significant impact on the terrain corrections calculation especially within the inner zone. The concept of interpolated heights of calculation points used instead of measured ones within the specified inner zone can considerably decrease the resulting errors. The choice of appropriate radius of the inner zone for use of interpolated heights is analysed on synthetic topography model as well as real data. The tests with synthetic models showed the appropriate radius of this zone is proportional to the deformation wavelength of the model. Simple statistical analysis of a particular elevation model can give an estimate of the appropriate radius for the calculation using interpolated heights. A concept with interpolated heights in the zone 0–250 m is used in actual practice in Slovakia. The analysis of regional gravity data from the Tatry Mountains test area indicates the searched radius should be about 100 m. Detailed gravity measurements from different areas showed the searched radius does not play so important role but the use of interpolated heights instead of measured ones is still relevant. The more reasonable method instead of using interpolated heights is also presented when calculating the topographic effect.

The role of near topography and building effects in vertical gravity gradients approximation

The gravitational effect of the topography and near-building structures and their contribution on the vertical gradient of gravity (VGG) was studied. The strong impact of near topography on the VGG values was found in the case of the mountainous areas – deviations of up to 88% of normal value were obtained by means of relative gravity measurements in selected parts of Slovakia. Newly developed software and a high-quality detailed digital terrain model of Slovakia was used for the evaluation of the topographical effect. The gravitational effect of near-building structures was estimated by means of simple 3D bodies approximation, i.e., rectangular or polygonal prisms. A very specific non-linear behaviour of VGG is demonstrated on model examples. A relatively good agreement between the measured and calculated (predicted) VGG values was achieved for a set of selected 32 real measurement points. The application of estimated (predicted) values of the VGG instead of the normal ones can lead to a quality improvement of global and local gravimetric reference networks, as well as prospecting VGG measurements.

The estimation of errors in calculated terrain corrections in the Tatra Mountains

The estimation of errors in calculated terrain corrections in the Tatra Mountains In general, calculation of terrain corrections can be a substantial source of errors in evaluating Bouguer anomalies, especially in rugged mountainous areas like the Tatra Mountains where we also get the largest values of the terrain corrections as such. It is then natural that analysis of their calculations in this area can shed light on the magnitude of correction-related errors within the whole Slovak territory. In the framework of our analysis we have estimated the effect of different computing approaches as well as the influence of accuracy of the inputs, i.e. the heights and positions of the measuring points, together with the used digital terrain models. For the sake of testing the computer programs which are currently in use, we have also substituted the real terrain by synthetic topography. We found that among the concerned constituents the most important factor is the used digital terrain model and its accuracy. The possible model-caused errors can exceed 10 mGal in the Tatra Mountains (for the density of 2.67 g.cm-3).

Some Remarks on the Early History of the Bouguer Anomaly

When discussing the various aspects of the Bouguer anomaly calculation in the past we came across numerous discrepancies in its definition expressed either in textbooks (sometimes even including modern texts) or in not less than 10 important articles and discussions which have been published within the last 25 years. Therefore we continued in investigating in more detail to determine how and when some of the key notions involved, as well as the used terminology, came into existence. For instance, one can find that the term “Bouguer reduction” is most likely accreditable to Helmert. This term was used in the context of the then popular geodetic concept of reducing gravity from the Earth surface to the sea level, although Bouguer himself had never reduced gravity values or pendulum lengths in such a manner. Another well-known procedure, namely the “free-air reduction” which was sometimes called “Faye reduction,” had in fact very little to do with Faye himself, as can be deduced from Faye’s original memoirs. However, we confirm that the foundations of the so-called “Bouguer anomaly” and the procedures applied to the measured gravity which are required by the gravity method of applied geophysics can be well tracked back to originate from the famous book of Pierre Bouguer published in 1749. Among others we call attention especially to one specific historical artefact, namely the misunderstanding associated with the gravity data reductions to the sea level in applied geophysics which, although geophysically unacceptable, has withstood the ravages of time and can be found in the literature even in the 21th century, as we illustrate in this contribution.

Chapter 7 – National Gravimetric Database of the Slovak Republic

Compilation of the Slovak gravimetric database with the actual amount of about 320,000 observation points is presented. Gravity data were collected during more than 50 years, which yields a very heterogeneous dataset, with large variations in the station coverage and processing methods. The regional gravimetric database (more than 212,000 points) was resumed in 2001. The compilation discussed herein (with more than 107,000 detailed gravity measurements) was made during 2011–14. Quality-control process and complete recalculation of the Bouguer anomalies is presented. Primary focus of this project was on a proper recalculation of the terrain corrections. New detected linear features in the Bouguer anomaly map were verified by the field measurements. A new software solution for reconstruction of the gravity acceleration values from the Bouguer anomaly map was developed for geodetic applications.

Comparison of Different Approaches to Gravity Determination and Their Utilization for Calculation of Geopotential Numbers in the Slovak National Levelling Network

Vertical reference system in the Slovak Republic is realized by the first and second order of the National levelling network with the normal heights according to Molodenski. The reference heights are still calculated by the traditional method using the components of gravity correction. Nowadays we are preparing a new realization of the height system which will be based on geopotential numbers. But there is a problem with the absence of the measured gravity values. Only at approximately 8% of levelling points we have the measured values of gravity. Therefore, we are trying to find the most reliable method for estimation of the gravity values and use them subsequently for determination of the geopotential numbers. The aim of this study is to analyze the different ways to the gravity determination and their application for calculation of the geopotential numbers on the points of the National levelling network. The first method is based on the reconstruction of the gravity on levelling points from the interpolated values of the complete Bouguer anomaly using the proprietary software. The second method is based on the modern global geopotential models improved by the residual terrain model approach. Calculated gravity was compared with directly measured gravity. The set of the points contained all geodetic control points within Slovakia where the gravity has been measured. Then, the calculated value of gravity was used to determine the geopotential numbers and normal heights according to Molodenski in the first order levelling lines of the National levelling network which connect the reference points determined within EVRF2007 adjustment for area of Slovakia.

High resolution Slovak Bouguer gravity anomaly map and its enhanced derivative transformations: new possibilities for interpretation of anomalous gravity fields

Abstract The paper deals with the revision and enrichment of the present gravimetric database of the Slovak Republic. The output of this process is a new version of the complete Bouguer anomaly (CBA) field on our territory. Thanks to the taking into account of more accurate terrain corrections, this field has significantly higher quality and higher resolution capabilities. The excellent features of this map will allow us to re-evaluate and improve the qualitative interpretation of the gravity field when researching the structural and tectonic geology of the Western Carpathian lithosphere. In the contribution we also analyse the field of the new CBA based on the properties of various transformed fields – in particular the horizontal gradient, which by its local maximums defines important density boundaries in the lateral direction. All original and new transformed maps make a significant contribution to improving the geological interpretation of the CBA field. Except for the horizontal gradient field, we are also interested in a new special transformation of TDXAS, which excellently separates various detected anomalies of gravity field and improves their lateral delimitation.

Prediction of vertical gradient of gravity and its significance for volcano monitoring – example from Teide volcano

Abstract We present a detailed calculation of the topographic contribution to the vertical gradient of gravity (VGG) based on high-resolution digital elevation model (DEM) and new developed software (Toposk) for the purpose of predicting the actual VGGs in the field. The calculations presented here were performed for the Central Volcanic Complex (CVC) of Tenerife. We aimed at identifying the most extreme VGGs within the CVC, as well as predicting the VGGs at benchmarks of the former microgravity/deformation network set up to monitor the 2004/5 unrest. We have carried out an observational campaign in June 2016 to verify the predicted VGG values, both the extreme ones and those at the benchmarks. The comparison between the predicted and the in-situ verified VGGs is presented here. We demonstrate the sensitivity of the VGG prediction to the choice of the topo-rock density, which is inherent to the volcanic areas with high variability of rock densities. We illustrate the significance of the use of actual VGG in volcano monitoring microgravimetric surveys on a couple of benchmarks of the CVC network.

An analysis of methods for gravity determination and their utilization for the calculation of geopotential numbers in the Slovak national levelling network

Abstract The vertical reference system in the Slovak Republic is realized by the National Levelling Network (NLN). The normal heights according to Molodensky have been introduced as reference heights in the NLN in 1957. Since then, the gravity correction, which is necessary to determine the reference heights in the NLN, has been obtained by an interpolation either from the simple or complete Bouguer anomalies. We refer to this method as the “original”. Currently, the method based on geopotential numbers is the preferred way to unify the European levelling networks. The core of this article is an analysis of different ways to the gravity determination and their application for the calculation of geopotential numbers at the points of the NLN. The first method is based on the calculation of gravity at levelling points from the interpolated values of the complete Bouguer anomaly using the CBA2G_SK software. The second method is based on the global geopotential model EGM2008 improved by the Residual Terrain Model (RTM) approach. The calculated gravity is used to determine the normal heights according to Molodensky along parts of the levelling lines around the EVRF2007 datum point EH-V. Pitelová (UELN-1905325) and the levelling line of the 2nd order NLN to Kráľova hoľa Mountain (the highest point measured by levelling). The results from our analysis illustrate that the method based on the interpolated value of gravity is a better method for gravity determination when we do not know the measured gravity. It was shown that this method is suitable for the determination of geopotential numbers and reference heights in the Slovak national levelling network at the points in which the gravity is not observed directly. We also demonstrated the necessity of using the precise RTM for the refinement of the results derived solely from the EGM2008.