Új direkt és inverz módszerek a nehézségi erőtér szintetikus modellezésében = New forward and inverse methods for the synthetic modelling of the gravity field

A kutatás során azt vizsgáltuk, hogy miképpen lehet olyan lokális/regionális tömegeloszlási modellt létrehozni, amely alkalmas a nehézségi tér tömegvonzási összetevőjének (potenciál, gradiens vektor, Eötvös tenzor) a geodéziai számításokhoz elegendő pontosságú meghatározására. E cél eléréséhez a modellből számítható Newton-féle tömegvonzási hatásnak jól kell illeszkednie a rendelkezésre álló mérési eredményekhez, amely feltétel az ún. inverziós feladat megoldásával teljesíthető. Ennek során egy valamilyen norma szerint (pl. L2) optimális sűrűség eloszlás modell jön létre, amelynek segítségével olyan erőtér paramétereket is analitikusan meghatározhatunk (direkt feladat), amelyeknek mérése esetleg nem is lehetséges. Inverzióra kifejlesztett megoldásainkban a derékszögű hasáb térfogatelemet alkalmaztuk (Ófalu, Dunaföldvár) és teszteltünk statisztikai vizsgálatokon alapuló iteratív algoritmusokat (Yilgarn craton, Australia). Az erőtér modelltéren kívüli szimulációjához vizsgáltuk a vékonyréteg modellek alkalmazhatóságát. Regularizációs módszerrel javítottuk az inverzióra felírt egyenlet-rendszer kondicionáltságát. A Kárpát-Pannon térség 3D kéregmodelljének leírásához alternatív megoldásként alkalmaztuk a polihedron térfogatelemeket is. Ezek használata biztosítja mind a sűrűség-határfelületek mind a földgörbület geometriailag pontosabb követését. A kifejlesztett számítási algoritmus kiküszöböli a számítási pont és a térfogatelem relatív helyzetéből adódó esetleges szingularitást. | During the present research the possibilities of the generation of local/regional mass models and their use for the simulation of gravity field parameters (potential, gradient vector, Eötvös tensor) to be applied in geodetic computations, were investigated. The required high precision needs good fit between the observed parameters and the Newtonian mass attraction response of the model. It can be provided by the solution of an inverse problem which results in an optimal density distribution according to a specific norm (e.g. L2). The model obtained by inversion can be used for the analytical forward computation of gravity field related parameters among them some are immeasurable. In the one-step solutions of the inversion problem rectangular volume elements (prisms) were applied on two areas (Ófalu, Dunaföldvár) and iterative algorithms based on statistical analysis were also tested (Yilgarn craton, Australia). For the simulation of the gravitational field in the exterior of the source space discrete thin layer models were introduced. A regularization method was developed for the improvement of the condition of the equation system set up for thin layer inversion. Polyhedrons were applied in the modeling of the 3D crustal structure of the Carpathian-Pannonian region. Their use leads to better geometrical representation of density interfaces and the Earth's curvature than what is provided by prisms. The formal singularities of the polyhedron formulae are properly handled

Estimation of an upper limit on prehistoric peak ground acceleration using the parameters of intact stalagmites and the mechanical properties of broken stalagmites in Domica Cave, Slovakia

Suitably shaped (tall, slim and more or less cylindriform), vulnerable, intact stalagmites (STM) in Domica cave have been examined. Some of these STMs are suitable to estimate the upper limit for horizontal peak ground acceleration generated by paleoearthquake. This research is the continuation of our previous examination of STMs in Baradla cave, north - east Hungary. The density, the Young’s modulus and the tensile failure stress of broken STM samples have been measured in mechanical laboratory, whereas the natural frequency and the heights and diameters of intact STMs were determined by in situ observation. The value of horizontal ground acceleration resulting in failure and the theoretical natural frequency of STM were assessed by theoretical calculations. The age of the samples taken from the STM(2.26m) standing in show part of Domica cave has been determined by Multi Collector – Inductively Coupled Plasma Mass Spectrometry analysis (MC-ICPMS). The a g value (the upper limit for horizontal peak ground acceleration ) need ed to break STM(5m) in Čertova diera (Ördög-lik) hall coming from theoretical calculation is almost the same (~ 0.059g) as - in case of STM(5.1m) in Olimposz hall (~0.055g) of Baradla cave. According to our measurements and theoretical calculations, in the last 2-5 kyears the geological structures close to Baradla and Domica caves have not generated paleoearthquakes, which would have produced horizontal ground acceleration larger than 0.061g. This value can be reached even in moderate size earthquakes. Our result has to be taken into account when calculating the seismic potential of faults near to Domica cave (e.g. Darnó,Plešivec (Pelsőc) and Rožňava (Rozsnyó) lines

Comprehensive investigation of intact, vulnerable stalagmites to estimate an upper limit on prehistoric ground acceleration

Non-intrusive in situ measurements were carried out in caves in Hungary, Bulgaria and Slovakia in order to determine the fundamental frequencies (FF) and horizontal ground accelerations (HGA) resulting in failure of intact, slim, vulnerable stalagmites. Similar investigations are planned in Austria at the Eastern Alps. The main steps of investigation are: 1) FF of intact stalagmites were determined by in situ observation. 2) Density, Young’s modulus and tensile fa ilure stress of broken stalagmites ha ve been measured in mechanical laboratory. 3) The value of HGA resulting in failure and FF of stalagmite were assessed by theoretical calculations. 4) Age determination of co re-samples. The upper limit for HGA, a g , for slim stalagmites determined by theoretical calculations, can arise even for moderate-sized eart hquakes. The FF of the investigated stalagmites are low. The geological stru ctures close to the investigated caves did not excite paleoearthquakes in the determined time period, corresponding to HGA larger than the determined a g values

Analysis of an earthquake based on extensometric and seismological measurements

The rock-deformation data series collected by extensometers provide an opportunity for studying various changes in the geological, rock-physical environment, caused by earthquakes (e.g.,displacement, deformation of rock mass). Hereby further information can be achieved about the nature of these effects, complementing the analysis of seismograms (as e.g. the frequency range embraced by extensometers can record changes with much higher time of periods). In order to investigate the appearance of effects of earthquakes in extensometric data, authors chose a registratum which was collected in the Matyashegy Gravity and Geodynamical Observatory in Budapest in the time of a significant M7.2 earthquake occurred in Turkey, and started its spectral analysis. Results of the examinations were compared to the spectrum of records of a typical, undisturbed lapse of time, as well as to the spectrum calculated from seismogram of Kövesligethy Radó Seismological Observatory in Budapest, nearby the gravity observatory