Lajos Völgyesi

Determination of gravity anomalies from torsion balance measurements

There is a dense network of torsion balance stations in Hungary, covering an area of about 40000 km2. These measurements are a very useful source to study the short wavelength features of the local gravity field, especially below 30 km wave- length. Our aim is thus to use these existing torsion balance data in combination with gravity anomalies. Therefore a method was developed, based on integration of horizontal gravity gradients over finite elements, to predict gravity anomaly differences at all points of the torsion balance network. Test computations were performed in a Hungarian area extending over about 800 km2. There were 248 torsion balance stations and 30 points among them where Δg values were known from measurements in this test area.

Pareto optimality solution of the Gauss-Helmert model

The Pareto optimality method is applied to the parameter estimation of the Gauss-Helmert weighted 2D similarity transformation assuming that there are measurement errors and/or modeling inconsistencies.In some cases of parametric modeling, the residuals to be minimized can be expressed in different forms resulting in different values for the estimated parameters. Sometimes these objectives may compete in the Pareto sense, namely a small change in the parameters can result in an increase in one of the objectives on the one hand, and a decrease of the other objective on the other hand. In this study, the Pareto optimality approach was employed to find the optimal trade-off solution between the conflicting objectives and the results compared to those from ordinary least squares (OLS), total least squares (TLS) techniques and the least geometric mean deviation (LGMD) approach.The results indicate that the Pareto optimality can be considered as their generalization since the Pareto optimal solution produces a set of optimal parameters represented by the Pareto-set containing the solutions of these techniques (error models). From the Pareto-set, a single optimal solution can be selected on the basis of the decision maker’s criteria. The application of Pareto optimality needs nonlinear multi-objective optimization, which can be easily achieved in parallel via hybrid genetic algorithms built-in engineering software systems such as Matlab. A real-word problem is investigated to illustrate the effectiveness of this approach.

Support Vector Machines (SVM)

In statistical learning theory (regression, classification, etc.) there are many regression models, such as algebraic polynomials,

Local gravity field modeling using surface gravity gradient measurements

Almost 100,000 surface gravity gradient measurements exist in Hungary over an area of about 45 000 km2. These measurements are a very useful source to study the short wavelength features of the local gravity field, especially below 30 km wavelength. Our aim is to use these existing gravity gradient data in gravity field modeling together with gravity anomalies. Therefore we predicted gravity anomalies from horizontal gravity gradients using the method of least-squares collocation. The cross-covariance function of gravity gradients and gravity anomalies was estimated over the area and a suitable covariance model was estimated for the prediction. The full covariance matrix would require about 15 GB storage, however, the storage requirement can be reduced to about 300 MB by inspecting the structure of the cross-covariance function. Using sparse linear solvers the computation proved to be manageable, and the prediction of gravity anomalies for the whole area was performed. The results were evaluated at those sites where †g values were known from measurements in the computational area.

Relation between the geological conditions and vertical surface movements in the Pannonian basin

Vertical surface movements can be attributable to two effects in young sedimentary basins (like the Pannonian Basin): compaction of sediments, on the one hand, and structural movements, on the other. The depths of the Quaternary, Lower and Upper Pannonian base were determined from different geological data along the main levelling lines and compared to the vertical surface movements. In spite of uncertainties in geological data, in most of the deep sedimentary regions positive correlation can be found between sediment thickness and subsidence. As a consequence of subsidence, gravity changes should be detected at surface points because the points change their position in the Earths’ gravity field. Calculating the effects of the vertical surface movements, the variation of gravity in general should be about 0.3 μGal/year (1 μGal = l0−8m/s2), but at special places it may reach more than 2 μGal/year in the Pannonian basin.

Combination of GPS/leveling and the gravimetric geoid by using the thin plate spline interpolation technique via finite element method

Abstract The purpose of this paper is to develop an improved local geoid model for Hungary combining GPS and leveling height data with a local gravimetric geoid model, via corrector surface, which accounts for datum inconsistencies, long-wavelength geoid errors and vertical network distortions. The improved model is the so-called GPS-gravimetric geoid, which can be constructed by adding the corrector surface to the original gravimetric geoid. The corrector surface can be represented by means of a Thin Plate Spline Interpolation (TPSI) and finite element solution. In this work 194 GPS/leveling points with a local gravimetric geoid were used to calculate the corrector surface and the combined geoid model. To estimate the realistic error of the solution 110 GPS/ leveling points were used as external control points. Attention is called to the importance of the homogeneous distribution of the GPS/leveling data. The mean accuracy of geoid heights of the used 110 control stations was 1–2 cm after the surface fitting.

Reducing the Measurement Time of the Torsion Balance

The main problem of torsion balance measurements is the long damping time however it is possible to significantly reduce the observation time by modern technology. The damping curve can be precisely determined by CCD sensors as well as computerized data collection and evaluation. The first part of this curve makes it possible at least theoretically to estimate the final position of the arm at rest. A finite element solution of a fluid dynamics model based on Navier–Stokes equations is presented here to solve the problem.

High-Resolution Measurements of Non-Linear Spatial Distribution of Gravity Gradients in Hungary

Linear changing of the gravity gradients between the adjoining network points is an important demand for different interpolation methods in geodesy (e.g. interpolation of the deflection of the vertical, geoid computations, and interpolation of the gravity values or the vertical gradients of gravity). To study the linearity of gravity gradients, torsion balance measurements were made both at the field and in a laboratory: one is at the southern part of the Csepel island, and the other in the Geodynamical Laboratory of Lorand Eotvos Geophysical Institute in the Matyas cave. The results of our investigations show that the linearity of the gravity gradients mainly depends on the given point density and the the geological fine structure of rocks and shallow subsurface density. It seems the given point density of the earlier torsion balance stations may be not enough for some geodetic purposes, moreover the problem could not be solved even applying topographic reduction of gravity gradients.

Approximation with Radial Bases Functions

The radial basis method (RBF) is one of the kernel methods, which can be employed for interpolation as well as approximation of data or functions given by values.

Particle Swarm Optimization

The idea of the Particle Swarm Optimization (PSO) was inspired by the social behavior of big groups of animals, e.g., flocking and schooling patterns of birds and fish as suggested by Russell and Kennedy (1995).