Analytical way is given to determine the error (Q or q) of the sample medians for arbitrary (i.e., also for very small) sample sizes. The also presented Monte Carlo solution is computer time consuming but valid for whatever estimates, too, e.q., for the most frequent values.
In this study we interpret the magnetic anomalies at satellite altitude over a part of Europe and the Pannonian Basin. These anomalies are derived from the total magnetic measurements from the CHAMP satellite. The anomalies are reduced to an elevation of 324 km. An inversion method is used to interpret the total magnetic anomalies over the Pannonian Basin. A three dimensional triangular model is used in the inversion. Two parameter distributions, Laplacian and Gaussian are investigated. The regularized inversion is numerically calculated with the Simplex and Simulated Annealing methods and the anomalous source is located in the upper crust. A probable source of the magnetization is due to the exsolution of the hematite-ilmenite minerals.
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.
Wireline logging surveys are routinely used for the reconnaissance and quantitative characterization of multi-mineral hydrocarbon structures. The interpretation of well-logging data, however, is quite a challenging task, because the conventionally used local inversion procedure becomes either an underdetermined or a slightly overdetermined problem that may result in poor parameter estimation. In order to determine the petrophysical model composed of several parameters, such as specific volumes of matrix components, water saturation, primary and secondary porosity and numerous zone-parameters, in a more reliable way a new inversion methodology is required. We suggest a joint inversion technique for the estimation of model parameters of multi-mineral rocks that inverts data acquired from a larger depth interval (hydrocarbon zone). The inverse problem is formulated assuming homogeneous intervals within the zone to get a highly overdetermined inversion procedure. The interval inversion method has been applied to shaly sandy hydrocarbon reservoirs, in this study, that is used for the estimation of petrophysical parameters of complex reservoirs. Numerical results with synthetic and field data demonstrate the feasibility of the inversion method in investigating carbonate and metamorphic structures.
This paper presents the principles of a new inversion method used for the determination of 3D geological structures. The horizontal variations of the layer parameters i.e. layer thicknesses and resistivities are discretized in the form of series expansion. The unknown coefficients of the series expansion are determined by an iterative linearized inversion method using weights specified by the Most Frequent Value Method (MFV). The result of the inversion is estimated from the data of the bi-directional VES (Vertical Electric Sounding) measurements with Schlumberger array in each profile and in multiple profiles. A 3D Finite Difference method was applied to forward modelling, however, the structure is approximated along the profile with a 2D model discretized by single-variable series expansion. The 3D forward modeling procedure gives the opportunity to calculate data measured in two or multiple directions. The suggested interpretation method gives an approximate solution. Proceeding more accurate 3D inversion will be provided by the binary series expansion.
Mars Orbiter Laser Altimeter (MOLA) team discovered “the striking difference” in elevation between northern and southern hemispheres: “on Mars, the South Pole lying about six km higher than the North Pole, … the planet’s center of mass (is) 3 km north of its geometric center” (Physics Today, Oct 1999, p. 34). The same topography we have for solid Earth: low Arctic and high Antarctic with the same difference 5–7 km. No sound explanation of NS asymmetry was proposed: impact, planetary evolution, mantle convection … are rather artificial and vague. Meanwhile, NS asymmetry is inherent property of any freely rotating flexible celestial body as it follows from Kozyrev’s Causal or asymmetrical mechanics. Relations of Causal mechanics are supported by experimental study of vertical component of causal force by weight change measurement of rotated gyroscope and the study of its horizontal component by pendulum deflection measurement. Kozyrev made measurements at latitudes φ from 45° to 84° and proved that causal force is directed along Earth rotation axis: to the North for φ < 73° and to South for φ > 73°. The magnitude of causal force has order (1–5) × 10−5 of gravity force.
In this study we introduce new rock physical models which describe the pressure dependence of seismic velocity and quality factor. The models are based on the idea (accepted in the literature) that microcracks in rocks are opened and closed under the change of pressure. The models were applied to acoustic P wave velocity data measured on core samples originated from oil-drilling wells (27 samples) and also seismic velocity and quality factor data sets published in international literature. During the measurements the pulse transmission and the spectral ratio techniques were used. Measurements were carried out at various incremental pressures and parameters of the models were determined by linearized inversion methods. The calculated data matched accurately with measured data proving that the new rock physical models apply well in practice.
In the community of geodesy it is well-known that the famous normal distribution is originated from the mathematical analysis of observational errors in astronomical and geodetic measurements.However, as far as we know this aspect of scientific history which is of considerable interest for the community of earth sciences has rarely been considered in the literature of earth sciences.In geodesy and related areas the bivariate normal distribution is one of the most frequently used probability distributions. Nowadays, in a wide range of problems arising from diverse areas of geodesy, geophysics, photogrammetry and astronomical geodesy we encounter numerous applications of the univariate and multivariate normal distributions.In the present paper the historical role of earth sciences in the origins of the bivariate normal distribution is briefly discussed. Some new evidences of Bravais’ contribution to the origin of the correlated bivariate normal distribution are considered. The new evidences and refinements established in this paper convey such a general methodological and intellectual content that is useful for the community of geodesy, geophysics, and furthermore in earth sciences.
This paper presents a new algorithm for the inversion-based 1D Fourier transformation. The continuous Fourier spectra are assumed as a series expansion with the scaled Hermite functions as square-integrable set of basis functions. The expansion coefficients are determined by solving an over-determined inverse problem. In order to define a quick and easy-to-use formula in calculating the Jacobi matrix of the problem a special feature of the Hermite functions are used. It is well-known, that the basic Hermite functions are eigenfunctions of the Fourier transformation. This feature is generalized by extending its validity for the scaled Hermite functions. Using the eigenvalues, given by this generalization, a very simple formula can be derived for the Jacobi matrix of the problem resulting in a quick and more accurate inversion-based Fourier transform algorithm. The new procedure is numerically tested by using synthetic data.
The multifractal analysis is applied to the study of geomechanical monitoring time series. Estimation of singularity spectra parameters within moving time window for this monitoring time series provides a possibility for splitting the history of observations into few adjacent fragments which could reflect e.g. hidden different states of the rock massif in the vicinity of measuring station. In this contribution, analysis of time series of measured distances is presented. A laser distance meter is used for measuring the height of a large chamber in the medieval Jeroným Mine (Czech Republic). This time series separation into individual segments using singularity spectra parameters is important for possible comprehensive analysis of data in individual time periods and/or between individual time periods.
The results of model calculation (direct problem solutions above model parameter space) determine an embedded continuous and differentiable surface in the Euclidean space of measurements. This multidimensional subspace contains the possible expected values of measurement vectors according to the assumed rock model as a projection of measurement points (expressing the model and real rock equivalences). The model parameters are the natural coordinates of this subspace, determining a contravariant curvilinear coordinate system (“flat world” for the inversion). The local curvature of this surface is very important factor of covariance matrices and the possible bias of estimated parameters. In this article the role of curvature is discussed and the shortage of conventional (first order) inversion is demonstrated by simple example and the possibility of bias correction.
The paper discusses the characteristics and feasibility of a multilayer kinematic refraction inversion method that is applicable to estimate the — even laterally changing — parameters of a geological model in the simultaneous evaluation of refraction data. The studied method has been developed at the Department of Geophysics of the University of Miskolc for the interpretation of parameters (layer thicknesses and seismic velocities) using series expansion based on adequately chosen basis functions. Besides revealing its resolution properties, ambiguity studies are also presented on synthetic data sets. In the terminology of refraction inversion uncertain and ambiguous results are frequently encountered problems in multilayer cases when all parameters (or all coefficients describing the parameters) are estimated simultaneously in the same inversion procedure. Results of resolution and ambiguity analyses of synthetic data sets and field examples are shown in this study.
This paper introduces the alternating conditional expectation (ACE) algorithm of Breiman and Friedman (1985) in multiple regression problems in groundwater monitoring data analysis. This special inverse nonparametric approach can be applied easily for estimating the optimal transformations of different groundwater monitoring data from the Bükk Mountains to obtain maximum correlation between observed aquifer variables. The approach does not require a priori assumptions of a mathematical form, and the optimal transformations are derived solely based on the groundwater data set. The advantages and applicability of the proposed approach to solve different multiple regression problems in hydrogeology or in groundwater management are illustrated by means of case studies from a Hungarian karst aquifer. It is demonstrated that the ACE method has certain advantages in some fitting problems of groundwater science over the traditional multiple regression. In the past, different groundwater monitoring data (like groundwater level, ground-water temperature and conductance, etc.) had been used for groundwater management purposes in the Bükk Mountains. One of the difficulties in earlier approaches has been the need to make some kind of assumption of the expected mathematical forms among the investigated reservoir and petrophysical variables. By using non-parametric regression, the need to assume a specific form of model is avoided, and a clearer vision of the relationships between aquifer parameters can be revealed in the Bükk Mountains, where karst water is the main source of potable water supply. Complex monitoring data from the Bükk Mountains were analyzed using the ACE inverse method, and results were verified successfully against quantitative and qualitative field observations.
All the elements of the Eötvös tensor can be measured by torsion balance, except the vertical gradient. The knowledge of the real value of the vertical gradient is more and more important in gravimetry and geodesy.Determination of the 3D gravity potential W(x, y, z) can be produced by inversion reconstruction based on each of the gravity data Wz (= g) measured by gravimeters and gravity gradients Wzx, Wzy, WΔ, Wxy measured by torsion balance. Besides vertical gradients Wzz measured directly by gravimeters have to be used as reference values at some points. First derivatives of the potential Wx, Wy (can be derived from the components of deflection of the vertical) may be useful for the joint inversion, too. Determination of the potential function has a great importance, because all components of the gravity vector and the elements of the full Eötvös tensor can be derived from it as the first and the second derivatives of this function. The second derivatives of the potential function give the elements of the full Eötvöstensor including the vertical gradients, and all these elements can be determined not only in the torsion balance stations, but anywhere in the surroundings of these points.Test computations were performed at the characteristic region of a Hungarian plate area at the south part of the Csepel Island where torsion balance and vertical gradient measurements are available. There were about 30 torsion balance, 21 gravity and 27 vertical gradient measurements in our test area. Only a part of the 27 vertical gradient values was used as initial data for the inversion and the remaining part of these points were used for controlling the computation.
The Earth topographic masses are compensated by an isostatic adjustment. According to the isostatic hypothesis a mountain is compensated by mass deficiency beneath it, where the crust is floating on the viscous mantle. For study of the impact of the compensating mass on the topographic mass a crustal thickness (Moho boundary) model is needed. A new gravimetric-isostatic model to estimate the Moho depth, Vening Meinesz-Moritz model, and two well-known Moho models (CRUST2.0 and Airy-Heiskanen) are used in this study. All topographic masses cannot be compensated by simple isostatic assumption then other compensation mechanism should be considered. In fact small topographic masses can be supported by elasticity of the larger masses and deeper Earth’s layers. We discuss this issue applying spatial and spectral analyses in this study. Here we are going to investigate influence of the crustal thickness and its density in compensating the topographic potential. This study shows that the compensating potential is larger than the topographic potential in low-frequencies vs. in high-frequencies which are smaller. The study also illustrates that the Vening Meinesz-Moritz model compensates the topographic potential better than other models, which is more suitable for interpolation of the gravity field in comparison with two other models. In this study, two methods are presented to determine the percentage of the compensation of the topographic potential by the isostatic model. Numerical studies show that about 75% and 57% of the topographic potentials are compensated by the potential beneath it in Iran and Tibet. In addition, correlation analysis shows that there is linear relation between the topographic above the sea level and underlying topographic masses in the low-frequencies in the crustal models. Our investigation shows that about 580±7.4 metre (in average) of the topographic heights are not compensated by variable the crustal root and density.
This paper illustrates the application of multidisciplinary data analysis to the Carpathian-Pannonian Region and on the basis of geodetical data presents verification of a tectonic model of the Carpathian-Pannonian lithosphere with impact on the possible risk and activity of the geodynamic and kinematical zones in consequence of the post-subduction processes. This approach and analyses can be used for the analyses any Carpathian area from the point of view of the recent movements tendencies.All available mentioned geodata were verified and unified on the basis of the same scale and in the Western Carpathians on the remote sensing data, too.Independent GPS epoch-wise observing campaigns took place in several regions and the whole territory is now covered by tens of permanent stations. The long-term observational series from permanent stations generally yield reliable site velocities, however, distribution of such stations is not dense enough to provide velocity field with sufficient resolution all over the monitored region.In the paper we also shortly describe velocity fields available from various national and regional GPS geo-kinematics projects. The heterogeneous velocity fields have been homogenized and used for construction of the intraplate GPS velocities in Central and South-East Europe and their interpretation, focusing on the chosen active zone. As one of most important we consider — so called — “rebounding area” in East Carpathians. The proposed interpretation and solution enable to consider new view on the Pliocene to recent period.
In connection with the EURISGIC WP2 project the authors present those procedures which have been used to construct a map in cells on the electrical resistivity distribution in Europe at least till to the asthenosphere. The data are based on the deep magnetotelluric soundings published in the international literature. This map is the basis of the calculation of the induction risk endangering the electric network and communication systems.
Soft computing techniques are widely used for the applications on most of the nonlinear problems related to the real world. Earth’s most of the nonlinear characteristics exhibit the uncertainty problem that has to be interpreted with most of the advanced soft computing tools. Here the three layer electrical resistivity data has taken for interpreting the subsurface parameters of the earth using Adaptive Neuro-Fuzzy inference (ANFIS) technique. ANFIS can be predictably used for most of the nonlinear problems. Its membership functions and rules with adjustable parameters will help the interpretation technique with less error percentage results. In the present study, the program is specially designed for the interpretation of three layer electrical resistivity data. The network model is successful in training with large number of data sets available. Interpretation using ANFIS technique will give the promising results with good accuracy. With much less error percentage, the program supports all types of three layer electrical resistivity data more than a conventional method can do. Typical problems with parameter estimation can be done more efficiently with this ANFIS program.
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.
