Remembering variogram and covariance function
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Abstract
This work reviews the the Empirical Covariance (CE) and Variogram (VAR) functions, related to (LSC) and Kriging Process. The paper aims get easier the learning of the LSC and Kriging showing cartographic problems when using techniques. It must rememebered LSC and kriging are used in analysis, interpolation/extrapolation of data in Geoscience and can be separated in two steps: 1) carring out the CE or VAR and 2) adjustment of those functions, usually by least squares adjustment (LSA) for predictioning. This work is focused in define Empirical Covariance and Variogram functions from original definitions with examples and points of view of authors. As application, the authors intend show differences in using geodetic reference systems and projection systems for h computation. The exposure of the coefficients adjusted by the LSA clearly shows the different responses. A last, it is suggested important observations to avoid errors in CE and VAR generation.
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References
BANDEIRA, Ana Luiza; KLEIN, Ivandro; VEIGA, Luis Augusto Koenig da. O Papel das Covariâncias na Análise de Deformação Aplicada ao Monitoramento Geodésico de Estruturas. Revista Brasileira de Cartografia, RBC, v. 73, p. 722–735, 2021. DOI: https://doi.org/10.14393/rbcv73n3-57873.
BOULOS, Paulo; CAMARGO, Ivan de. Introdução à Geometria Analítica no Espaço. São Paulo: Makron Books, 1997. P. 239.
BURROUGH, P.A.; MCDONNELL, R.A.; LLOYD, C.D. Principles of Geographical Information Systems. New York: Oxford University Press, 2015. P. 313.
CAMARGO, E.C.G.; FUCKS, S. Geoprocessamento para Projetos Ambientais. 1996. Disponível em: <http://www.dpi.inpe.br/gilberto/tutoriais/gis_ambiente/>.
CHEN, H. Techniques of fine reservoir description. In . Fine Reservoir Description. Cambridge: Elsevier, 2022. cap. 3.
COSTA, M.F. da; SANTOS, M.C. dos; FERREIRA, L.D.D. Determinação dos parâmetros para a transformação de coordenadas usando uma matriz covariância estimada por meio da colocação por mínimos quadrados. Boletim de Ciências Geodésicas, Curitiba, 2008.
FRANÇA MARQUES, Samuel de; PITOMBO, Cira Souza. Intersectando Geoestatística com Modelagem da Demanda por Transportes: um Levantamento Bibliográfico.Revista Brasileira de Cartografia, RBC, v. 72, p. 1004–1027, 2020. DOI: https://doi.org/10.14393/rbcv72nespecial50anos-56467.
GEMAEL, C. Introdução a Geodésia Física. Curitiba: Editora da UFPR, 2012.
JOURNEAU, R. Traitemaent des Mesures: Interprétation, Modélisation, Outil Statistique. Paris: Ellipses, 2009.
JOURNEL, A.G.; HUIJBREGTS, CH. J. Mining Geostatistics. New York: Academic Press, 1978. P. 593.
KAULA, W.M. Determination of the Earth’s gravitational field. [S.l.], 1963.
KENT, J.T; MARDIA, K.V.M. Spatial Analysis. Hoboken e Chichester: J.Wiley, 2022. P. 397.
KRARUP, Torben. A contribution to the mathematical foundation of physical geodesy. [S.l.], 1969.
LANDIM, P.M.B. Análise Estatatística de Dados Geológicos. São Paulo: Fundação Editora da Unesp, 1998. P. 226.
MEYER, P. L. Probabilidade: Aplicações à Estatística. 2. ed. Rio de Janeiro: Livros Técnicos e Científicos, 1983.
MORAES, C.V. Ajustamento de Observações Geodésicas - Caderno Didático. Santa Maria: UFSM, 2002. P. 150.
MORITZ, H. Advanced Least Squares Methods. Reports of OSU. n. 175. [S.l.], 1972.
OGUNDARE, J.O. Understanding least squares estimation and geomatics data analsis. Pondicherry: John Wiley Sons, Ltd, 2018.
PEREIRA, Rogers Ademir Drunn; CASTRO, Henry Montecino; FREITAS, Sílvio Rogério Correia de; DALMOLIN, Quintino; FERREIRA, Vagner Gonçalves. Determinação de função covariância local para a predição de anomalias da gravidade Bouguer e valores da gravidade visando à obtenção de números geopotenciais. Boletim de Ciências Geodésicas, v. 17, n. 2, p. 239–256, 2011.
RAMPAL, Kunwar K. Least squares collocation in Photogrammetry. Photogrammetric Engineering e Remote Sensing, v. 42, n. 5, p. 659–669, 1976.
RUFFHEAD, A. An Introduction to least squares collocation. Survey Review, v. 29, n. 224, p. 85–94, 1987.
SÁ, N.C. de; BLITZKOW, D. Colocacão por mínimos quadrados na interpolação de anomalias gravimétricas. Anais do Encontro Regional de Geofísica, Salvador, 1987.
SANSÒ, F.; SIDERIS, M. Carl Christian Tscherning: a scientific adventure in Geodesy. Journal of Geodesy, Springer, v. 89, p. 835–836, 2015. DOI: 10.1007/s00190-018-1143-1.
SNYDER, John P. Map Projections - A Working Manual. Washington: US Government, 1987. P. 397.
SOUZA, Sérgio Florêncio de; SÁ, Nelsi Cogo de. SOBRE A ESTIMAÇÃO E MODELAGEM DE FUNÇÕES COVARIÂNCIAS NA COLOCAÇÃO POR MÍNIMOS QUADRADOS. Revista Brasileira de Cartografia, RBC, v. 60, p. 99–110, 2008. DOI: https://doi.org/10.14393/rbcv60n1-44887.
TORGE, Wolfang; MÜLLER, Jürgen. Geodesy. Berlim: WalterDe Gruyter, 2012. P. x, 433.
WACKERNAGEL, H. Multivariate Geostatistics. An Introduction with Applications. Berlim: Springer Berlin, Heidelberg, 2003. P. xv, 388.