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This paper presents a new approach for precision estimation for algebraic ellipse fitting based on combined least squares method. Our approach is based on coordinate description of the ellipse geometry to determine the error distances of the fitting method. Since it is an effective fitting algorithm the well-known Direct Ellipse Fitting method was selected as an algebraic method for precision estimation. Once an ellipse fitted to the given data points, algebraic distance residuals for each data point and fitting accuracy can be computed. Generally, the adopted approach has revealed geometrical aspect of precision estimation for algebraic ellipse fitting. The experimental results revealed that our approach might be a good choice for precision estimation of the ellipse fitting method.

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Probabilistic seismic hazard assessment of Albania
Authors: A. Fundo, Duni Ll, Sh Kuka, E. Begu and N. Kuka

A new probabilistic seismic hazard assessment for Albania is carried out using the smoothed gridded seismicity approach. Albania’s earthquake catalogue is already revised and expanded, covering a study area limited by 38 − 44.5°N Latitude and 18 − 24°E Longitude, and the time period from 58BC to 31/12/2008. The ground motion hazard map is presented over a 10 km grid in terms of peak ground acceleration for 10% probability of exceedance in 50 years, corresponding to 475-year return period. The reference site condition is firm rock, defined as having an average shear-wave velocity in the upper 30 m of the crust of 800 m/sec. It is the standard reference site condition used by the European seismic code (Eurocode 8) for seismic zonation and building codes. The main finding is that if this map is accepted as a reference indicator to establish a new regulatory national seismic zonation, design acceleration will be much higher than that applied in the current regulation. This implies that the competent authorities should take into consideration the obtained results to improve the existing design code in a more reliable and realistic basis in order to increase the safety level of constructions in the country.

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Quality description for gravimetric and seismic moho models of fennoscandia through a combined adjustment
Authors: M. Eshagh and M. Bagherbandi

The gravimetric model of the Moho discontinuity is usually derived based on isostatic adjustment theories considering floating crust on the viscous mantle. In computation of such a model some a priori information about the density contrast between the crust and mantle and the mean Moho depth are required. Due to our poor knowledge about them they are assumed unrealistically constant. In this paper, our idea is to improve a computed gravimetric Moho model, by the Vening Meinesz-Moritz theory, using the seismic model in Fennoscandia and estimate the error of each model through a combined adjustment with variance component estimation process. Corrective surfaces of bi-linear, bi-quadratic, bi-cubic and multi-quadric radial based function are used to model the discrepancies between the models and estimating the errors of the models. Numerical studies show that in the case of using the bi-linear surface negative variance components were come out, the bi-quadratic can model the difference better and delivers errors of 2.7 km and 1.5 km for the gravimetric and seismic models, respectively. These errors are 2.1 km and 1.6 km in the case of using the bi-cubic surface and 1 km and 1.5 km when the multi-quadric radial base function is used. The combined gravimetric models will be computed based on the estimated errors and each corrective surface.

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The laws of nature in general, and the relations and laws in geodesy in particular can be expressed in most cases by nonlinear equations which are in general solved by transforming them to linear form and applying iteration. The process of bringing the equations to linear form implies neglections and approximation. In certain cases it is possible to obtain exact, correct solutions for nonlinear problems. In the present work we introduce parameters into the rotation matrix, and using this we derive solutions for the 2D and 3D similarity transformations. This method involves no iteration, and it does not require the transformation of the equations to linear form. The scale parameter is determined in both cases by solving a polynomial equation of second degree. This solution is already known, but our derivation is worth consideration because of its simple nature.

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Some remarks on linear least squares fits with errors in both coordinates
Author: L. Bányai

The exact least squares line fit with errors in both coordinates (Reed 1992) is investigated together with the approximate solution based on the formalism of the linear Gauss-Helmert model or the unified adjustment approach of the classical textbook by Mikhail (1976). The similarities and the differences are described in details. In spite of the small differences the exact solution is preferable and the calculations are simpler.This paper does not deal with the errors-in-variables (EIV) models solved by the total least squares (TLS) principle, since the exact line fit solution is used to validate this general approach, which is basically designed to solve more sophisticated nonlinear tasks.In the most general case the fit of Person’s data with York’s weights is iteratively solved starting with the arbitrary zero initial value of the slope. The test computation with different but systematically chosen weights proved that in special cases — e.g. the weighted least squares sum of the distances between the data points and the estimated line is minimised — there is no need for iterations at all.It is shown that methods described by Detrekői (1991) and Závoti (2012) are special cases of the general exact solutions.Reed (1992) derived the variances of the slope and intercept parameters without their covariance. The simple linear estimation of variance-covariance matrix of the exact solution is also demonstrated. The importance of the stochastic models coupled with exact solution is also demonstrated.

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Comparative deformation analysis for Abu Dabbab area, Egypt
Authors: A-M. Mohamed, M. Becker and M. Saleh

Abu-Dabbab area is characterized by high seismicity and complex tectonic setting, for these facts, a local geodetic network consisting of eleven geodetic benchmarks has been established. The crustal deformation data in this area are collected using the GPS techniques. Five campaigns of GPS measurements have been collected, processed and adjusted to get the more accurate positions of the GPS stations. The horizontal velocity vectors, the dilatational, the maximum shear strains and the principal strain rates were estimated. The magnitude of the movements is distributed inhomogeneous over the area and it varies in average between 3 and 6 mm/yr. The results of the deformation analyses indicate a significant contraction and extension across the southern central part of the study area which is characterized by high seismic activity represented by the clustering shape of the microearthquakes that trending NE-SW direction. The north and north-eastern parts are characterized by small strain rates. This study is an attempt to provide valuable information about the present state of the crustal deformation and its relationship to seismic activity and tectonic setting at Abu-Dabbab area.

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In the region of the Carpathian-Pannonian Basin (44–50N; 13–28E) 81 earthquakes have moment magnitude (M w); 61 of them are crustal events (focal depth <65 km) while 20 earthquakes belong to the intermediate focal depth region of the Vrancea (Romania) zone. For crustal events the regression of moment magnitude (M w) on local magnitude (M l) shows a better fit for large magnitudes using a second order equation against to a linear relationship, and the actual quadratic formula based on 61 events is the following: \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\begin{gathered} M_w = 1.37( \pm 0.28) + 0.39( \pm 0.18)M_l + 0.061( \pm 0.026)M_l^2 \hfill \\ (M_w :1.9 - 5.5;M_l :1.4 - 5.5). \hfill \\ \end{gathered}$ \end{document}.In the intermediate focal depth Vrancea zone of the south-eastern bend of the Carpathians (44.5–46.5N; 25.5–28.0E) the number of body wave magnitudes is the largest one (20) among the local (8), the surface wave (14) and the duration (17) magnitudes. The linear relationship between the moment (M w) and the body wave (M b) magnitudes has the following form: \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $M_w = 1.20( \pm 0.08)M_b - 0.76( \pm 0.40)(M_w :4.1 - 7.7;M_b :3.8 - 7.3).$ \end{document}.The relationships of the different (M l, M s, M b, M d) magnitudes are also presented in the paper.

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The new fundamental gravimetric network of Slovenia
Authors: B. Koler, K. Medved and M. Kuhar

The paper presents all stages of the development and processing of the fundamental gravimetric network of Slovenia, which consists of a zero order network, which has six absolute gravity stations, and twenty nine first order gravimetric stations. Descriptions are given of the design of the network, the geological assessment of the gravimetric stations, the gravity survey of the first order network, and the post-processing and adjustment of the gravimetric observations, which was performed in two stages. First the observations in the zero order network were adjusted as a free network, and then a standard adjustment of the first order network was performed. Finally, the adjusted gravity values at the stations were analysed against the Potsdam system, which was the basis of all previous gravimetric calculations in Slovenia. In the analyses an equation for the transformation of gravity values between the Potsdam system and the IGSN71 system (International Gravity Standardization Network 1971) has been derived.

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One-dimensional P-wave velocity model for the territory of Hungary from local earthquake data
Authors: Z. Gráczer and Z. Wéber

We determined a new one-dimensional P-wave velocity model for the territory of Hungary based on the first arrival times of local earthquakes. During the computations 910 P-wave arrival data of 86 events from the time period between 1985 and 2010 have been used. The applied methodology is a combination of a genetic algorithm based procedure and an iterative linearized joint inversion technique. The preferred velocity profile has been chosen from the best models based on the data of a series of controlled explosions.The resulting flat-layered model consists of three crustal layers and a half-space representing the uppermost mantle. The crustal compressional velocities vary in the range of 5.3-6.3 km/s, while the uppermost mantle velocity was found to be 7.9 km/s. The Moho is located at an average depth of 26 km.Additionally, the V p/V s ratio was calculated by the Wadati-method, which gave a value of 1.74±0.05.

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Treating the Fourier transform as an over-determined inverse problem is a new conception for determining the frequency spectrum of a signal. The concept enables us to implement several algorithms depending on the applied inversion tool. One of these algorithms is the Hermit polynomial based Least Squares Fourier Transform (H-LSQ-FT). The H-LSQ-FT is suitable for reducing the influence of random noise. The aim of the investigation presented in the paper was to study the noise reduction capability of the H-LSQ-FT in some circumstances. Four wavelet-like signals with different properties were selected for testing the method. Examinations were completed on noiseless and noisy signals. The H-LSQ-FT provided the best noise reduction for the noisy signal having low peak frequency and wide band width. Finally, the results obtained by the H-LSQ-FT were compared to those of other traditional methods. It is showed that the H-LSQ-FT yields better noise filtering than these methods do.

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