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EN
Inversion of seismic tomography is non-uniqueness and bad-conditioned problem. Reconstruction of velocity field is a process of minimization error function between estimated and received travel times. Classical, deterministic method, like matrix decomposition or conjugate gradient, is known for finish calculation in local minimums. Other problems with deterministic methods were application of constraints to the solution. Stochastic algorithms are methods that can be helpful in solving inverse problem in seismic tomography. This paper presents application of the following two stochastic algorithms to reconstruct velocity field: Metropolis algorithm (MA) and simulated algorithm (SA). The Metropolis algorithm is an iterative method and it was first described by Metropolis et al. (1953). This method uses Boltzmann distribution to calculate probability of replacing current solution by worse one, which is modification of current. Level of acceptance is given by value of a temperature. The simulated annealing was first described by Kirkpatrick et al. (1983) and it is a modification of Metropolis algorithm. This algorithm decreased temperature during iterative process. Both algorithms were modified by adding two dimensional median filtration in a place of modification of current velocity field. This filtration was applied with some small probability. Estimation of travel times of primary seismic waves was performed using two ray-based methods: a straight line and a shortest path method (Moser 1991, Pięta & Dwornik 2009). The first method was very fast but nonrealistic in heterogeneous geological medium. The second method had over one hundred times longer calculation time, but provided real ray trajectories. The algorithms were tested in series by ten independent numerical simulations for each parameter of configuration to minimize random effects of stochastic methods. Both algorithms were initialized in two ways: by random velocity fields and by velocity field obtained by SIRT algorithm (Lo & Inderwiesen 1994). Application of median filtration and initializing by SIRT solution decreased calculation time and improved quality of inversion.
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Content available remote Bayesian seismic AVO inversion with a group optimization strategy
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EN
The seismic amplitude-versus-offset (AVO) inversion based on the Bayesian framework is effective for obtaining the elastic parameters of the stratum from observed seismic data. Usually, this algorithm is used to obtain sparse reflectivity levels of elastic parameters through a proper long-tailed prior probability distribution. Considering the high correlation between underground parameters, a group optimization strategy was used for Bayesian AVO inversion, where the model parameters were inverted in groups at reflection interfaces. A group Cauchy constraint consisting of Cauchy constraint and l2-norm was designed. In the constraint, the Cauchy constraint is executed between groups to promote the sparsity of model parameters, and l2 regularization is executed within each group for constraining uniformity. The new Bayesian AVO inversion algorithm based on the group optimization strategy can help estimate the reflectivity levels of elastic parameters with desired sparsity. Additionally, even in the absence of the covariance matrix, the algorithm can still ensure the correlation of resulting solutions. It has been demonstrated that good results have been obtained from both numerical and field examples.
EN
The effective hydrocarbon exploration activity depends largely on the quantitative estimate of reservoir characteristics of promising intervals of the cross-section. Today the main task of seismologists is not only determination of the collector position in section, but also of fluid primer-sealer type, quantitative estimate of porosity, fracturing and other petrophysical parameters. The necessary data are tightness and velocities of Р- and S-waves. Such problems solving is in the detailed survey of dynamic properties of wave field. The author of this report used one of the most advanced methods of studying of the dynamic wave field — AVO-analysis for the first time on the territory of the Prypyatsky depression. We obtained preliminary positive results for predicting reservoir properties in the target interval. In spite of numerous contradictions concerning implementation of these methods and rather complex seismic and geological conditions of Prypiat downfold, this work illustrates applicability of AVO-analysis and shows good results.
EN
The inversion reaction coordinate of free amino acids (alanine, aspartic acid) have been computationally calculated by semi-empirical methods AM1. A transition state for free alanine and aspartic acid were obtained as a three membered ring in which the α-C-H and α-C-CH3 are slightly elongated, 1.2 and 2.17 Å respectively in the alanine transition state. The activation energy of alanine is 77.52 kcal/mol in the gas phase and 76.66 kcal/mol in aqueous phase, and for aspartic acid is 54.87 kcal/mol in the gas phase and 50.86 kcal/mol in aqueous phase.
EN
This article regards Norwid’s Tajemnica Lorda Singelworth in the context of his anthropology as well as historical and cultural background. The author’s notion of “cleanliness,” inspired in some measure by the Gospels, is connected to the circumstances of both Norwid himself and the main character of his puzzling novella. This reading revolves around the image of a balloon flight during which the Lord – as it is argued, following hints already present in studies of Norwid – discards a piece of paper with “physiological content.” This scene is placed in the context of other literary balloon flights and the eccentricity of Baudelaire’s friend Philoxène Boyer. Finally, the article discusses Norwid’s law of inversion, which can be applied in the case of Singelworth.
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Solution of the gradiometric boundary value problems leads to three integral formulas. If we are satisfied with obtaining a smooth solution for the Earth’s gravity field, we can use the formulas in regional gravity field modelling. In such a case, satellite gradiometric data are integrated on a sphere at satellite level and continued downward to the disturbing potential (geoid) at sea level simultaneously. This paper investigates the gravity field modelling from a full tensor of gravity at satellite level. It studies the truncation bias of the integrals as well as the filtering of noise of data. Numerical studies show that by integrating Tzz with 1 mE noise and in a cap size of 7°, the geoid can be recovered with an error of 12 cm after the filtering process. Similarly, the errors of the recovered geoids from Txz,yz and Txx-yy, 2xy are 13 and 21 cm, respectively.
EN
Determination of spherical harmonic coefficients of the Earth’s gravity field is often an ill-posed problem and leads to solving an ill-conditioned system of equations. Inversion of such a system is critical, as small errors of data will yield large variations in the result. Regularization is a method to solve such an unstable system of equations. In this study, direct methods of Tikhonov, truncated and damped singular value decomposition and iterative methods of v, algebraic reconstruction technique, range restricted generalized minimum residual and conjugate gradient are used to solve the normal equations constructed based on range rate data of the gravity field and climate experiment (GRACE) for specific periods. Numerical studies show that the Tikhonov regularization and damped singular value decomposition methods for which the regularization parameter is estimated using quasioptimal criterion deliver the smoothest solutions. Each regularized solution is compared to the global land data assimilation system (GLDAS) hydrological model. The Tikhonov regularization with L-curve delivers a solution with high correlation with this model and a relatively small standard deviation over oceans. Among iterative methods, conjugate gradient is the most suited one for the same reasons and it has the shortest computation time.
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The paper deals with the conformal mapping of finite, plane, simply connected domains, representing oceans, lakes, estuaries, bays, lagoons, and other natural water bodies of this kind. As a rule, they are bounded by geometrically complex shorelines. The partial differential problems investigated in Oceanology and posed in such domains have turned out to be difficult to solve for at least three reasons. They follow on from the mathematical properties of the differential equations governing such problems, from the just-mentioned geometrical complexity of the domains of solution, and from the sensitivity of the solutions to boundary conditions. In view of the last reason the contours admitted as boundaries of the domains of the solution ought to be as close to the real shorelines as possible. The obviously inaccurate approximation of the shorelines by ‘staircases’, which appears rather often (cf. Catewicz & Jankowski 1983, Lin & Chandler-Wilde 1996) as a consequence of applying finite difference methods to the solution of the partial differential problems, raises serious doubts from the point of view of Numerical Fluid Mechanics. It is recalled in the paper that such inaccuracies are not unavoidable: that complicated plane domains can be transformed accurately by means of properly applied conformal mapping onto regular, canonical domains – in particular, onto discs or squares. Such a transformation is demonstrated on the rather difficult example of the Vistula Lagoon. The transformation begins with the decomposition of the domain into five plane subdomains, each one of which is eventually transformed onto a disc. Every such result is arrived at quite independently of the remaining subdomains, by means of a set of properly selected consecutive mappings. Hence, the final canonical domain consists in this case of a system of five discs which, however, within the framework of this differential problem, have to be treated as interconnected. The interconnections involve images of four segments of straight lines, separating the original subdomains. The transformations and the resulting canonical domain presented in the paper are intended to be applied to the solution of certain hydrodynamical problems concerning the Vistula Lagoon, which will be published elsewhere.
PL
Sondaż akustyczny atmosfery jest jedną z aktywnych technik teledetekcyjnych, wykorzystywanych do określania warunków dyspersji zanieczyszczeń powietrza. Jest on prowadzony za pomocą radaru akustycznego, zwanego sodarem. Prędkość rozchodzenia się fal akustycznych w danym ośrodku jest uwarunkowana przez zmiany temperatury oraz wilgotności ośrodka. Analiza danych z pionowego sodaru dopplerowskiego opiera się na metodzie korelacyjnej, skojarzeniu charakterystycznych form echa akustycznego z procesami zachodzącymi w atmosferze. Na podstawie analizy obrazów uzyskanych z pionowego sodaru dopplerowskiego, teorii propagacji dźwięku w atmosferze, teorii fizyki chmur, została podjęta próba identyfikacji niskich chmur rodzaju Stratus na sodarogramach. Oszacowano prędkości dźwięku w powietrzu, w którym nie zachodzi kondensacja oraz w powietrzu, w którym zachodzi kondensacja i parowanie, przeprowadzono eksperyment z użyciem balonu na uwięzi. Prędkość dźwięku w powietrzu, w którym nie zachodzi kondensacja, jest większa o ok.10% od prędkości dźwięku w powietrzu, w którym zachodzi kondensacja i parowanie. Stwarza to możliwość zaistnienia dobrych warunków do zarejestrowania echa sygnału powracającego przez sodar. Przedstawiono kilka rejestracji sodarowych, których echo z dużym prawdopodobieństwem można interpretować jako powstałe w wyniku rozproszenia fali akustycznej od obszaru chmurowego. Podstawa oraz rodzaj chmury podczas wybranych rejestracji były konsultowane z Lotniskowym Biurem Meteorologicznym w Balicach. Pozyskany materiał doświadczalny jest zbyt skąpy, aby na jego podstawie jednoznacznie określić różnice między echem sodarowym powstałym z rozproszenia fali dźwiękowej w obszarze chmurowym a echem powstałym z rozproszenia fali dźwiękowej od innych obszarów rozpraszających. Oczekuje się, że synchronicznie prowadzone w ZTA obserwacje lidarowe pozwolą poszerzyć wiedzę dotyczącą interpretacji sodarogramów.
EN
Acoustic sounding of the atmosphere is one of the active remote-sensing techniques used for the designation of the conditions of dispersion of air pollutions. Acoustic sounding is made with use of acoustic radar called sodar. The velocity of acoustic waves depends on the temperature and humidity of air. The analysis of data from Vertical Doppler Sodar is based on the correlation method, associating characteristic forms of acoustic echo with the atmospheric processes. The testing of identification possibilities of the low Stratus clouds on sodar records was based on the analysis of the images of sodar records (from Vertical Doppler Sodar), on the theory of sound propagation, and on the theory of cloud physics. Evaluation was made of the sound velocity in the air in which no condensation is present and in the air in which both condensation and evaporation are active. An experiment was made with use of the tethered balloon. Sound velocity in the air without condensation is about 10% higher from that in the air with condensation and evaporation. This creates the possibility that the conditions for recording the echo of returning sodar signal will be good. Several sodar records are presented in which high probability exists that the recorded sodar echo is created by dispersion of the acoustic wave in cloud. Data on cloud base height and cloud type, for elected records, were consulted with the Airport Meteorological Station in Balice. The collected experimental material is not enough ample as to distinguish unmistakably the differences between the sodar echo from clouds from the sodar echo from other dispersing areas. It is expected that the interpretation of sodar records may become more ample thanks to the parallel sounding of the atmosphere by lidar. The synchronic sodar - lidar soundings are made by the Division of Remote Sensing of the Atmosphere.
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We generalize the known construction of "parabein model" of the affine plane geometry to arbitrary finite dimension and study some transformations characteristic for the obtained structures.
EN
Upper Cretaceous quartz arenites that fill the North Sudetic Synclinorium on the northern periphery of the Variscan Bohemian Massif show high compositional but low textural maturity. They have been interpreted for years as derived largely from nearby granite plutons, i.e. as first-cycle sediments. A different provenance was revealed on the basis of a combined light and heavy mineral analysis, and particularly a detrital tourmaline study, given that tourmaline is a sensitive indicator of granitic/metamorphic/sedimentary (multi-recycling) origin. Cenomanian, Turonian, Coniacian and Santonian sandstones contain abundant angular tourmaline grains, together with zircon and rutile, and subordinately staurolite, garnet, anatase, kyanite, sillimanite and monazite. The successive – Cenomanian to Santonian – tourmaline populations are similar with regard to shape, colour and chemical composition. The latter points unambiguously to various metamorphic rocks with a predominant group of Al-rich metapelites (Al-rich, F-poor dravite). It is concluded that, in the Late Cretaceous, large Sudetic granite plutons such as the Karkonosze and Strzegom–Sobótka massifs were not exposed but were buried under a thick siliciclastic cover. These results coupled with published apatite fission-track data from the granitic Karkonosze Pluton and the gneissic/migmatitic Góry Sowie Massif reveal that Late Cretaceous quartz arenites of the North Sudetic Synclinorium reflect gradual exhumation of the surrounding massifs, but do not record the final exposure of crystalline rocks. Since the latest Turonian, this exhumation corresponded to the Late Cretaceous inversion episode in Central Europe. The textural immaturity of Upper Cretaceous sandstones is misleading in terms of their recycled origin, and it is inherited from immature clastic source rocks.
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The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical consistency and reconstruction problems for two directions in discrete tomography can be solved in polynomial time, it turns out that these window constraints cause various unexpected complexity jumps back and forth from polynomialtime solvability to NP-hardness.
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The sedimentary basins of the Outer Carpathians are regarded as the remnant oceanic basins that were transformed into the foreland basin. These basins developed between the colliding European continent and the intra-oceanic arcs. In the pre-orogenic and syn-orogenic evolution of the Carpathian basins the following prominent periods can be established: Middle Jurassic — Early Cretaceous opening of basins and post-rift subsidence, Late Cretaceous—Palaeocene inversion, Palaeocene toMiddle Eocene subsidence, Late Eocene–Early Miocene synorogenic closing of the basins. In the Outer Carpathian sedimentary area the important driving forces of the tectonic subsidence were syn- and post-rift thermal processes as well as the emplacement of the nappe loads related to the subduction processes. Similar to the other orogenic belts, the Outer Carpathians were progressively folded towards the continental margin. This process was initiated at the end of the Palaeocene at the Pieniny Klippen Belt Magura Basin boundary and completed during Early Burdigalian in the northern part of the Krosno flysch basin.
EN
The paper concerns the effect of thermal inversions on PM10 concentrations in winter seasons between 2004–2005 and 2012–2013 in Tricity. Temperature inversions were analyzed using aerological measurements timed at 00 UTC and 12 UTC obtained from the aerological station in Łeba. The PM10 concentrations were obtained from five Agency of Regional Air Quality stations in the Gdańsk metropolitan area (ARMAAG). The effect of inversion conditions on the variability of daily PM10 concentrations was assessed using single and multiple linear regressions. The unfavorable conditions of PM10 dispersion in the lower troposphere were mostly determined by elevated inversions, which occurred with comparable frequency, nearly 90%, during the day as well as at night. Surface inversions were recorded at a frequency of 30% at night and only 10% during day-time. The strongest adverse effect on PM10 concentrations and their variability during the period of calendar winter was found to be related to the thickness of surface inversions at night. A significant yet substantially less adverse effect during both day and night, however, was found to be related to the thickness of the lowest layer of upper inversion. The high location of the base of upper inversion, primarily during the day-time, contributed to a decrease in PM10 concentration.
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2-D dipping dike model is often used in the magnetic anomaly interpretations of mineral exploration and regional geodynamic studies. However, the conventional interpretation techniques used for modeling the dike parameters are quite challenging and time-consuming. In this study, a fast and efficient inversion algorithm based on machine learning (ML) techniques such as K-Nearest Neighbors (KNN), Random Forest (RF), and XGBoost is developed to interpret the magnetic anomalies produced by the 2-D dike body. The model parameters estimated from these methods include the depth to the top of the dike (z), half-width (d), Amplitude coefficient (K), index angle (α), and origin (x0). Initially, ML models are trained with optimized hyper-parameters on simulated datasets, and their performance is evaluated using Mean absolute error (MAE), Root means squared error (RMSE), and Squared correlation (R2). The applicability of the ML algorithms was demonstrated on the synthetic data, including the effect of noise and nearby geological structures. The results obtained for synthetic data showed good agreement with the true model parameters. On the noise-free synthetic data, XGBoost better predicts the model parameters of dike than KNN and RF. In comparison, its performance decreases with increasing the percentage of noise and geological complexity. Further, the validity of the ML algorithms was also tested on the four field examples: (i) Mundiyawas-Khera Copper deposit, Alwar Basin, (ii) Pranhita–Godavari (P-G) basin, India, (iii) Pima Copper deposit of Arizona, USA, and (iv) Iron deposit, Western Gansu province China. The obtained results also agree well with the previous studies and drill-hole data.
EN
We applied the technique of the genetic algorithms and a local methodology integrating the Gauss–Newton and Conjugate Gradient (GNCG) techniques to test one-dimensional inverse modeling of synthetic magnetotelluric data. The result of this modeling applied to a homogeneous and isotropic five-layer model led to the development a hybrid algorithm (GAGNCG), combining the aforementioned techniques, for inverse modeling of one-dimensional magnetotelluric data. The GAGNCG modeling of the synthetic data performs more efciently than the local methodology in terms of both procedure and results. This showed that the hybridization procedure maximized the advantages of using the global search methodology and minimized the disadvantages of the local technique. Based on these results, we developed another hybrid methodology (GA2D), built from some characteristics of the genetic algorithm and the simulated annealing method, for the inverse modeling of two-dimensional magnetotelluric data. The results were satisfactory, and the GA2D algorithm was a good starting point for the inverse modeling of two-dimensional data.
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Content available remote Rough Set Algebras as Description Domains
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Study of the so called knowledge ordering of rough sets was initiated by V.W. Marek and M. Truszczynski at the end of 90-ies. Under this ordering, the rough sets of a fixed approximation space form a domain in which every set ↓α is a Boolean algebra. In the paper, an additional operation inversion on rough set domains is introduced and an abstract axiomatic description of obtained algebras of rough set is given. It is shown that the resulting class of algebras is essentially different from those traditional in rough set theory: it is not definable, for instance, in the class of regular double Stone algebras, and conversely.
EN
A deformation problem of an isotropic elastic liquid-saturated porous medium has been discussed by finding a general solution to the field equations of poroelasticity under axisymmetric conditions. An eigenvalue approach using the Laplace and the Hankel transforms is applied to get the solution. To show the utility of the solution obtained, an application of an infinite space with a concentrated point force acting at some interior point of the medium has been considered. The transformed solutions are inverted numerically, using a numerical inversion technique to invert the Laplace and the Hankel transforms. The results in the form of displacement and stress components have been obtained numerically and discussed graphically for a particular model.
EN
Between 2017 and 2019, the CSIR-NGRI, Hyderabad, Telangana, established a broad-band seismic-network with fifty-five 3-component broadband seismometers in the Himalayan region of Uttarakhand, India. Out of 55 three component broadband seismic (BBS) networks, we chose 17 for the present study. Using digital waveform data from twenty-one (21) regional Indian earthquakes of Mw 5.0-6.2 that were recorded in the 17 broadband seismometer, we compute fundamental mode group-velocity dispersion (FMGVD) characteristics of surface waves (Love and Rayleigh waves) and the average one-dimensional regional shear-wave velocity (Vs) structure of the Uttarakhand Himalayan region. First, we compute FMGVD curves for Love waves (6-73 s) and Rayleigh waves (at 6.55-73 s) period, and then, we finally invert these dispersion curves to compute the final average one-dimensional regional crustal & sub-crustal shear-wave velocity (Vs) structure below the Uttarakhand Himalaya. Our best model in Uttarakhand Himalayan region, India, reveals the 8-layered crust with a mid-crustal low velocity layer (MC-LVL) (approximately a drop of 1.5-2.3% in Vs) between 8 and 20 km depth in the proximity of MCT (Main Central Thrust). In the upper crustal part (0-20 km depths), our modelling suggests shear velocities (Vs) varies from 3.1 to 3.9 km/sec while shear velocities (Vs) in the lower crustal part (20-45 km depth) are modelled to be varying from 3.7 to 4.69 km per sec. The Moho-depth is calculated to be 45 km deep below the K-G Himalaya, and the shear-velocity (Vs) in the sub-crustal sector is 4.69 km/sec. Our estimated mid-crustal low-velocity layer (MC-LVL) could be linked to the presence of metamorphic fluids in the fractured Main Himalayan Thrust (MHT), resulting from the weakening of the crustal material at the interface between the overriding Eurasian plate and upper part of the underthrusting Indian plate.
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