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1

Geostatistical investigations of displacements on the basis of data from the geodetic monitoring of a hydrotechnical object

Namysłowska-Wilczyńska B., Wynalek J.

Studia Geotechnica et Mechanica

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2017

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Vol. 39, nr 4

59--75

EN

Geostatistical methods make the analysis of measurement data possible. This article presents the problems directed towards the use of geostatistics in spatial analysis of displacements based on geodetic monitoring. Using methods of applied (spatial) statistics, the research deals with interesting and current issues connected to space-time analysis, modeling displacements and deformations, as applied to any large-area objects on which geodetic monitoring is conducted (e.g., water dams, urban areas in the vicinity of deep excavations, areas at a macro-regional scale subject to anthropogenic influences caused by mining, etc.). These problems are very crucial, especially for safety assessment of important hydrotechnical constructions, as well as for modeling and estimating mining damage. Based on the geodetic monitoring data, a substantial basic empirical material was created, comprising many years of research results concerning displacements of controlled points situated on the crown and foreland of an exemplary earth dam, and used to assess the behaviour and safety of the object during its whole operating period. A research method at a macro-regional scale was applied to investigate some phenomena connected with the operation of the analysed big hydrotechnical construction. Applying a semivariogram function enabled the spatial variability analysis of displacements. Isotropic empirical semivariograms were calculated and then, theoretical parameters of analytical functions were determined, which approximated the courses of the mentioned empirical variability measure. Using ordinary (block) kriging at the grid nodes of an elementary spatial grid covering the analysed object, the values of the Z* estimated means of displacements were calculated together with the accompanying assessment of uncertainty estimation – a standard deviation of estimation σk. Raster maps of the distribution of estimated averages Z* and raster maps of deviations of estimation σk (in perspective) were obtained for selected years (1995 and 2007), taking the ground height 136 m a.s.l. into calculation. To calculate raster maps of Z* interpolated values, methods of quick interpolation were also used, such as the technique of the inverse distance squares, a linear model of kriging, a spline kriging, which made the recognition of the general background of displacements possible, without the accuracy assessment of Z* value estimation, i.e., the value of σk. These maps are also related to 1995 and 2007 and the elevation. As a result of applying these techniques, clear boundaries of subsiding areas, upthrusting and also horizontal displacements on the examined hydrotechnical object were marked out, which can be interpreted as areas of local deformations of the object, important for the safety of the construction. The effect of geostatistical research conducted, including the structural analysis, semivariograms modeling, estimating the displacements of the hydrotechnical object, are rich cartographic characteristic (semivariograms, raster maps, block diagrams), which present the spatial visualization of the conducted various analyses of the monitored displacements. The prepared geostatistical model (3D) of displacement variability (analysed within the area of the dam, during its operating period and including its height) will be useful not only in the correct assessment of displacements and deformations, but it will also make it possible to forecast these phenomena, which is crucial when the operating safety of such constructions is taken into account.

2

Możliwości wykorzystania zasobów wodnych i energetycznych w podziemnych kopalniach surowców mineralnych

Namysłowska-Wilczyńska B., Wilczyński A., Wojciechowski H.

Zeszyty Naukowe Instytutu Gospodarki Surowcami Mineralnymi i Energią PAN

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2016

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nr 95

47--57

PL

W kopalniach, oprócz tradycyjnie wydobywanych surowców mineralnych, występują jeszcze inne zasoby, tj. wodne i energetyczne, które w ogóle nie są wykorzystywane, lub też mają praktyczne zastosowanie w niewielkim stopniu. Pozyskiwanie wymienionych zasobów mogłoby poprawić efektywność ekonomiczną kopalń czynnych lub przedłużyłoby okres aktywności kopalń zamykanych. W artykule omówiono potencjalne możliwości wykorzystania zasobów energetycznych, pozostających poza sferą podstawowej działalności górniczej, związanej z wydobyciem złóż węgla kamiennego, ale także z eksploatacją różnorodnych surowców użytecznych. Podjęto również aspekt szerszego zagospodarowania kopalnianych wód podziemnych. Nawiązano do skutków likwidacji kopalń węglowych, na przykładzie Wałbrzyskiego Zagłębia Węglowego. Podkreślono ważność i aktualność podjętej problematyki. Przedstawione propozycje mogą stanowić wkład w urzeczywistnienie zasady zrównoważonego rozwoju, poprzez koncentrowanie się na trzech jego wymiarach – ekonomicznym, ekologicznym i społecznym. Jednocześnie byłby to sposób na zrównoważone zarządzanie środowiskiem wodnym na obszarach antropopresji, na terenach przemysłowych i post-przemysłowych, dla celów pozyskiwania wody, poprawy jej jakości oraz skorzystania z lokalnych źródeł energii, takich jak: ciepło i energia związana z potencjałem wodnym. Ponadto wskazano na możliwość magazynowania energii, co jest niezwykle ważne w dobie intensywnego rozwoju niekonwencjonalnych źródeł energii elektrycznej (farm wiatrowych, źródeł solarnych, elektrowni wodnych etc.), określanych wręcz jako źródła chimeryczne, gdyż ich cechą jest nieregularna praca.

EN

In addition to the traditionally mined mineral resources, water resources and energy are still present in the mines. Those resources are not used at all, or are intended for practical use, but to a lesser degree. The acquisition of these resources could improve the economic efficiency of active mines or prolong the period of activity of the closed mines. The article discusses the possibilities of using energy resources which are outside the sphere of the core business of mining and have taken a broader aspect of the development of underground water from mines. The proposals constitute a contribution to the implementation of the principles of sustainable development by focusing on three of its dimensions - economic, environmental and social. At the same time it would be a way for the sustainable management of the water environment in the areas of anthropopressure, in industrial and post-industrial areas, for the purpose of collecting water, improving water quality and the use of local energy sources, such as heat and energy associated with potential water. The possibility of energy storage, which is extremely important in the era of an intensive development of unconventional sources of energy (wind farms, solar sources, hydroelectric, etc.), the characteristics of which are irregular, referred to simply as chimeric sources, also exists.

3

Geostatistical analysis of space variation in underground water various quality parameters in Kłodzko water intake area (SW part of Poland)

Namysłowska-Wilczyńska B.

Studia Geotechnica et Mechanica

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2016

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Vol. 38, nr 3

15--34

EN

This paper presents selected results of research connected with the development of a (3D) geostatistical hydrogeochemical model of the Kłodzko Drainage Basin, dedicated to the spatial variation in the different quality parameters of underground water in the water intake area (SW part of Poland). The research covers the period 2011–2012. Spatial analyses of the variation in various quality parameters, i.e., contents of: iron, manganese, ammonium ion, nitrate ion, phosphate ion, total organic carbon, pH redox potential and temperature, were carried out on the basis of the chemical determinations of the quality parameters of underground water samples taken from the wells in the water intake area. Spatial variation in the parameters was analyzed on the basis of data obtained (November 2011) from tests of water taken from 14 existing wells with a depth ranging from 9.5 to 38.0 m b.g.l. The latest data (January 2012) were obtained (gained) from 3 new piezometers, made in other locations in the relevant area. A depth of these piezometers amounts to 9–10 m. Data derived from 14 wells (2011) and 14 wells + 3 piezometers (2012) were subjected to spatial analyses using geostatistical methods. The evaluation of basic statistics of the quality parameters, including their histograms of distributions, scatter diagrams and correlation coefficient values r were presented. The directional semivariogram function γ(h) and the ordinary (block) kriging procedure were used to build the 3D geostatistical model. The geostatistical parameters of the theoretical models of directional semivariograms of the water quality parameters under study, calculated along the wells depth (taking into account the terrain elevation), were used in the ordinary (block) kriging estimation. The obtained results of estimation, i.e., block diagrams allowed us to determine the levels of increased values of estimated averages Z* of underground water quality parameters.

4

Geostatistical Characteristics of the Structure of Spatial Variation of Electrical Power in the National 110 KV Network Including Results of Variogram Model Components Filtering

Namysłowska-Wilczyńska B., Wilczyński A.

Acta Energetica

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2015

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nr 1

72--87

EN

The paper provides results of analysing the superficial variability of electrical power using two geostatistical methods – lognormal kriging and ordinary kriging. The research work was to provide detailed characterization and identification of the electrical load variability structure at nodes of a 110 kV network over the whole territory of Poland having been analyzed on the basis of results from kriging techniques applied. The paper proposes the methodology using two techniques of modelling and estimating average values Z* of electrical powers, i.e. lognormal kriging and ordinary kriging. The input data for calculations were electrical powers at nodes of 110 kV network related to the same time moment, i.e. 11:00 a.m. in summer and winter seasons. Kriging calculations were made for various variants of examinations. Filtering was carried out for assumed complex theoretical models of semivariograms of electrical powers, which means their dividing into several models components of the covariance (nugget effect, 1 spherical model, 2 spherical model), which were filtered out successively. Then, estimations were made for average values Z* of powers while particular components are passed over. The results of analyses made with considering particular components of semivariograms models were shown in raster maps providing distributions of estimated average values Z* of electrical powers. This allowed the orientation of variations in values of this parameter, both over the territory of the whole country and in time domain, for two seasons – summer and winter, and also when various models components were assumed of semivariograms of the loads. Detailed analysis of spatial-time variability of average values Z* of electrical loads over the country allowed to identify their range and nature of variability.

PL

W artykule przedstawiono rezultaty analizy powierzchniowej zmienności mocy elektrycznych z wykorzystaniem dwóch metod geostatystycznych – krigingu lognormalnego i krigingu prostego. Celem pracy było dokładne scharakteryzowanie i rozpoznanie struktury zmienności obciążeń elektrycznych w węzłach sieci 110 kV na obszarze całego kraju, analizowanej na podstawie uzyskanych rezultatów użycia technik krigingowych. W artykule zaproponowano metodologię wykorzystującą dwie techniki modelowania i szacowania wartości średnich Z* mocy elektrycznych, tj. kriging lognormalny i kriging prosty. Danymi wejściowymi do obliczeń były moce elektryczne w węzłach sieci 110 kV, związane z tym samym momentem czasowym, tj. godz. 11.00, w okresach letnim i zimowym. Obliczenia krigingowe wykonano przy założeniu różnych wariantów badania. Przeprowadzano filtrowanie przyjętych złożonych modeli teoretycznych semiwariogramów mocy elektrycznych, czyli rozdzielenie modeli na różne składowe (efekt samorodków, 1 model sferyczny, 2 model sferyczny), które były kolejno odfiltrowywane. Następnie szacowano wartości średnich Z* mocy, z pominięciem poszczególnych składowych. Rezultaty analiz wykonanych z uwzględnieniem kolejnych składowych modeli semiwariogramów przedstawiono na mapach rastrowych rozkładów wartości średnich estymowanych Z* mocy. Pozwoliło to na zorientowanie się w zmianach wartości tego parametru zarówno na obszarze całego kraju, jak i w czasie, w dwóch sezonach roku, letnim i zimowym, a także przy założeniu różnych składowych modeli semiwariogramów obciążeń. Dokładna analiza zmienności przestrzenno-czasowej średnich Z* obciążeń elektrycznych, przeprowadzona dla obszaru kraju, umożliwiła zorientowanie się w ich zakresie i charakterze zróżnicowania.

5

Geostatistical hydrogeochemical 3D model for Kłodzko underground water intake area. Part I., Estimation of basic statistics on quality parameters of underground waters

Namysłowska-Wilczyńska B.

Studia Geotechnica et Mechanica

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2013

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Vol. 35, nr 1

157--182

EN

The paper presents the first stage of research on a geostatistical hydrogeochemical 3D model dedicated to the horizontal and vertical spatial and time variation in the topographical, hydrological and quality parameters of underground water in the Kłodzko water intake area. The research covers the period 1977–2012. For this purpose various thematic databases, containing original data on coordinates X, Y (latitude and longitude) and Z (terrain elevation and time – years) and on regionalized variables, i.e., the underground water quality parameters in the Kłodzko water intake area determined for different analytical configurations (22 wells, 14 wells, 14 wells + 3 piezometers), were created. The data were subjected to spatial analyses using statistical methods. The input for the studies was the chemical determination of the quality parameters of underground water samples taken from the wells in the water intake area in different periods of time. Both archival data (acquired in the years 1977–1999, 1977–2011) and the latest data (collected in November 2011 and in January 2012) were analyzed. First, the underground water intake area with 22 wells was investigated. Then in order to assess the current quality of the underground water, 14 wells out of the 22 wells were selected for further chemical analyses and a collection siphon wall was included. Recently, three new piezometers were installed in the water intake area and so new water samples were taken, whereby the databases were supplemented with new chemical determinations. The variation in the topographical parameter (terrain elevation) and in the hydrogeological parameters: water abstraction level Z (with and without the land layout being taken into account) and the depth of occurrence of the water table, was examined. Subsequently, the variation in quality parameters was studied on the basis of data coming from 22 wells, then 14 wells and finally from 14 wells and 3 piezometers. The variation in: Fe, Mn, ammonium ions NH4+, nitrite anion NO3 – and phosphate anion PO4 –3 content values, total organic carbon (TOC) C content, the pH reaction and temperature (°C) of the water was investigated. The basic statistics and distribution histograms of the topographical, hydrogeological and quality parameters (22 wells, 14 wells, 14 wells + 3 piezometers; the years: 1977–1999, 2011, 2011–2012) were estimated and detailed characteristics of the variation in the parameters in the whole underground water intake area over the years were obtained. Generally, the behaviour of the underground water quality parameters has been found to vary in space and time. Thanks to the multidirectional spatial analyses of the variation in the quality parameters in the Kłodzko underground water intake area some regularities in the variation in water quality have been identified.

6

Wstępna ocena jakości wód podziemnych w wybranym rejonie Kotliny Kłodzkiej

Biedroń I., Świderska-Bróż M., Traczewska T.M., Trusz-Zdybek A., Namysłowska-Wilczyńska B., Wolska M.

Instal

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2013

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nr 6

41--44

PL

Celem badań było scharakteryzowanie składu oraz ocena stanu sanitarnego wód podziemnych z obszaru Kotliny Kłodzkiej, a w szczególności okolic miasta Kłodzka. Woda pobrana z rzeki Bystrzycy Kłodzkiej charakteryzowała się znacznym zanieczyszczeniem mikrobiologicznym oraz obecnością organizmów patogennych i potencjalnie patogennych. Natomiast wody pobrane z trzech grup studni różniły się poziomem zanieczyszczenia mikrobiologicznego oraz właściwościami fizyczno-chemicznymi. Stwierdzono, że największy wpływ na jakość wód podziemnych miał sposób zagospodarowania terenów zlokalizowanych w pobliżu studni.

EN

The aim of this work was to characterize the composition and assessment the sanitary conditions of the groundwater from Kłodzko Valley area, particularly in the vicinity of the city Kłodzko. Water from the Bystrzyca Kłodzka river was characterized by a significant microbiological contamination, and the presence of potentially pathogenic organisms and pathogens. While, the water from the three groups of wells was differed by level of microbial contamination and physico-chemical properties. It was found that the greatest impact on groundwater quality was kind of land development located near the well.

7

Analiza geostatystyczna zmienności parametrów technologicznych popiołożużli zdeponowanych na składowisku odpadów przemysłowych

Namysłowska-Wilczyńska B., Skorupska B., Wieniewski A.

Ochrona Środowiska

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2012

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Vol. 34, nr 2

43-48

PL

Przedmiot badań geostatystycznych stanowiła część składowiska popiołożużli (zbiornik A), związanego z działalnością przemysłu energetycznego, znajdującego się w rejonie Świecia w województwie kujawsko-pomorskim. Przeanalizowano przestrzenne zróżnicowanie dwóch parametrów technologicznych, tj. zawartości popiołu i wilgotności popiołożużli, zdeponowanych na składowisku. Przeprowadzono analizę strukturalną zmienności tych parametrów, z zastosowaniem funkcji wariogramu kierunkowego, a następnie estymację wartości średnich (Z*) z użyciem krigingu zwyczajnego (blokowego) (3D). Przed-stawiono model geostatystyczny (3D) zmienności tych parametrów technologicznych składowiska, co pozwoliło na rozpoznanie przestrzennego zróżnicowania ich wartości w poziomym i pionowym rozprzestrzenieniu warstw popiołożużli. Wykazano, że zastosowanie metod geostatystycznych do opisu parametrów technologicznych popiołożużli, traktowanych jako złoże antropogeniczne, pozwoliło uzyskać ważną bazę danych, stanowiących komplet informacji do ewentualnego podjęcia prac nad gospodarczym wykorzystaniem materiału zdeponowanego na składowisku.

EN

The object under study is an industrial waste disposal site located in the proximity of Swiecie (district Wojewodztwo Kujawsko-Pomorskie), which receives ash-slags from power generation. Geostatistical analysis was carried out for some part of this waste disposal site (Tank?A). Two technological parameters of the ash-slags were made subject to analysis of spatial variation: ash content and moisture content. Structural analysis of variation in the two parameters was conducted using the directional variogram function, and was followed by estimation of average values (Z*) using ordinary (block) kriging (3D). A geostatistical model (3D) was established, which describes variations in the technological parameters of the waste disposal site, thus visualizing the spatial variation of their values in the horizontal and vertical extension of the ash-slag layers. It has been demonstrated that the use of geostatistical methods for describing the technological parameters of the ash-slags (treated as an anthropogenic deposit) offers the possibility of building up a comprehensive database that provides complete input information for a research project on the utilization of the material being disposed of.

8

The analysis of vertical displacements for a hydrotechnical facility using geostatistics. Part I. Structural analysis and estimation of displacements

Namysłowska-Wilczyńska B., Wynalek J.

Studia Geotechnica et Mechanica

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2011

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Vol. 33, nr 1

33-54

EN

The effect of geostatistical studies, including structural analysis, modelling, estimation and forecast, is the cartographic characteristic of the displacements of the hydro-technical object - the Opatowice weir. In the nodes of the spatial grid, covering the object analyzed, the average estimated values Z* of displacements were calculated together with the assessment of the uncertainty of estimation - the standard deviation of estimation ?k. If necessary, the parameters Z* and ?k can be determined directly in the kriging calculation, at every point of the object. The obtained variograms, raster maps and block diagrams represent the spatial visualization of the results of the various displacements, derived from the geodesic monitoring of the dam. Applying an ordinary block kriging it is possible to separate the clear boundaries of the zones of the subsidences and to determine the elevations of the hydro-technical object, marking on the raster maps the distributions of the average Z* values, which can be interpreted as the areas of local deformation that are important when the safety of buildings is considered. The maps of quick interpolation allow identification of a general background of displacements, without the accuracy estimation of the interpolated values Z*. Probability maps enable us to predict the significant risk areas associated with a possible change in the geometry of an object, i.e., its local deformation. Due to an area-time prognosis we can determine the forecasted values Z* of displacements for the following year, with reference to the history of this process, i.e. the estimations from prior years. Taking account of a wide range of different applications of geostatistical techniques, we can conclude that they are also effective tools in the analysis of spatial displacement, in this case, for a relatively small hydro-technical object (weir). The research undertaken may be useful for a complete monitoring of relevant environmental factors, differing only "seemingly identical" objects, and not only for the results of successive control measurements of displacements. These concerns a proper treatment of all spatial and time factors associated with the interpretation of the displacements, which allows the deterministic safety operation of a hydro-technical object to be identified.

9

The analysis of vertical displacements for a hydrotechnical facility using geostatistics. Part II. Determining the probability of displacement occurrence and its prediction

Namysłowska-Wilczyńska B., Wynalek J.

Studia Geotechnica et Mechanica

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2011

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Vol. 33, nr 2

67-75

EN

The results of the geostatistical spatial analyses of measuring data that reflect the monitoring of vertical displacements of a small hydrotechnical facility are presented. Of some weirs on the Oder River the Opatowice facility was chosen due to the scale of the displacements measured. The databases of current displacements pa and total displacements pc obtained in the X-Y (2D) and X-Y-Z (3D) coordinate systems formed the basis for the geostatistical investigation. The application of variogram function enabled establishing the theoretical parameters of analytical functions that approximate the isotropic and directional empirical variograms of present and total displacements and, as a result, determining the variation of specified parameters for the geostatistical model. Consequently, using the ordinary block kriging method and the methods of quick interpolation, i.e., the inverse distance squared method and the linear kriging model, the raster maps of the mean estimated distributions Z*, estimated standard deviation ?k and also interpolated values of Z* were calculated for the facility analyzed. In further analyses, indicator variograms and raster maps of the probability distributions for displacement occurrence were constructed. This allows determining the subregions with various susceptibilities to exceeding particular probability thresholds of deformation occurrence. A spatial-time prognosis was also made enabling us to calculate of the predicted Z* values for the displacements in successive periods (block diagrams) of hydrotechnical facility operation.

10

Koncepcja warstwowej taryfy przesyłowej

Tymorek A., Namysłowska-Wilczyńska B., Wilczyński A.

Rynek Energii

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2011

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nr 2

106-111

PL

Podstawowym obowiązkiem operatorów systemów przesyłowych jest tworzenie jak najlepszych taryf przesyłowych, wynikających z czynników i miejsc powstawania kosztów funkcjonowania sieci. Dotychczas znane metody alokacji kosztów w taryfach wykorzystywały najczęściej grupową lub węzłową ich reprezentację. W referacie proponuje się zasto-sowanie pośredniego rozwiązania taryfy przesyłowej, tzw. warstwowej, posiadającej wszystkie dobre cechy modelu węzło-wego, a jednocześnie będącej znacznym jego uproszczeniem. Ten rodzaj taryfy przesyłowej uzyskano dzięki nowa-torskiemu zastosowaniu metod statystki stosowanej do analizy przestrzennej jednostkowych kosztów krańcowych. Reko-mendowane jest stosowanie warstwowej taryfy przesyłowej w alokacji kosztów stałych i zmiennych funkcjonowania sieci.

EN

Elementary duty TSO is creating the best transmission tariffs which reflect the network operational costs. Up to now well-known methods of costs allocation in tariffs used the most postage stamp or nodal their representation. Indirect solution of transmission tariff - stratified has proposed in the paper. This solution has an all good features of nodal model and simultaneously being considerable his simplification. This kind of transmission tariff was the result of innovatory use of applied (spatial) statistics methods for analysing of marginal prices. In allocation of fixed and variable network operational costs has been recommended applying of the stratified transmission tariff.

11

Analiza przestrzenna wzbogacalności popiołożużli z wykorzystaniem metod geostatystycznych

Namysłowska-Wilczyńska B., Skorupska B. B., Wieniewski A.

Górnictwo i Geoinżynieria

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2011

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R. 35, z. 2

451-461

PL

Przedmiot badań geostatystycznych stanowił zbiornik A, wypełniony popiołożużlami, związanymi z działalnością przemysłu energetycznego, znajdujący się w rejonie Świecia (Toruń), w województwie Kujawsko-Pomorskim. Analizowano przestrzenne zróżnicowanie wzbogacalności e' popiołożużli występujących w zwałowisku stanowiącym hałdę odpadów, definiowanej jako odzysk węgla (w kilogramach) z 1 t popiołożużli. Przeprowadzono analizę strukturalną (wariograficzną) zmienności tego parametru, z zastosowaniem funkcji wariogramu kierunkowego, a następnie estymację (3D) średnich Z*, z użyciem krigingu zwyczajnego (blokowego). Przedstawiono model geostatystyczny zmienności parametrów technologicznych zwałowiska odpadów, co pozwala na rozpoznanie przestrzennego zróżnicowania ich wartości w poziomym i pionowym rozprzestrzenieniu warstw popiołożużli. Zastosowanie geostatystyki do opisu parametrów technologicznych odpadów traktowanych jako złoże antropogenne, umożliwiło uzyskanie różnych baz danych stanowiących komplet cennych informacji do ewentualnego podjęcia prac nad gospodarczym wykorzystaniem zdeponowanego materiału.

EN

Spatial analyses were carried out to develop a 3D geostatistical model of the spatial variation in the technological parameters of an ash-slags heap connected with the operation of the power utilities located near Świecie (Toruń). Tank A filled with ash-slags was the subject of geostatistical studies. The spatial variation of recoverability e' (defined as the amount of carbon kg recovered from 1 ton of ash- slags), was analyzed. The variation of these parameters in the horizontal and vertical extents of the ash-slags heap was subjected to structural (variographic) analysis using the directional variogram function. The parameters of geostatistical models approximating the directional variogram recoverability e' were the basis for the estimation. Averages Z* and corresponding standard estimation deviations delta/k were estimated for the particular depths of the tank using (3D) ordinary (block) kriging. Thanks to the application of the geostatistical methods to describe the parameters of the waste material (treated as an anthropogenic deposit) databases containing complete valuable input information for a project aimed at utilizing the deposited material were created.

12

Analizy przestrzenne z zastosowaniem metod geostatystycznych (Modelowanie 3D porfirowego złoża miedzi Rio Blanko w Peru)

Namysłowska-Wilczyńska B.

Roczniki Geomatyki

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2007

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T. 5, z. 1

91-103

EN

Research methods for geostatistical spatial analyses are presented on the example of the results of 3D modelling of deposit data. The variation in the parameters of the Rio Blanco porphyritic copper deposit in Peru was investigated. Copper and molybdenum grades, deposit thickness and copper accumulation averages Z* were estimated and quantity of the copper deposit.s reserves was calculated. Geostatistical methods, i.e. variogram and covariance functions and the ordinary (block) kriging technique, were used to estimate averages Z*. Spatial analyses drew from a large database (n = 5121 samples), containing values of coordinates X, Y and Z (depth ordinate) and Cu and Mo content and deposit thickness determinations for 104 boreholes distributed over the deposit area. In addition, databases with assumed three cut-off values of Cu content, i.e. 0.7% Cu (n = 1903 samples), 0.5% Cu (n = 2905 samples) and 0.3% Cu (n = 4011 samples), were used in the geostatistical studies. The isotropic empirical variograms and covariograms of the deposit.s parameters were computed. Then a 3D analysis of the directional empirical variograms and covariograms, computed along 4 regular directions in the reference plane and perpendicularly to this plane, was carried out. These variograms and covariograms were calculated for a slicing height of 7.97 m. Then, averages Z* and standard estimation deviation ók of the above parameters were estimated in 3D for the considered deposit series and the cut-off values of Cu content, taking into account different spatial copper ore specific weight. The estimation was based on the results of modelling empirical covariograms by means of theoretical functions. The estimated averages Z* of the deposit parameters were presented in the form of raster maps for selected deposit (porphyritic rocks) layers at depth levels: of 10, 15, 25, 30, 40, 45, 50, 55, 65, 75 within the 1935-2685 m vertical profile interval. As a result of the spatial analyses, a 3D geostatistical model of the Rio Blanco porphyritic copper deposit.s parameter variation was obtained.

13

Zastosowanie metod geostatystycznych do analizy przestrzennej zmienności obciążeń elektrycznych dla obszaru Polski

Namysłowska-Wilczyńska B., Wilczyński A.

Roczniki Geomatyki

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2005

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T. 3, z. 2

125-134

EN

Estimation kriging techniques were used to analyse data on electrical loads measured at the nodes of 220 and 400 kV transmission network and a 110 kV closed network over the whole area of Poland. The data were for a selected moment in time, i.e. 11 a.m. in the summer season (a Wednesday in July) in 2001. A sample population of N=103 and a much larger sample population of N=1029 were analysed for respectively the 220 and 400 kV transmission network and the 110 kV network. Original databases containing information on: the numbers of successive measurements, the values of coordinates X and Y (specifying the locations where the power measurements were performed) and the investigated parameter - electrical power). First semivariogram function ?(h) was used to analyse the degree and character of electric load variation. Then different kriging estimators, such as ordinary kriging and lognormal kriging, were used to represent the superficial variation in estimated electrical load averages Z over the whole territory of Poland. Isotropic semivariograms, computed for the given moment in time, are best approximated by spherical, exponential and cubic models. Empirical semivariograms based on the power data are characterized by a large share of random component UL (the C0 nugget effect) in the overall load variability, regardless of the power network variant. Then the whole territory of Poland was covered with a grid of 10 km x 10 km elementary blocks in order to estimate electrical power averages Z. For 5776 elementary block centres different geostatistical parameters, including coordinates X and Y (estimated averages Z and standard deviations estimation ? k in their number), were computed. Also the effectiveness and quality of the estimation of the poweraverages Z were examined. Besides the basic geostatistical parameters Z and ? k, also other major parameters, including the sum of positive weights wi assigned to power measurements in kriging, correlation r between the original Z values and estimated averages Z and covariance C of original Z values and estimated averages Z were computed. As a result, new, very comprehensive databases were obtained. They were used to compute raster maps, isoline maps and spatial block diagrams. The spatial visualization of the obtained pictures of power variation for the area of Poland reveals subareas of highly reliable estimation of averages Z and subareas for which the kriged estimates (averages Z) are rather unreliable.

14

Zastosowanie geostatystyki i GIS do analizy wpływu czynników naturalnych i antropogenicznych na koncentrację metali ciężkich w glebach rejonu olkuskiego

Namysłowska-Wilczyńska B., Rusak K.

Roczniki Geomatyki

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2005

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T. 3, z. 2

115-124

EN

The distribution and concentration of metals in soils depends on many natural and anthropogenic factors such as: the percentages of clayey, dusty and sandy fractions, the soil's pH, the lithology of surface formations, the wind directions, the kind of flora, the distance from pollution sources and the type of building and land development. The subject of the investigations was the Olkusz region where Zn and Pb ore deposits occur and are mined. The soils in the area show one of the greatest Cd-Pb-Zn anomalies in Poland, associated with ore-bearing dolomite outcrops and the historical and contemporary mining, processing and smelting of Zn and Pb ores. As part of this research an analysis of the factors affecting the distribution of heavy metals in the Olkusz industrialized area was carried out using GIS and geostatistics. The combination of these tools allowed more accurate estimation of soil Cd and Zn content averages Z and the computation of an estimation accuracy measure, i.e. standard deviation sk for averages Z. First numerical surface maps were constructed using GIS spatial analysis and the MicroStation GeoGraphics software. Topographical and geological maps at a scale of 1:50 000 were vectorized to create various thematic overlays such as: land development, building development, transport, waters and geologic structure elements. The object-oriented structure of the map elements was taken into account in the vectorization. Then geostatistical studies based on the results of geochemical analyses of soil samples taken in a regular (1 km 1 km) grid from a depth of 0.0.0.2 m within a study area of 171 km2 in the years: 2000 (50 samples) and 2001 (70 samples) were carried out. The studied area was covered by a grid of 250 100 m elementary blocks. The total number of block centres for which estimated averages Z were calculated was 7696. Prior to the geostatistical analysis basic statistical parameters were calculated. Then the empirical isotropic semivariograms were computed. The linear model combined with the nugget effect, was used to approximate the heavy metals (Zn and Cd) content semivariograms. In the last stage of the structural analysis, the cross-validation procedure was applied. For the studied sampling subpopulation (N = 120) the values of the standardized estimation error . a measure of model fit show that the adopted mathematical model represents well the empirical Cd and Zn content semivariograms. Then ordinary (block) kriging was used to estimate the averages Z of the Cd and Zn. The analyses have shown that the presence of the ore-bearing dolomites in the substratum has no significant effect on the spatial distribution of estimated Cd and Zn content averages Z. The existing high Cd and Zn concentration centre is associated with the activity of the Boles3aw Mining-Smelting Works operating in this area for several decades and with the smelting wastes accumulated in the nearby dumps and sedimentation tanks. The geostatistical studies have corroborated the geochemical Zn and Cd anomaly which is unrelated to the shape or surface extent of the current mining areas in the Olkusz region, where mining is carried on underground. The elevated Cd and Zn content subareas show similar spatial distributions of the two metals and coincide to a large extent with the location of the historical and contemporary Zn-Pb ore mining.

15

Analiza przestrzenna zawartości miedzi w środowisku gruntowo-wodnym Legnicko-Głogowskiego Okręgu Miedziowego

Namysłowska-Wilczyńska B., Pyra J.

Roczniki Geomatyki

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2005

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T. 3, z. 4

137-147

EN

The paper presents the results of the application of geostatistical methods to the spatial analysis of the variation of Cu content in the soil-water environment of the Legnica-Głogów Copper District . an industrial area with the predominance of copper ore mining and smelting in the industrial mix. Semivariogram function analysis, ordinary kriging and kriging with external drift, were used to analyse the environmental conditions. The comprehensive set of soil Cu content data was characterized by a large number of samples (n = 908) uniformly covering the area of LGCD. The data were the determinations of the Cu content in the near-surface layer of soil. The empirical Cu content semivariograms were approximated by the spherical model, the exponential model and the linear model combined with the nugget effect. Cu content averages Z were estimated at 6120 nodes of an elementary grid using ordinary (point) kriging. The elementary field dimensions were 1km´1km. The data sets for underground waters were based on a much smaller sample size (n = 31). The information, on Cu content, was collected from a network of piezometers and wells irregularly located over the analysed area. Similarly as for soil, semivariograms were computed for the Cu content in underground waters. Then the semivariograms were approximated by the spherical model and the linear model with the nugget effect. Taking into account the parameters values of the theoretical models fitted to the semivariograms, averages Z of the Cu content in the waters at 6120 nodes of the same elementary grid as the one adopted for soil were estimated using ordinary kriging. Then kriging with external drift was applied to estimate underground waters Cu content averages Z*. The data from the preceding ordinary kriging computations, i.e. estimated averages Z of the Cu content in the surface layer of soil, were used. The raster maps of the distributions of averages Z, i.e. the kriged estimates of soil contamination with Cu, constituted the background (external drift) used for the more accurate computation of underground waters Cu content averages Z The detailed analysis of the different factors which affect the spatial distribution of the elements content in the environment, such as the geological structure of the subsoil and the surface formations, the environment.s pH, the atmospheric factors and the effects of the mining and smelting operations, made it possible to determine more precisely the genesis of the analysed elements content in the natural environment and to classify it as pollution or natural geochemical enrichments.

16

Modelowanie powierzchniowego obrazu zmian obciążeń elektrycznych z zastosowaniem krigingu lognormalnego

Namysłowska-Wilczyńska B., Wilczyński A., Tymorek A.

Elektroenergetyka

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2004

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nr 1

1-15

17

Funkcja wariogramu jako narzędzie badania zmienności obciążeń elektrycznych w układzie powierzchniowym

Namysłowska-Wilczyńska B., Wilczyński A.

Elektroenergetyka

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2003

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nr 4

18-34

18

Badania geostatystyczne rozkładu zawartości metali ciężkich w gruntach

Namysłowska-Wilczyńska B., Wilczyński A.

Geoinformatica Polonica

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2000

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T. 2

51-65

PL

W artykule przedstawiono metodologię badawczą związaną z metodami geostatystyki liniowej (wariogram, kriging, kokriging), jak też nieliniowej (wariogram wskaźnikowy, kriging wskaźnikowy, symulacja warunkowa - turning bands), zastosowaną do przetwarzania danych pochodzących z monitoringu środowiskowego. Dane wejściowe do badań geostatystycznych stanowiły wyniki analiz chemicznych koncentracji zawartości w glebach metali ciężkich, tj. cynku, ołowiu, kadmu i chromu. Analizy te wykonano dla przypowierzchniowej warstwy gruntów o grubości 0,20 m. Podstawą analizy geostatystycznej była baza danych zawierająca oznaczenia zawartości metali ciężkich: Zn, Pb, Cd i Cr oraz współrzędne X i Y, określające lokalizacje poboru próbek gleby. Analizowano zasięg i stopień zanieczyszczenia gleb w rejonach znajdujących się w obszarze bezpośredniego oddziaływania przemysłu górniczo-hutniczego. Proponowane metody geostatystyczne reprezentują użyteczne narzędzia do identyfikacji anomalii geochemicznych koncentracji zawartości metali ciężkich i innych składników toksycznych w gruntach, symulacji zanieczyszczenia oraz obliczania prawdopodobieństwa wystąpienia stref o wysokim ryzyku zagrożenia.

EN

A research methodology, based on linear (variogram, kriging, co-kriging) and nonlinear geostatistics (indicator variogram, indicator kriging, conditional (turning bands) simulation), applied to the processing of environmental monitoring data is presented. Chemical analyses of heavy metals (zinc, lead, cadmium, chromium) concentrations in soils for a 0.20 m thick surface soil layer were used as input data. A database containing the data on: Zn, Pb, Cd and Cr content and coordinates X and Y specifying the sample locations constituted a basis for the geostatistical analysis. The extent and degree of soil pollution in areas directly exposed to the adverse effect of mining and metallurgical industries were analyzed. The proposed geostatistical methods are useful tools for identifying geochemical anomalies in heavy metal and other toxic constituent concentrations in soils, simulating pollution and calculating the probability of occurrence of high - hazard zones.

19

Rozpoznawanie obrazów w prospekcji stref naftowych w cenomanie i malmie synklinorium Nidy

Kotlarczyk J., Jucha S. F., Mastej W., Namysłowska-Wilczyńska B.

Gospodarka Surowcami Mineralnymi

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1999

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T. 15, z. spec.

45-68

PL

Autorzy zastosowali metodę funkcji potencjalnych (metoda rozpoznawania obrazów) w połączeniu z metodami geostatystycznymi do wskazania nowych potencjalnych obszarów akumulacji węglowodorów w mezozoicznym piętrze strukturalnym podłoża zapadliska przedkarpackiego, w jego części obejmującej S przedłużenie synklinorium nidzińskiego. Obiektami badań były otwory wiertnicze opisane zestawem 16 cech informatywnych. Cechy te charakteryzują głębokość i miąższość osadów cenomanu, ich porowatość i przepuszczalność, mineralizację i napory potencjometryczne wód wgłębnych, jak również gradienty tych cech. 16-wymiarowa informacja o każdym otworze wiertniczym została ostatecznie przetworzona w prawdopodobieństwo, że otwór odwiercony w dowolnym punkcie badanego obszaru nawierci złoże. W efekcie wskazano 9 rejonów o podwyższonym prawdopodobieństwie odkrycia złoża.

EN

Sub-Miocene basement of the Carpathian foredeep contains, most probably , unrecognized areas of potential hydrocarbon deposits, occurring in analogous conditions as those already discovered. Particularly rich data come from the area, being the prolongation of Nida synclinorium and refers to Cenomanian and Malmian deposit (fig. 1). This area was intensely explored what resulted in the discovery of several deposits (figs. 1, 2). Usually they occur in the zone where Cenomanian sandstones are wedging out (trap of 1st type), as well as in weathered, porous, karstified Malmian carbonate rocks (trap of 2nd type), also in areas where Cenomanian rocks do not occur (fig. 1). Rarely, hydrocarbon deposits appear in planar domes within the top of thick Cenomanian sandstone sequences (trap of the 3rd type e.g. Rylowa deposit). All these traps are sealed by hardly permeable Upper Cretaceous or Miocene deposits. There are credible premises indicating that in some boreholes, due to imperfect drilling technology, the presence of economic hydrocarbon accumulation could be overlooked and, thus, they were classified as barren. Moreover, vast areas between almost 700 boreholes may also contain undiscovered deposits. As follows from above data, further exploration works are needed, using different methods. As far as mathematical methods are concerned, the most useful can be the pattern recognition methods (PRM), applied jointly with geostatistical ones. The experiments on application of these methods in the area studied is the aim of investigation presented in this paper. In the analyzed case, the application of PRM consist in the calculation of probability of membership of each borehole studied to one of two target classes: to class of wells with economic hydrocarbon accumulation (R) or to those barren (W) i.e. to the computation of P[R] and P[W]. This procedure should be preceded by calculation of probability of membership of each borehole to one of two predictor classes: R* and W*, connected with appropriate target classes R and W. The predictor is the mathematical representation of a given borehole. Predictors are multivariate vectors of features, the values of which are measured in each borehole. The predictor class R* (or W*) is formed by vectors of features measured in boreholes selected from class R (and respectively W) and assented as their patterns. In the analyzed case, pattern boreholes from each deposit were selected for the predictor class R*, more or less proportionally to the number of wells in each deposit (tab. 2). Pattern boreholes for predictor class W* were selected systematically from the whole surface of the areas, situated outside deposits. 16 features were selected from the set of 27 measured (or computed) for the boreholes, the values of which were obtained in the most credible manner (tab. 1). These features were characterizing the depth and thickness of Cenomanian deposits (numbers: 1, 2, 3), their porosity and permeability (numbers: 4, 6), mineralization and potentiometric heads of groundwaters (numbers: 7-10, 17), as weIl as gradients of these teatures (numbers: 22, 23, 25-27). The examination of informativity of these features by means of Puri-Sen-Tamura test of comparison of multivariate means has shown them to form one signiticantly informative combination (fig. 3). The method of potential function in probabilistic version was applied as that of PRM. Consequently, each borehole (pattern and nonpattern, altogether 691) was characterized by one probability value of membership to predictor class R*. The application of block kriging was necessary for the production of maps of the above probability for the whole area. Preliminary geostatistical studies aIlowed to apply the compound variability model to kriging computations (figs. 4, 5). The interpolation of P[R*] probabilities and kriging standard deviations reIated with them are presented in maps (figs. 6, 7). The elaboration of resulting map needs the computation of conditional probabilities (P[RIR*], P[WIR*], P[RIW*], P[WIW*]) (cf. tab. 3). Moreover, the corrections ER and EW proposed by the present authors should be taken into consideration, according to the formula: P[R] = P[R*] (P[RIR*] + ER) + (1 - P[R*]) (P[RIW*] + Ew) where: ER = P[WIR*] P[R'IW] P[R*IR] / P[R*IW] and Ew = P(WIW*] P(R'IW] P(W*IR] / P(W*IW]. These corrections take into account the effect of faulty identification of boreholes (i.e. \delta error) during drilling on the value of the membership probability of a given well to class R. The result of such erroneous identitication is that within the class W there can be incorporated the boreholes forming subclass R' i.e. those, penetrating existing hydrocarbon deposits (fig. 12). The value of this error, expressed as P(R'IW] probability, can be estimated but a priori. The effect of the error in question on prognosis is, in fact, small (tab. 4) but by taking into account the proposed corrections we are increasing the adequacy of recognition. The probability of membership of each point of the area to target class R, is presented in isoline map (cf. fig. 8). All the known deposits considered in our experiment are Iocated in this map within the areas showing the probability higher then 0.5. Moreover, new potential areas of occurrence of deposits were indicated as isolated maxima showing probability more then 0.5. They are representing first of all the traps of 1st type (arrow numbers 1, 3, 5), as well as of 2nd one (arrow numbers 2, 4, 7). Only in one case they represent also 3rd type (arrow number 6). Consequently, there were indicated first of all the regions, characterized by small thickness of Cenomanian deposits, similarly as the vast majority of known deposits that have delivered the patterns. Therefore, other potential deposits, occurring in traps of 3rd type i.e. not related with zones where Cenomanian deposits are thin or lacking, could not be discovered. In order to explain this situation, the second experiment was carried out, in which thickness and the features correlated with it: porosity, permeability and thickness gradient of Cenomanian deposits were eliminated. The result of computation, like in previous experiment, are presented in appropriate maps (figs. 9, 10, 11). Final results of recognition have revealed almost aIl the above indicated new potential zones of hydrocarbon accumulations (excluding maximum no 6) and, moreover two successive, just representing the 3rd type of traps (fig. 11, numbers 8, 9). One of the Iast zones (no 8) showing high probability of occurrence of deposit, amounting to 0.65 has appeared SW of Rylowa deposit. Irrespective of the studies presented here, the borehole Rajsko-1 has, in fact, penetrated a deposit in that zone. This is an important confirmation of reality of results obtained by means of the pattern recognition method.