115 research outputs found

    Probabilistic waveform inversion: Quest for the law

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    Full-waveform inversion (FWI) is an algorithm (and a part of the measuring procedure in a wide sense) with the aim to find the governing law of a physical system using the partially measured physical fields with limited computational resources. A law is a forward theory equipped with the model parameters and the data parameters. The main characteristic of the law is the realizability assumption: the law explains all subsets of the measured data parameters and predicts all subsets of the unmeasured (in the given experiment) data parameters. To find the law, we have to guess a law (a forward theory and parametrization), measure some data parameters and check the realizability assumption. To put it more precisely, I formulate a new probabilistic setting for inverse problems and full-waveform inversion. Instead of using the Bayes\u27 theorem, the Tarantola-Valette conjunction or the principle of maximum entropy based on the prior information for the averaged quantities, I propose a principle of minimum relative information using the prior information for the non-averaged quantities. The Tarantola-Valette formula is obtained as a special case under the assumption that the theoretical and prior measures exist. Using the realizability assumption as a prior information, the principle of minimum relative information provides the parametric probabilistic solution with the arbitrary misfit functions. Maximization of the parametric probabilistic solution leads to a multiobjective minimization problem. All global Pareto optima are the sample points of the probabilistic solution with the highest values of the volumetric measure. Unfortunately, even a local multiobjective minimization problem is computationally intractable for FWI with many millions of model parameters. To make it computationally attractive for large-scale FWI and to find at least a few local solutions of the multiobjective minimization problem, I implement the bilevel multiobjective waveform inversion (BMWI) using a single randomly chosen shot gather at each iteration. BMWI is a stochastic, nested algorithm with an adaptive parabolic line search and multiscale strategy. The computational cost per iteration is five forward modellings only. BMWI can worsen some of the single-shot misfit functions and the different random runs of BMWI converge to different points in the model manifold. I interpret these inverted models as the sample points of the probabilistic solution. I estimate the solution, uncertainty and sensitivity using the sample estimates of the mean, standard deviation and initial deviation of the sample points, respectively. Using the numerical examples with the Marmousi-2 model, I illustrate the potential of BMWI for automatic uncertainty and sensitivity analysis with just two-three sample points. To test the idea with real-world data, I apply stochastic single-shot BMWI in a 2D acoustic finite-difference approximation to a 2D line of pressure data acquired in a shallow-water river delta with ocean bottom cables. I use minimal data preprocessing (only a new 3D-to-2D transform which is strictly valid in a linear-gradient medium), the linear gradient starting models and the diagonal preconditioners with a negligible regularization. I estimate the theoretical uncertainties due to the neglected 3D effects using the 3D-to-2D transforms. The uncertainties estimated by the random sequences of BMWI are higher than the uncertainties related to the 3D-to-2D transforms. I provide the estimates of the solution, uncertainty and sensitivity using up to fourteen sample points inverted with the different linear-gradient starting models, the differently 3D-to-2D-transformed real data sets and the different random sequences of descent directions. The uncertainty of sound velocities is the lowest in the central semicircle with the radius 3 km equal to half the length of the ocean bottom cable. The uncertainty of mass densities is the highest in the central semicircle. The sensitivity of the measuring procedure with respect to sound velocity and mass density is the highest in the central semicircle representing a footprint of the acquisition geometry. Outside the central semicircle the parameters are not falsifiable in the specified setting. Full-waveform inversion is the quest for the unique governing law of the physical system under study. If the governing law is deterministic and the sample mean, standard deviation and initial deviation of the sample points represent the insufficient description of the solution, uncertainty and sensitivity, then the measuring procedure in a wide sense has to be improved

    Knowledge graphs in BERD and in NFDI

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    Knowledge graphs are able to capture, enrich and disseminate research data objects so that the FAIR and Linked Data principles are fulfilled. How knowledge graphs can improve the domain-specific (BERD) and cross-domain (NFDI) research data infrastructures? The answer is based on the use cases in BERD@NFDI and on activities of the NFDI working group “Knowledge graphs”. First, we describe the architecture, knowledge graphs and use cases in BERD@NFDI. Then, we present the NFDI working group “Knowledge Graphs”, its work plan and potential base services

    Accuracy in calculating the parameters of scattered radiation

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    The angular characteristics of radiation scattered by particles are calculated. The effect of the accuracy of the number representation during computations (number of decimal places) on the calculation results is analyzed. It is shown that, in order to obtain reliable results within the available algorithm, it is often necessary to use a precision that is much higher than computer precision. An algorithm is proposed and implemented that makes it possible to avoid going beyond computer precision in calculations in a considerably extended range of input parameters. A simple approximate formula is proposed to restrict the number of terms in infinite sums, which ensures the required accuracy in calculating the scattering indicatrix and the radiative properties of particles

    BERD@BW – A Science Data Center to foster Open Science in Business, Economics and Social Sciences

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    The Center for Business, Economic and Related Data in Baden-Württemberg(BERD@BW) is one of the four science data centers funded by the Ministry of Science, Research and Arts of Baden-Württemberg within the digitization strategy “digital@bw”. BERD@BW is aimed to improve sharing, finding and reusing unstructured and semi-structured research data in the social sciences in accordance with the FAIR principles (findable, accessible, interoperable and reusable). BERD@BW is built by the University of Mannheim and the Leibniz Center for European Economic Research (ZEW). Both institutions are experienced in infrastructure projects and in the empirical social sciences, including business and economics. BERD@BW is based on four pillars: 1) building up methodological knowledge, 2) developing tools and services dealing with unstructured and semistructured data, 3) training and consulting with respect to legal and technical issues in research data management, and 4) engaging in national and international networking. The services and materials developed within BERD@BW are available as openly as possible on the project homepage: https://www.berd-bw.de

    Detecting parameters of impact assessment of SDW landfill sites on water bodies (on the example of the Samosyrovsk land fill, Kazan, Russia)

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    Annually in Russia there not less than 3,5 billions tones of wastes are produced, from which only a quarter is processed, the rest is burned or removed to special landfills. Most of landfills is situated directly nearby built-up and natural areas. The objective of investigation in this work is revelation of parameters for impact assessment of Samosyrovsk landfill in Kazan on water bodies on the example of the river Krutovka. The main tasks of investigation are: gathering and analyzing data about Samosyrovsk landfill in Kazan; hydrochemical analysis of water samples of the river Krutovka and waste waters of the Samosyrovsk landfill on chemical elements content in it; hydrobiological investigation of the river Krutovka; separation of the most important parameters for further monitoring. Analyses were made on the basis of the international laboratory of the urban explorations of the Institute of social investigations on modernization of society and department of nature development and water use of KFU. It has been analyzed the existing monitoring system of landfills. The ecological state of the river Krutovka on hydrochemical and hydrobiological parameters has been assessed. It has been revealed chloride, copper, magnesium, calcium pollution of the stream. It has been shown parameters of zoobenthos allowing to more precisely assess the state of the water body. Such indicators are: aspectual content, ratio of quantity and biomasses of the basic groups of organisms, calculation of Shannon and Simpson indices, account of presence chironomidae organisms in assays

    Spin response in HTSC cuprates: Generalized RPA approach with projection operators method

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    © Kazan Federal University (KFU). We derive the dynamical spin susceptibility in the t-J-G model combining the random phase approximation (RPA) and projection operator method, which allows describing the mutual interplay between the local and the itinerant components of susceptibility. Near the antifer- romagnetic wave vector the calculated dispersion of the spin excitations reproduces well the so-called hour-glass dispersion, characteristic for several layered cuprates. It is formed as a result of competition between the original spin-gap in magnon-like excitations spectrum and the superconducting gap, which affects the itinerant component of the susceptibility. Further- more, the calculated collective spin excitations along (0, 0)-(0, π) are in agreement with the positions of the absorption peaks in the inelastic X-ray scattering spectra. They refer to the paramagnon-like modes, characteristic to the itinerant spin system, rather than magnon-like excitations that originate from short range order effect in the system of local spins at Cu sites

    "ENERGY APPROACH" FOR CALCULATING THE ECONOMIC VALUE OF BIORESOURCES OF THE HUNTING FARM "SVIYAZHSKOE"

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    O papel dos animais no ecossistema é determinado por uma ampla gama de fatores. Este é, antes de tudo, o número, a biomassa e a natureza da alimentação. Devido ao fato de que a taxa metabólica em diferentes grupos de animais não é a mesma, o indicador mais importante de sua importância no funcionamento do ecossistema é o fluxo de energia que passa pela comunidade (energia transformável). O artigo apresenta dados sobre o uso de energia transformável para avaliar os recursos de espécies terrestres de vertebrados nas condições da fazenda de caça "Sviyazhskoe. A abordagem implementada pode ser aplicada a diferentes territórios. Uma limitação fundamental pode ser apenas a ausência de dados sistemáticos sobre os registros de todos os grupos.The role of animals in the ecosystem is determined by a wide range of factors. This is, first of all, the number, biomass and nature of feeding. Due to the fact, that the metabolic rate in different groups of animals is not the same, the most integral indicator of their significance in the functioning of ecosystem is the energy flow, passing through the community (transformable energy). The article presents data on the use of transformable energy for assessing the resources of terrestrial vertebrate species in the conditions of the hunting farm "Sviyazhskoe. The implemented approach can be applied to different territories. A fundamental limitation can only be the absence of systematic data on the records of all groups.El papel de los animales en el ecosistema está determinado por una amplia gama de factores. Este es, en primer lugar, el número, la biomasa y la naturaleza de la alimentación. Debido al hecho de que la tasa metabólica en diferentes grupos de animales no es la misma, el indicador más integral de su importancia en el funcionamiento del ecosistema es el flujo de energía, que pasa a través de la comunidad (energía transformable). El artículo presenta datos sobre el uso de energía transformable para evaluar los recursos de las especies de vertebrados terrestres en las condiciones de la granja de caza "Sviyazhskoe. El enfoque implementado puede aplicarse a diferentes territorios. Una limitación fundamental solo puede ser la ausencia de datos sistemáticos sobre Los registros de todos los grupos
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