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Ambara, Joseph, Kadiri Serge Bobo, Juvenal Donfack Demesse, and Antoine David Mvondo-Ze. "Caractérisation de la compétition et de la croissance de Pericopsis elata (Harms) Van Meeuven dans les plantations de la Réserve Forestière de Deng-Deng (Est, Cameroun)." International Journal of Biological and Chemical Sciences 15, no. 2 (June 22, 2021): 559–77. http://dx.doi.org/10.4314/ijbcs.v15i2.15.
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Pericopsis elata est une espèce ligneuse à grande valeur commerciale menacée d’extinction. Les plantations d’Assamela installées dans la Réserve Forestière de Deng-Deng en 1974 ont été abandonnées après leur mise en place. Dès lors, très peu de connaissances relatives au développement de ces peuplements sont disponibles. L’objectif de la présente étude est de contribuer à la compréhension des conditions de croissance de Pericopsis elata dans la réserve et induire un aménagement efficace. Trois inventaires exhaustifs ont été conduits, au cours desquels les données dendrométriques et structurales ont été collectées. Les indices de compétition de Hegyi, les semi-variogrammes et la distribution spatiale des tiges ont été analysés et interprétés. Les densités actuelles sont sans effet limitant pour la croissance des tiges. Les effets du milieu se révèlent comme étant le facteur qui a plus d’impact sur la croissance des tiges de Pericopsis elata. La plantation de recrû (33,21 cm), moins sensible à l’effet de la densité en termes de croissance comparée aux plantations des grands layons (26,91 cm et 26,89 cm), enregistre les meilleures performances de croissance en diamètre. Ainsi, des travaux d’entretien et des éclaircies portées vers une réduction considérable des compétitions interspécifique et intra spécifique sont nécessaires.Mots clés : Indice de Hegyi, méthodes sylvicoles, modes de compétition, plantations équiennes, semi-variogramme, Cameroun.
English Title: Characterization of the competition and growth of Pericopsis elata (Harms) Van Meeuven in the plantations of the Deng-Deng Forest Reserve (East, Cameroon)Pericopsis elata is a valuable woody species threatened with extinction. The Assamela plantations established in the Deng-Deng Forest Reserve in 1974 were abandoned after their establishment. As a result, very little knowledge about the development of these stands is available. The objective of the present study is to contribute to the understanding of the growing conditions of Pericopsis elata in the Reserve and to induce proper management. Three exhaustive inventories were conducted, during which dendrometric data were collected. Hegyi’s competition indices, variograms and spatial distribution of stems were developed. Current densities have no limiting effect on stem growth. Environmental effects were found to be the factor that had the greatest impact on the growth of Pericopsis elata stems. The recruiting plantation (33.21 cm), which is less sensitive to the effect of density in terms of growth compared to the large layon method (26.91 cm and 16.89 cm), has the best growth in diameter performance. Thus, maintenance work and thinning leading to a considerable reduction in interspecific and intraspecific competition is necessary.Keywords: Regular plantations, Hegyi’s competition index, mode of competition, Silvicultural methods, semi-variogram, Cameroon.
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Champion, Hervé. "Variogramme et évolution des structures spatiales : la population de l'aire métropolitaine marseillaise." Méditerranée 79, no. 1 (1994): 75–78. http://dx.doi.org/10.3406/medit.1994.1855.
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Carbonara, Pierluigi, Teresa Silecchia, Maria Spedicato, Alessandra Acrivulis, and Giuseppe Lembo. "A GEOSTATISTICAL APPROACH TO THE ASSESSMENT OF THE SPATIAL DISTRIBUTION OF PARAPENAEUS LONGIROSTRIS (LUCAS, 1846) IN THE CENTRAL-SOUTHERN TYRRHENIAN SEA." Crustaceana 72, no. 9 (1999): 1093–108. http://dx.doi.org/10.1163/156854099504040.
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AbstractThe spatial distribution of the abundance indices of the deep-water rose shrimp Parapenaeus longirostris was investigated applying geostatistical techniques on data collected in the central southern Tyrrhenian Sea from bottom trawl surveys carried out in the autumn since 1994. Experimental variograms (auto and cross) were constructed on the variable "abundance index", expressed in kg/km2, and those variogram models best describing the spatial continuity were detected and validated by the jackknife technique. The spatial structure of the "abundance index", exhibiting a similar pattern throughout the surveys, was described by a spherical model and characterized by a spatial continuity at a small scale level in the whole area. The linear geostatistical approach was applied by different kriging techniques and the estimates extended to the spatio-temporal dimension, in this case adopting the co-regionalized models and applying the cokriging technique. This method applied to the spatial dimension (abundance index and depth). Also, linking the spatial and temporal dimension of the abundance indices, measured in two different years, contributed to represent a more accurate picture of the abundance distribution, and allowed the detection of a temporal persistence of the localization of areas with higher abundance, reducing the standard deviation of the estimation error. This information, if coupled with an analysis of the geographical allocation of the fishing effort, could be of importance in stock assessment, allowing some variant application of the composite surplus production models. La distribution spatiale des indices d'abondance de la crevette rose d'eau profonde Parapenaeus longirostris a ete etudiee en appliquant les techniques de la geostatistique aux donnees collectees dans le centre-sud de la mer Tyrrhenienne au cours des campagnes de chalutage demersal realisees pendant l'automne, depuis 1994. Les variogrammes experimentaux (auto et cross) ont ete construits sur la variable "indice d'abondance", exprimee en kg/km2, et les modeles de variogramme decrivants le mieux la continuite spatiale ont ete determines et valides par la technique du "jackknife". La structure spatiale de l'indice d'abondance a presente le meme aspect pour tous les echantillonages; elle a ete decrite au moyen d'un modele spherique et caracterisee par une continuite spatiale a petite echelle dans toute la zone. La geostatistique lineaire a ete appliquee en utilisant differentes techniques du krigeage, et les estimations ont ete etendues a la dimension spatio-temporelle en appliquant les modeles coregionalises et la technique du cokrigeage. Cette methode, appliquee soit dans la dimension spatiale (indice d'abondance et profondeur), soit dans la dimension spatio-temporelle en considerant l'indice d'abondance echantillonne en deux annees differentes, a contribue a representer une image plus precise de la distribution de l'abondance, et a permis de detecter une persistance temporelle de la localisation des aires a plus grande abondance, en reduisant l'ecart type de l'erreur d'estimation. Cette information, avec l'analyse de l'allocation geografique de l'effort de peche, pourrait etre importante dans l'evaluation des stocks, en permettant l'application, avec quelques variantes, des modeles composites de production.
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Rakotonirina, M. D. L., and Jean-Paul Ngbolua. "Modélisation géologique et estimation d’un gisement de Fer de Bekisopa, Madagascar." Revue Congolaise des Sciences & Technologies 2, no. 4 (February 10, 2022): 498–504. http://dx.doi.org/10.59228/rcst.023.v2.i4.56.
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Cette étude a pour objectif de réaliser une analyse approfondie de la géologie du gisement de fer en question et d'explorer son potentiel d'exploitation. En combinant des observations sur le terrain, des opérations de forage, des analyses géologiques et l'utilisation d'outils de modélisation, notre intention est de parvenir à une compréhension approfondie de la composition, de la distribution et des caractéristiques géologiques du gisement de fer de Bekisopa découvert par H. Besairie en 1933. L'évaluation des réserves de fer a été menée en appliquant des méthodes géostatistiques, notamment le krigeage. Les données issues des forages, conjointement avec les informations géologiques provenant des modèles tridimensionnels, ont servi à établir des variogrammes et des modèles de continuité spatiale. Cette démarche a permis d'aboutir à une estimation quantitative des réserves de fer présentes dans le gisement. Un total de trente forages a été réalisé sur une superficie d'un kilomètre carré. Ces données de forages ont été cruciales pour calculer un volume du gisement de l'ordre de 25 000 000 de mètres cubes, compte tenu d'une densité moyenne du gisement de 4 500 kg/m3 et d'une teneur moyenne de 40%. Cette estimation a conduit à une valeur de ressources ferreuses avoisinant les quarante millions (40 000 000) de tonnes. Étant donné que le minerai se trouve à une profondeur relativement accessible en surface, l'option d'une exploitation à ciel ouvert se présente comme une alternative envisageable et attrayante. Ce type d'exploitation implique l'extraction du minerai à partir de vastes fosses découvertes, une approche économiquement viable lorsque les ressources minérales sont situées près de la surface. Mots clés : Modélisation, caractéristiques géologiques, Bekisopa, krigeage, variogramme.
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Maus, Stefan, K. P. Sengpiel, B. Röttger, B. Siemon, and E. A. W. Tordiffe. "Variogram analysis of helicopter magnetic data to identify paleochannels of the Omaruru River, Namibia." GEOPHYSICS 64, no. 3 (May 1999): 785–94. http://dx.doi.org/10.1190/1.1444588.
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The geomagnetic field over sedimentary basins is very sensitive to variations in basement depth. Therefore, magnetic surveys are widely used to map basement topography in petroleum and groundwater exploration. We propose variogram analysis as a more accurate alternative to power spectral methods. Data variograms are computed from aeromagnetic flight‐line data. To estimate depth, the data variograms are compared with model variograms for a range of source depths. We use the exact space domain counterparts of a fractal power spectral model as model variograms. To demonstrate the utility of this method for groundwater exploration, we map the basement topography of the Omaruru Alluvial Plains in Namibia. A comparison with electromagnetic (EM) resistivities and drilling information confirms the high accuracy—but also the limitations—of variogram analysis depth. Variogram analysis makes maximum use of short‐wavelength contributions to the magnetic signal, which is the key to the resolution of shallow basement topography. Moreover, by using a realistic source model and avoiding extensive data preconditioning and the transform to wavenumber domain, variogram analysis is likely to provide improved magnetic depth estimates even for deep basins.
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Bénina, Touaïbia, Inegliz Souhila, and Ould Amara Arezki. "Couplage d’une analyse en composantes principales et d’une approche géostatistique pour l’élaboration de cartes pluviométriques du Centre de l’Algérie du Nord." Revue des sciences de l'eau 19, no. 3 (September 13, 2006): 213–19. http://dx.doi.org/10.7202/013539ar.
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Résumé Nous examinons dans cet article, la répartition spatiale de la pluviométrie annuelle en vue de sa cartographie en combinant l’analyse en composantes principales (ACP) et la théorie des variables régionalisées. Deux vecteurs régionaux représentant la tendance pluviométrique la plus probable pour l’homogénéisation des données se sont dégagés. Les pluies annuelles probables de période de retour cinq et dix ans sont évaluées afin de compléter l’information donnée par les pluies annuelles. Les meilleurs modèles de la relation pluie-relief sont aussi recherchés. Par régression multiple, un certain nombre de paramètres morphométriques susceptibles d’expliquer les pluies est identifié, pour leur évaluation en tout point de l’espace. Le variogramme des résidus a présenté une structure spatiale nette. Par krigeage, les paramètres variographiques définis sont calés pour leur interpolation entre les postes pluviométriques. La cartographie automatique a permis d’élaborer les cartes des pluies moyennes annuelles et celles de période de retour cinq et dix ans.
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Maus, Stefan. "Variogram analysis of magnetic and gravity data." GEOPHYSICS 64, no. 3 (May 1999): 776–84. http://dx.doi.org/10.1190/1.1444587.
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Model variograms describe the space domain statistics of magnetic and gravity data. Variogram analysis can be used to map intensity, depth, and scaling exponent (self‐correlation) of source. In previous statistical methods the measured data were gridded and transformed to the wavenumber domain; then their power spectrum was analyzed using a spectral model. To avoid the loss and distortion of information during gridding and wavenumber domain transform, I transform the spectral model to the space domain instead. Variograms are the appropriate space domain counterparts of magnetic and gravity power spectra. The variogram of the field above a self‐similar half‐space model is governed by three parameters: intensity, depth, and scaling exponent. These source parameters can be mapped with high resolution and accuracy by fitting model variograms directly to magnetic and gravity line data variograms.
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Skøien, J. O., and G. Blöschl. "Catchments as space-time filters – a joint spatio-temporal geostatistical analysis of runoff and precipitation." Hydrology and Earth System Sciences Discussions 3, no. 3 (June 12, 2006): 941–85. http://dx.doi.org/10.5194/hessd-3-941-2006.
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Abstract. In this paper catchments are conceptualised as linear space-time filters. Catchment area A is interpreted as the spatial support and the catchment response time Tis interpreted as the temporal support of the runoff measurements. These two supports are related by T~Aκ which embodies the space-time connections of the rainfall-runoff process from a geostatistical perspective. To test the framework, spatio-temporal variograms are estimated from about 30 years of quarter hourly precipitation and runoff data from about 500 catchments in Austria. In a first step, spatio-temporal variogram models are fitted to the sample variograms for three catchment size classes independently. In a second step, variograms are fitted to all three catchment size classes jointly by estimating the parameters of a point/instantaneous spatio-temporal variogram model and aggregating (regularising) it to the spatial and temporal scales of the catchments. The exponential, Cressie-Huang and product-sum variogram models give good fits to the sample variograms of runoff with dimensionless errors ranging from 0.02 to 0.03, and the model parameters are plausible. This indicates that the first order effects of the spatio-temporal variability of runoff are indeed captured by conceptualising catchments as linear space-time filters. The scaling exponent κ is found to vary between 0.3 and 0.4 for different variogram models.
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Skøien, J. O., and G. Blöschl. "Catchments as space-time filters – a joint spatio-temporal geostatistical analysis of runoff and precipitation." Hydrology and Earth System Sciences 10, no. 5 (September 26, 2006): 645–62. http://dx.doi.org/10.5194/hess-10-645-2006.
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Abstract. In this paper catchments are conceptualised as linear space-time filters. Catchment area A is interpreted as the spatial support and the catchment response time T is interpreted as the temporal support of the runoff measurements. These two supports are related by T~Aκ which embodies the space-time connections of the rainfall-runoff process from a geostatistical perspective. To test the framework, spatio-temporal variograms are estimated from about 30 years of quarter hourly precipitation and runoff data from about 500 catchments in Austria. In a first step, spatio-temporal variogram models are fitted to the sample variograms for three catchment size classes independently. In a second step, variograms are fitted to all three catchment size classes jointly by estimating the parameters of a point/instantaneous spatio-temporal variogram model and aggregating (regularising) it to the spatial and temporal scales of the catchments. The exponential, Cressie-Huang and product-sum variogram models give good fits to the sample variograms of runoff with dimensionless errors ranging from 0.02 to 0.03, and the model parameters are plausible. This indicates that the first order effects of the spatio-temporal variability of runoff are indeed captured by conceptualising catchments as linear space-time filters. The scaling exponent κ is found to vary between 0.3 and 0.4 for different variogram models.
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Díaz, Arturo Buelga, César Castañón Fernández, Gonzalo Ares, Daniel Arias Prieto, and Isidro Diego Álvarez. "RecMin Variograms: Visualisation and Three-Dimensional Calculation of Variograms in Block Modelling Applications in Geology and Mining." International Journal of Environmental Research and Public Health 19, no. 19 (September 29, 2022): 12454. http://dx.doi.org/10.3390/ijerph191912454.
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Variogram calculation is a fundamental tool for studying ore grade data in mineral deposits. It allows the discovery of hidden structures within the data and preferential directions of mineralization where the geological continuity is longer. The variogram allows us to classify samples and to define both the search radii for interpolation and the use of kriging as an interpolation and resource classification method. It is not difficult to use it in one dimension; complexity increases in two dimensions as the necessity to search for possible grade anisotropies in all directions arises. Three-dimensionally it is even more difficult to try to define the parameters of lag, bandwidth, and tolerances that define the data of the variogram calculation algorithm. There are rules of thumb to help in the development, but a trial-and-error approach is used in order to find enough sample pairs to allow the generation of variograms truly representative of the data. In this paper, two strategies are shown to help in variogram construction, the use of variogram maps and the graphical representation of the pair search areas (cones or pencils). The freeware tool RecMin Variograms has been developed and is freely available for download at its website; it is easy to learn and use. R code based on RGeostats libraries is used to check the operation and results of RecMin Variograms. Applying geostatistics to mineral deposits is essential to know the areas with the highest grades, thus allowing exact planning of future mining exploitation and minimizing mine footprint and environmental impact.
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García-Pérez, Alfonso. "New Robust Cross-Variogram Estimators and Approximations of Their Distributions Based on Saddlepoint Techniques." Mathematics 9, no. 7 (April 1, 2021): 762. http://dx.doi.org/10.3390/math9070762.
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Let Z(s)=(Z1(s),…,Zp(s))t be an isotropic second-order stationary multivariate spatial process. We measure the statistical association between the p random components of Z with the correlation coefficients and measure the spatial dependence with variograms. If two of the Z components are correlated, the spatial information provided by one of them can improve the information of the other. To capture this association, both within components of Z(s) and across s, we use a cross-variogram. Only two robust cross-variogram estimators have been proposed in the literature, both by Lark, and their sample distributions were not obtained. In this paper, we propose new robust cross-variogram estimators, following the location estimation method instead of the scale estimation one considered by Lark, thus extending the results obtained by García-Pérez to the multivariate case. We also obtain accurate approximations for their sample distributions using saddlepoint techniques and assuming a multivariate-scale contaminated normal model. The question of the independence of the transformed variables to avoid the usual dependence of spatial observations is also considered in the paper, linking it with the acceptance of linear variograms and cross-variograms.
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Bhowmik, A. K., and P. Cabral. "Spatially shifting temporal points: estimating pooled within-time series variograms for scarce hydrological data." Hydrology and Earth System Sciences Discussions 12, no. 2 (February 20, 2015): 2243–65. http://dx.doi.org/10.5194/hessd-12-2243-2015.
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Abstract. Estimation of pooled within-time series (PTS) variograms is a frequently used technique for geostatistical interpolation of continuous hydrological variables in spatial data-scarce regions conditional that time series are available. The only available method for estimating PTS variograms averages semivariances, which are computed for individual time steps, over each spatial lag within a pooled time series. However, semivariances computed by a few paired comparisons for individual time steps are erratic and hence they may hamper precision of PTS variogram estimation. Here, we outlined an alternative method for estimating PTS variograms by spatializing temporal data points and shifting them. The data were pooled by ensuring consistency of spatial structure and stationarity within a time series, while pooling sufficient number of data points for reliable variogram estimation. The pooled spatial data point sets from different time steps were assigned to different coordinate sets on the same space. Then a semivariance was computed for each spatial lag within a pooled time series by comparing all point pairs separable by that spatial lag, and a PTS variogram was estimated by controlling the lower and upper boundary of spatial lags. Our method showed higher precision than the available method for PTS variogram estimation and was developed by using the freely available R open source software environment. The method will reduce uncertainty for spatial variability modeling while preserving spatiotemporal properties of data for geostatistical interpolation of hydrological variables in spatial data-scarce developing countries.
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Taylor, James A., John-Paul Praat, and A. Frank Bollen. "Spatial Variability of Kiwifruit Quality in Orchards and Its Implications for Sampling and Mapping." HortScience 42, no. 2 (April 2007): 246–50. http://dx.doi.org/10.21273/hortsci.42.2.246.
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Published statistics on the spatial variation of fruit quality observed in orchards has been rudimentary to date. Dry matter and fruit weight data were collected spatially within 11 kiwifruit (Actinidia deliciosa var. deliciosa ‘Hayward’) orchards in the Bay of Plenty, New Zealand, to characterize the variability in fruit quality in terms of nonspatial and spatial statistics. Fruit weight was statistically more variable and exhibited a stronger spatial structure than the dry matter data. Individual variograms were derived for each orchard and then all the data were collated into average variograms for both quality attributes. The average variogram parameters were used to determine the optimum spacing for grid sampling to achieve a desired level of confidence when interpolating the data. A grid spacing of 28 m appears suitable for mapping fruit quality, provided sufficient area exists to collect enough points to perform block kriging. Plots of individual orchard and average variograms, and a table of nonspatial and variogram statistics are presented as a reference for future work in this area.
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Hamada, Szoldatits, Grippo, and Hartmann. "Remotely Sensed Spatial Structure as an Indicator of Internal Changes of Vegetation Communities in Desert Landscapes." Remote Sensing 11, no. 12 (June 24, 2019): 1495. http://dx.doi.org/10.3390/rs11121495.
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Desert environments are sensitive to disturbances, and their functions and processes can take many years to recover. Detecting early signs of disturbance is critical, but developing such a capability for expansive remote desert regions is challenging. Using a variogram and 15-cm resolution Visible Atmospherically Resistant Index (VARI) imagery, we examined the usefulness of the spatial structure of desert lands for monitoring early signs of habitat changes using the Riverside East solar energy zone located within Riverside County, California. We tested the method on four habitat types in the region, Parkinsonia florida–Olneya tesota, Chorizanthe rigida–Geraea canescens, Larrea tridentata–Ambrosia dumosa, and Larrea tridentata–Encelia farinosa alliances. The results showed that the sill, range, form, and partial sill of the variogram generated from VARI strongly correlate with overall vegetation cover, average canopy size, canopy size variation, and spatial structure within a dryland habitat, respectively. Establishing a baseline of variogram parameters for each habitat and comparing to subsequent monitoring parameters would be most effective for detecting internal changes because values of variogram parameters would not match absolute values of landscape properties. When monitoring habitats across varying landscape characteristics, a single appropriate image resolution would likely be the resolution that could adequately characterize the habitat dominated by the smallest vegetation. For the variogram generated from VARI, which correlates to vegetation greenness, the sills may indicate the health of vegetation communities. However, further studies are warranted to determine the effectiveness of variograms for monitoring habitat health. Remotely sensed landscape structure obtained from variograms could provide complementary information to traditional methods for monitoring internal changes in dryland vegetation communities.
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Dimov, Luben D., Jim L. Chambers, and Brian Roy Lockhart. "Spatial Continuity of Tree Attributes in Bottomland Hardwood Forests in the Southeastern United States." Forest Science 51, no. 6 (December 1, 2005): 532–40. http://dx.doi.org/10.1093/forestscience/51.6.532.
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Abstract Sustainable forest management and conservation require understanding of underlying basic structural and competitive relationships. To gain insight into these relationships, we analyzed spatial continuity of tree basal area (BA) and crown projection area (CPA) on twelve 0.64-ha plots in four mixed bottomland hardwood stands in Louisiana, Arkansas, and Mississippi. Variogram range indicated that BA spatial continuity of trees with dbh >10.0 cm extended an average 4.5 m. This distance equaled the quadratic mean crown radius (QMCR) of the overstory trees. Overall, 95% of the variability in BA was accounted for by the spatially structured variance and could be modeled as spatial dependence. Removal of suppressed trees from the analyses reduced the variability in BA at small separation distances and increased the variogram range. The average spatial continuity of unsuppressed trees averaged 18.2 m and was 17.6, 18.5, and 18.5 m based on the BA variograms, CPA variograms, and cross-variograms, respectively. This distance corresponded to four times the QMCR of the overstory trees and extended far enough to encompass the first- and second-order neighbors. The results suggest an existence of complex competitive influences and confirm findings in nonwoody vegetation that competitive effects can propagate beyond the direct neighbors. FOR. SCI. 51(6):532–540.
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Chiverton, A., J. Hannaford, I. P. Holman, R. Corstanje, C. Prudhomme, T. M. Hess, and J. P. Bloomfield. "Using variograms to detect and attribute hydrological change." Hydrology and Earth System Sciences 19, no. 5 (May 20, 2015): 2395–408. http://dx.doi.org/10.5194/hess-19-2395-2015.
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Abstract. There have been many published studies aiming to identify temporal changes in river flow time series, most of which use monotonic trend tests such as the Mann–Kendall test. Although robust to both the distribution of the data and incomplete records, these tests have important limitations and provide no information as to whether a change in variability mirrors a change in magnitude. This study develops a new method for detecting periods of change in a river flow time series, using temporally shifting variograms (TSVs) based on applying variograms to moving windows in a time series and comparing these to the long-term average variogram, which characterises the temporal dependence structure in the river flow time series. Variogram properties in each moving window can also be related to potential meteorological drivers. The method is applied to 91 UK catchments which were chosen to have minimal anthropogenic influences and good quality data between 1980 and 2012 inclusive. Each of the four variogram parameters (range, sill and two measures of semi-variance) characterise different aspects of the river flow regime, and have a different relationship with the precipitation characteristics. Three variogram parameters (the sill and the two measures of semi-variance) are related to variability (either day-to-day or over the time series) and have the largest correlations with indicators describing the magnitude and variability of precipitation. The fourth (the range) is dependent on the relationship between the river flow on successive days and is most correlated with the length of wet and dry periods. Two prominent periods of change were identified: 1995–2001 and 2004–2012. The first period of change is attributed to an increase in the magnitude of rainfall whilst the second period is attributed to an increase in variability of the rainfall. The study demonstrates that variograms have considerable potential for application in the detection and attribution of temporal variability and change in hydrological systems.
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Chiverton, A., J. Hannaford, I. Holman, R. Corstanje, C. Prudhomme, T. M. Hess, and J. P. Bloomfield. "Using variograms to detect and attribute hydrological change." Hydrology and Earth System Sciences Discussions 11, no. 10 (October 23, 2014): 11763–95. http://dx.doi.org/10.5194/hessd-11-11763-2014.
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Abstract. There have been many published studies aiming to identify temporal changes in river flow time-series, most of which use monotonic trend tests such as the Mann–Kendall test. Although robust to both the distribution of the data and incomplete records, these tests have important limitations and provide no information as to whether a change in variability mirrors a change in magnitude. This study develops a new method for detecting periods of change in a river flow time-series using Temporally Shifting Variograms, TSV, based on applying variograms to moving windows in a time-series and comparing these to the long-term average variogram, which characterises the temporal dependence structure in the river flow time-series. Variogram properties in each moving window can also be related to potential meteorological drivers. The method is applied to 94 UK catchments which were chosen to have minimal anthropogenic influences and good quality data between 1980 and 2012 inclusive. Each of the four variogram parameters (Range, Sill and two measures of semi-variance) characterise different aspects of change in the river flow regime, and have a different relationship with the precipitation characteristics. Three variogram parameters (the Sill and the two measures of semi-variance) are related to variability (either day-to-day or over the time-series) and have the largest correlations with indicators describing the magnitude and variability of precipitation. The fourth (the Range) is dependent on the relationship between the river flow on successive days and is most correlated with the length of wet and dry periods. Two prominent periods of change were identified: 1995 to 2001 and 2004 to 2012. The first period of change is attributed to an increase in the magnitude of rainfall whilst the second period is attributed to an increase in variability in the rainfall. The study demonstrates that variograms have considerable potential for application in the detection and attribution of temporal variability and change in hydrological systems.
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Lv, Yingbo, Yifei Liang, and HongXue Wang. "Research on variogram analysis method for 3D modeling of sandstone reservoir." E3S Web of Conferences 416 (2023): 01018. http://dx.doi.org/10.1051/e3sconf/202341601018.
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Analysis of variogram is a necessary step in 3D stochastic modeling, and different settings of variograms can directly affect the final distribution of model attribute. How to optimize the setting of variogram parameters by unit and facies type has become a key step in geological modeling. This article focuses on the reservoir within sedimentary background of fluvial-deltas in the layer SII7+8 which develops multiple sedimentary microfacies, such as fluvial channels, abandoned fluvial channels, flood plains, and natural levee with strong heterogeneity, so as to study the impact of changes of the variogram parameters on the simulation results of reservoir properties, in order to explore the analysis method of the variogram. On this basis, the reservoir is divided into 3 types of sand bodies and 11 types of sedimentary microfacies based on net pay thickness, sedimentary environment, and main sand scale and morphology. The distribution characteristics and extension scale of different facies types on the plane are classified and studied, in order to determine the characteristic parameters of the variogram of different types of sand bodies, accurately simulate the distribution characteristics of reservoir physical property, and further improve the accuracy of the 3D attribute model.
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Du, Dewen, Shijuan Yan, Fengli Yang, Zhiwei Zhu, Qinglei Song, and Gang Yang. "Kriging Interpolation for Evaluating the Mineral Resources of Cobalt-Rich Crusts on Magellan Seamounts." Minerals 8, no. 9 (August 29, 2018): 374. http://dx.doi.org/10.3390/min8090374.
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The evaluation of mineral resources on seamounts by geostatistics faces two key challenges. First, the conventional distance/orientation- and the simple distance-based variogram functions used are ineffective at expressing the spatial self-correlation and continuity of cobalt-rich crust thicknesses on seamounts. Second, the sampling stations used for a single seamount are generally very sparsely distributed because of the high survey costs, which results in an insufficient number of information points for variogram fitting. Here, we present an alternative geostatistical method that uses distance/gradient- and distance/relative-depth-based variograms to process data collected from several neighboring seamounts, allowing the variogram fitting. The application example reported for the Magellan seamounts demonstrates the suitability of the method for evaluating the mineral resources of cobalt-rich crusts. The method could be effective also for the analysis of surface data obtained from mountain slopes on land (e.g., soil).
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Kint, Vincent, Marc van Meirvenne, Lieven Nachtergale, Guy Geudens, and Noël Lust. "Spatial Methods for Quantifying Forest Stand Structure Development: A Comparison Between Nearest-Neighbor Indices and Variogram Analysis." Forest Science 49, no. 1 (February 1, 2003): 36–49. http://dx.doi.org/10.1093/forestscience/49.1.36.
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Abstract Insight into forest stand structure is of capital importance for understanding forest ecosystem structure and function. The ability of two spatial methods—based on (1) nearest-neighbor indices and (2) geostatistical variogram analysis—to quantify forest stand structure and its development over short time periods was investigated in two mixed Scots pine stands. Results show that the two methods are complementary in quantifying the three components of forest stand structure: positioning, mixture, and differentiation. The principal advantage of nearest-neighbor indices was their capacity for detecting subtle structure changes; moreover, they are easy to calculate and interpret. Variograms of height and indicator variograms of presence/absence data were more complicated in their use and required more input data, but provided additional information on the number, impact, and range of structure-determining factors such as competition and management. In this context, the concept of the mark variograms is discussed. FOR. SCI. 49(1):36–49.
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Lark, R. Murray, Elliott M. Hamilton, Belinda Kaninga, Kakoma K. Maseka, Moola Mutondo, Godfrey M. Sakala, and Michael J. Watts. "Planning spatial sampling of the soil from an uncertain reconnaissance variogram." SOIL 3, no. 4 (December 13, 2017): 235–44. http://dx.doi.org/10.5194/soil-3-235-2017.
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Abstract. An estimated variogram of a soil property can be used to support a rational choice of sampling intensity for geostatistical mapping. However, it is known that estimated variograms are subject to uncertainty. In this paper we address two practical questions. First, how can we make a robust decision on sampling intensity, given the uncertainty in the variogram? Second, what are the costs incurred in terms of oversampling because of uncertainty in the variogram model used to plan sampling? To achieve this we show how samples of the posterior distribution of variogram parameters, from a computational Bayesian analysis, can be used to characterize the effects of variogram parameter uncertainty on sampling decisions. We show how one can select a sample intensity so that a target value of the kriging variance is not exceeded with some specified probability. This will lead to oversampling, relative to the sampling intensity that would be specified if there were no uncertainty in the variogram parameters. One can estimate the magnitude of this oversampling by treating the tolerable grid spacing for the final sample as a random variable, given the target kriging variance and the posterior sample values. We illustrate these concepts with some data on total uranium content in a relatively sparse sample of soil from agricultural land near mine tailings in the Copperbelt Province of Zambia.
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Gomes, Natalino M., Carlos R. de Mello, Manoel A. de Faria, Antônio M. da Silva, and Marcelo S. de Oliveira. "AJUSTE DE VARIOGRAMAS NO ESTUDO DA CONTINUIDADE ESPACIAL DE ATRIBUTOS FÍSICOS DO SOLO." IRRIGA 12, no. 1 (March 27, 2007): 92–107. http://dx.doi.org/10.15809/irriga.2007v12n1p92-107.
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AJUSTE DE VARIOGRAMAS NO ESTUDO DA CONTINUIDADE ESPACIAL DE ATRIBUTOS FÍSICOS DO SOLO Natalino M. Gomes1; Carlos R. de Mello2; Manoel A. de Faria2; Antônio M. da Silva2; Marcelo S. de Oliveira31Universidade Federal de Lavras, Lavras, MG, natalagricola@yahoo.com.br2Departamento de Engenharia, Universidade Federal de Lavras, Lavras, MG3Departamento de Ciências Exatas, 1Universidade Federal de Lavras, Lavras, MG 1 RESUMO Este trabalho teve como objetivo estudar a seleção de métodos e modelos de ajuste de variogramas aplicados a atributos físicos do solo, importante etapa na análise da estrutura de continuidade espacial. O trabalho foi desenvolvido a partir de dados de: densidade do solo (Ds), teor de matéria orgânica (MO), argila dispersa em água (ADA) e frações texturais – areia, silte e argila, coletados na camada de0 a0,15 mna bacia hidrográfica do ribeirão da Marcela, Região Alto Rio Grande, obedecendo grid quadrado de240 mx240 m(macro escala) e60 mx60 mmicroescala, totalizando 165 pontos amostrais. Os dados foram submetidos à análise estatística descritiva e geoestatística, com o ajuste de variogramas do tipo esférico e exponencial pelos métodos dos quadrados mínimos ponderados (QMP) e máxima verossimilhança (MV), utilizando o programa GeoR. Os valores de coeficiente de variação para a densidade do solo e teor de argila foram da ordem de 9,02% e 12,01%, respectivamente, superior a 30% para os demais atributos. Observou-se ocorrência de dependência espacial para todos os atributos, com grau moderado (25% £ GD £ 75%) para densidade do solo e forte (GD > 75%) para os demais. Constatou-se também ligeira superioridade do ajuste feito por máxima verossimilhança para o modelo exponencial para todos os atributos, exceção feita à matéria orgânica, cujo melhor modelo foi o esférico ajustado por quadrados mínimos ponderados. UNITERMOS: Geoestatística, quadrados mínimos ponderados, máxima verossimilhança. GOMES, N. M.; MELLO, C. R. de; FARIA, M. A. de; SILVA, A. M. da; OLIVEIRA, M. S. de. VARIOGRAM ADJUSTMENT FOR CONTINUITY SPATIAL STUDY OFSOIL PHYSICAL CHARACTERISTICS 2 ABSTRACT This study aimed to examine the selection of methods and models of variograms adjustment applied to soil physical characteristics because it is an important stage of the continuity spatial structure analysis. This study was developed using data from soil bulk density (BD), organic matter (OM), clay water disperses (CWD), and particle-size distribution – sand, silt and clay. Soil samples were collected from 0-0.15-m layer, in Ribeirão Marcela Watershed, Alto Rio Grande region, Minas Gerais state, following a 240m x 240m square grid (macro-scale) and a 60m x 60m one(micro-scale), summing up 165 sampled points. Data were submitted to descriptive statistical and geostatistical analyses, with spherical and exponential variogram models, through weighted minimum square (QMP) and maximum likelihood (MV) methods, using a GeoR software. Variation coefficient values for soil bulk density and clay percentage were higher than the other studied variables. Spatial dependence was observed for all variables, with moderate degree (25% £ GD £ 75%) for soil bulk density and strong (GD > 75%), for the others. A slightly superior exponential model, adjusted by maximum likelihood for all variables, except for organic matter, was verified. The best model was the spherical one, adjusted by weighted minimum square. KEYWORDS: Geostatistics, weighted minimum square, maximum likelihood
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Herzfeld, Ute Christina, Helmut Mayer, Wolfgang Feller, and Matthias Mimler. "Geostatistical analysis of glacier-roughness data." Annals of Glaciology 30 (2000): 235–42. http://dx.doi.org/10.3189/172756400781820769.
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AbstractIn most glaciological and hydrological models, surface roughness of snow and ice is an important parameter. However, roughness is generally used only as an estimated parameter for lack of available observations. In this paper, we present a method to collect and analyze ice-surface-roughness data using a specially designed instrument for survey and geostatistical methods for analysis. The glacier-roughness sensor (GRS), built at the University of Trier, records variations in microtopography at 0.2 m × 0.1 m resolution when pulled across an ice surface. Global positioning system data are used for location. After several processing steps, the data are analyzed using geostatistical methods. The mathematical tool used to achieve a morphological characterization of ice-surface types is the variogram. GRS data, variograms and surface roughness analysis are ideal matches for morphological characterization, because none of them requires or provides absolute elevation values. Morphology is described not by absolute elevation values, but by the change of elevation in space which is the derivative of elevation (surface-roughness values). The variogram is calculated from incremental values. Parameters extracted from variograms of GRS data serve to distinguish lake surfaces, wind structures, ridge-and- vaUey systems, melting structures and blue-ice areas. Examples are from Jakobshavn Isbræ drainage basin, West Greenland.
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He, Y., D. Chen, B. G. Li, Y. F. Huang, K. L. Hu, Y. Li, and I. R. Willett. "Sequential indicator simulation and indicator kriging estimation of 3-dimensional soil textures." Soil Research 47, no. 6 (2009): 622. http://dx.doi.org/10.1071/sr08218.
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The complex distribution characteristics of soil textures at a large or regional scale are difficult to understand with the current state of knowledge and limited soil profile data. In this study, an indicator variogram was used to describe the spatial structural characteristics of soil textures of 139 soil profiles. The profiles were 2 m deep with sampling intervals of 0.05 m, from an area of 15 km2 in the North China Plain. The ratios of nugget-to-sill values (SH) of experimental variograms of the soil profiles in the vertical direction were equal to 0, showing strong spatial auto-correlation. In contrast, SH ratios of 0.48–0.81 in the horizontal direction, with sampling distances of ~300 m, showed weaker spatial auto-correlation. Sequential indicator simulation (SIS) and indicator kriging (IK) methods were then used to simulate and estimate the 3D spatial distribution of soil textures. The outcomes of the 2 methods were evaluated by the reproduction of the histogram and variogram, and by mean absolute error of predictions. Simulated results conducted on dense and sparse datasets showed that when denser sample data are used, complex patterns of soil textures can be captured and simulated realisations can reproduce variograms with reasonable fluctuations. When data are sparse, a general pattern of major soil textures still can be captured, with minor textures being poorly simulated or estimated. The results also showed that when data are sufficient, the reproduction of the histogram and variogram by SIS was significantly better than by the IK method for the predominant texture (clay). However, when data are sparse, there is little difference between the 2 methods.
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Soltani-Mohammadi, Saeed, and Mohammad Safa. "A Simulated Annealing based Optimization Algorithm for Automatic Variogram Model Fitting." Archives of Mining Sciences 61, no. 3 (September 1, 2016): 635–49. http://dx.doi.org/10.1515/amsc-2016-0045.
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AbstractFitting a theoretical model to an experimental variogram is an important issue in geostatistical studies because if the variogram model parameters are tainted with uncertainty, the latter will spread in the results of estimations and simulations. Although the most popular fitting method is fitting by eye, in some cases use is made of the automatic fitting method on the basis of putting together the geostatistical principles and optimization techniques to: 1) provide a basic model to improve fitting by eye, 2) fit a model to a large number of experimental variograms in a short time, and 3) incorporate the variogram related uncertainty in the model fitting. Effort has been made in this paper to improve the quality of the fitted model by improving the popular objective function (weighted least squares) in the automatic fitting. Also, since the variogram model function (£) and number of structures (m) too affect the model quality, a program has been provided in the MATLAB software that can present optimum nested variogram models using the simulated annealing method. Finally, to select the most desirable model from among the single/multi-structured fitted models, use has been made of the cross-validation method, and the best model has been introduced to the user as the output. In order to check the capability of the proposed objective function and the procedure, 3 case studies have been presented.
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Chihi, Hayet, Michel Tesson, Alain Galli, Ghislain de Marsily, and Christian Ravenne. "Geostatistical modelling (3D) of the stratigraphic unit surfaces of the Gulf of Lion western margin (Mediterranean Sea) based on seismic profiles." Bulletin de la Société Géologique de France 178, no. 1 (January 1, 2007): 25–38. http://dx.doi.org/10.2113/gssgfbull.178.1.25.
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Abstract The purpose of this study is to build efficiently and automatically a three-dimensional geometric model of the stratigraphic units of the Gulf of Lion margin on the basis of geophysical investigations by a network of seismic profiles, using geostatistics. We want to show that geostatistics can produce unbiased maps of the morphology of submarine stratigraphic units, and furthermore that some specific features of these units can be found, that classical manual mapping may ignore. Depth charts of each surface identified by seismic profiling describe the geometry of these units. The geostatistical approach starts with a statistical analysis to determine the type and parameters of the variograms of the variable “depth” of each identified surface. The variograms of these surfaces show that they are mostly non-stationary. We therefore tried the following two non-stationary methods to map the desired surfaces : (i) the method of universal kriging in case the underlying variogram was directly accessible; (ii) the method of increments if the underlying variogram was not directly accessible. After having modelled the variograms of the increments and of the variable itself, we calculated the surfaces by kriging the variable “depth” on a small-mesh estimation grid. The depth charts of each surface calculated with the geostatistical model are then interpreted in terms of their geological significance, which makes it possible to suggest hypotheses on the influence of major processes, such as tectonics and rivers (Rhône, Hérault, etc.) on the sedimentary structure of the gulf of Lion margin. The added value of geostatistics for this interpretation is emphasized. These unusual geostatistical methods are capable of being widely used in earth sciences for automatic mapping of “non-stationary” geometric surfaces, i.e. surfaces that possess a gradient or a trend developing systematically in space, such as piezometric or concentrations surfaces.
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Ma, Chunsheng. "Stochastic Processes with a Particular Type of Variograms." Research Letters in Signal Processing 2007 (2007): 1–5. http://dx.doi.org/10.1155/2007/61579.
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This paper is concerned with a class of stochastic processes or random fields with second-order increments, whose variograms have a particular form, among which stochastic processes having orthogonal increments on the real line form an important subclass. A natural issue, how big this subclass is, has not been explicitly addressed in the literature. As a solution, this paper characterizes a stochastic process having orthogonal increments on the real line in terms of its variogram or its construction. Our findings are a little bit surprising: this subclass is big in terms of the variogram, and on the other hand, it is relatively “small” according to a simple construction. In particular, every such process with Gaussian increments can be simply constructed from Brownian motion. Using the characterizations we obtain a series expansion of the stochastic process with orthogonal increments.
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Adams, Charles F., Bradley P. Harris, and Kevin D. E. Stokesbury. "Geostatistical comparison of two independent video surveys of sea scallop abundance in the Elephant Trunk Closed Area, USA." ICES Journal of Marine Science 65, no. 6 (April 15, 2008): 995–1003. http://dx.doi.org/10.1093/icesjms/fsn053.
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Abstract Adams, C. F., Harris, B. P., and Stokesbury, K. D. E. 2008. Geostatistical comparison of two independent video surveys of sea scallop abundance in the Elephant Trunk Closed Area, USA. – ICES Journal of Marine Science, 65: 995–1003. Geostatistical prediction at unsampled locations is done by kriging, an interpolation technique that minimizes the error variance. Our goal was to verify the technique by comparing kriged abundance estimates with observed counts from an area containing the highest densities of sea scallop (Placopecten magellanicus) offshore of the northeastern USA. In 2006, two independent video surveys of scallop abundance were made in the Elephant Trunk Closed Area, one using a 5.6 × 5.6-km sampling grid and the other with a 2.2 × 2.2-km sampling grid. We generated kriged surfaces of scallop abundance with the 5.6-km grid data, using different combinations of variograms and theoretical models, then tested the null hypothesis of no difference between the predicted and assumed true values (i.e. the 2.2-km grid data). There were significant differences between predicted and true values for three out of four combinations of variogram–model fits to untransformed data, assuming isotropy. In contrast, there was no significant difference between kriged and true values for any combination of variogram–model fits to log-transformed, detrended, anisotropy-corrected data. Classical and robust variograms performed equally well. Kriging can be used to generate accurate maps of scallop abundance if the assumptions of geostatistics are met.
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Zawadzki, Jarosław, and Piotr Fabijańczyk. "On the Influence of the Nugget Effect on the Efficiency of Magnetometric Soil Surface Screening." Ecological Chemistry and Engineering S 29, no. 4 (December 1, 2022): 525–35. http://dx.doi.org/10.2478/eces-2022-0038.
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Abstract The paper presents selected aspects of calculations and modelling of variograms from measurements of soil surface magnetic susceptibility for rapid screening of surface soil contamination with Technogenic Magnetic Particles (TMP). In particular, the methodology of variogram analysis in the case of multiple magnetometric measurements in one measurement location with the use of the MS2D Bartington sensor was discussed. A new approach to analysing such measurements was proposed that allows determining and using the nugget effect from standard, already existing measurements. This is of key importance for the quality of spatial analyses, and thus the screening results obtained by means of field magnetometry. In the paper, it was shown, step by step, that averaging the measurements performed at one measurement point during the calculation of the empirical variograms does not result in the loss of information on spatial variability in the microscale. As it was calculated non-averaged measurements were characterised by the nugget-to-sill ratio of about 96 % which was much higher than in the case of averaged measurements (close to 0 %). A range of correlation was similar in both cases and was equal to about 300 m - 400 m. The local variogram revealed a range of correlation of about 80 cm. As a result, the screening results are more reliable than is the case with the traditional procedure. An additional advantage of the work was the performance of all calculations in free R software.
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van de Beek, C. Z., H. Leijnse, P. J. J. F. Torfs, and R. Uijlenhoet. "Climatology of daily rainfall semi-variance in The Netherlands." Hydrology and Earth System Sciences 15, no. 1 (January 18, 2011): 171–83. http://dx.doi.org/10.5194/hess-15-171-2011.
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Abstract. Rain gauges can offer high quality rainfall measurements at their locations. Networks of rain gauges can offer better insight into the space-time variability of rainfall, but they tend to be too widely spaced for accurate estimates between points. While remote sensing systems, such as radars and networks of microwave links, can offer good insight in the spatial variability of rainfall they tend to have more problems in identifying the correct rain amounts at the ground. A way to estimate the variability of rainfall between gauge points is to interpolate between them using fitted variograms. If a dense rain gauge network is lacking it is difficult to estimate variograms accurately. In this paper a 30-year dataset of daily rain accumulations gathered at 29 automatic weather stations operated by KNMI (Royal Netherlands Meteorological Institute) and a one-year dataset of 10 gauges in a network with a radius of 5 km around CESAR (Cabauw Experimental Site for Atmospheric Research) are employed to estimate variograms. Fitted variogram parameters are shown to vary according to season, following simple cosine functions. Semi-variances at short ranges during winter and spring tend to be underestimated, but semi-variances during summer and autumn are well predicted.
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CARTER, M. R., and J. R. PEAREN. "GENERAL AND SPATIAL VARIABILITY OF SOLONETZIC SOILS IN NORTH CENTRAL ALBERTA." Canadian Journal of Soil Science 65, no. 1 (February 1, 1985): 157–67. http://dx.doi.org/10.4141/cjss85-016.
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The general and spatial variation of several soil profile chracteristics, and properties of agronomic and ameliorative importance, were determined on a regional and local area of Solonetzic soil in north central Alberta. Differences in general variation as characterized by the mean, median, coefficient of variation (CV), and range allowed grouping of soil properties according to high (e.g. EC in the Ap horizon), medium and low (e.g. pH of the Ap horizon) variation. Such grouping, along with specific differences in soil variation between the regional and local area was associated with the saline-sodic characteristics of these Solonetzic soils. Spatial variability was studied using a geostatistical method (variograms) on soil samples obtained from a 5-m grid. The variograms for most of the various soil properties did not reveal strong spatial dependence. Large nugget variances accounted for 60–90% of the total variance. The semivariance approximated the overall variance usually within 10 m. Variograms suggested periodic variation for the pH and EC of the Ap horizon. Extractable Ca in the Bnt horizon and the depth of the Ap and Bnt horizons were anisotropic showing significant spatial dependence with direction of sampling. The implication of soil variability in regard to soil sampling is discussed. Key words: Spatial variability, Solonetzic soil, saline-sodic soil, soil sampling, variogram
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Omoseebi, A. O., and I. Y. Tanko. "Geochemistry and Determination of Mineral Properties of Dolomite Deposit in Ikpeshi Southern, Nigeria." European Journal of Environment and Earth Sciences 2, no. 5 (October 4, 2021): 41–46. http://dx.doi.org/10.24018/ejgeo.2021.2.5.175.
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This work focused on the geochemistry and determination of the mineral properties’ distribution of dolomite deposit from Ikpeshi, using variogram analysis, Samples collected from the study area were subjected to laboratory analysis to determine the porosity, water content and geochemical properties. Variograms maps were constructed and fitted to the model. The results of the variogram analysis were used in plotting of predictive maps which show the property distribution of the dolomite. The porosity varies between 0.68%–3.24% and the Water Content varies between 0.1–1.65%. The geochemical analyses reveal that the average concentration of the elemental oxides is 1.790, 0.461, 0.299, 0.045, 20.380 and 46.130 for SiO2, Al2O3, Fe2O3, MnO, MgO and CaO, respectively. CaO and MgO are more abundant when compared with other major elements; the predictive maps of the distribution and directions of the mineral properties and the distribution are not uniform in all directions which indicates that the mineral properties of the dolomite deposit are anisotropic.
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Wilson, David, Leslie Smith, Colleen Atherton, Lianna J. D. Smith, Richard T. Amos, David R. Barsi, David C. Sego, and David W. Blowes. "Diavik Waste Rock Project: Geostatistical Analysis of Sulfur, Carbon, and Hydraulic Conductivity Distribution in a Large-Scale Experimental Waste Rock Pile." Minerals 12, no. 5 (May 3, 2022): 577. http://dx.doi.org/10.3390/min12050577.
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One of the large-scale field waste rock experiments (test piles) conducted as part of the Diavik Waste Rock Project was deconstructed, providing a spatially located set of geochemical, mineralogical, and particle-size distribution samples. Geostatistical analyses were conducted for sulfur and carbon content and saturated hydraulic conductivity, which affect the geochemical evolution of waste rock, to investigate the spatial dependence of these parameters. Analyses included population statistics, experimental semi-variogram estimation, and theoretical semi-variogram fitting. Population statistics were calculated for additional data sets from samples collected during the construction of the test piles. The population statistical analyses indicated that log-normal distribution provided the best fit for all investigated data sets. Experimental semi-variograms were estimated for the spatially located data set (test pile deconstruction) using the classical estimator, and theoretical semi-variograms were fitted. This investigation showed that the spatial distribution of sulfur, carbon, and hydraulic conductivity within the core of the test-pile experiments can be approximated using a log-normal distribution with a mean and standard deviation calculated using the samples collected during construction of the piles, and that little to no spatial relationship was present for these parameters at the scale of sampling. That the saturated hydraulic conductivity of the matrix material can be represented by the same statistical distribution throughout the test pile is significant because water flow, as well as mineral surface area and reactivity are dominantly controlled within the matrix portion of the test pile. Reactive transport simulations are included to demonstrate the influence of the matrix material on effluent geochemistry.
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Muchtadi-Alamsyah, Intan, Mohamad Nur Heriawan, Gantina Rachmaputri, Elvira Rahmadiantri, and Made Putri Lawiyuniarti. "Application of Three-Dimensional Direct Least Square Method for Ellipsoid Anisotropy Fitting Model of Highly Irregular Drill Hole Patterns." Applied Sciences 12, no. 15 (August 4, 2022): 7848. http://dx.doi.org/10.3390/app12157848.
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Ellipsoid or geometric anisotropy is a widely used method in geostatistical analysis to obtain variograms with different ranges in different directions (azimuth) and relatively similar sill variance. Ellipsoid anisotropy is indispensable in mining when a resource geologist intends to understand the spatial continuity of variables related to any geological controls of the mineralization. For example, when dealing with mineralization related to tabular deposits, a porphyritic deposit with an irregular drill hole pattern (fan drilling), three-dimensional ellipsoid anisotropy is quite challenging to model. We assume that the variables’ spatial continuity is isotropic, and we model it using a three-dimensional omnidirectional variogram. However, if the actual spatial continuity of the variables has a three-dimensional anisotropy, then assuming a three-dimensional omnidirectional variogram will generate imprecise resource estimations. This study presents a new practical three-dimensional ellipsoid model-fitting method using a three-dimensional direct least square method. We investigated a zinc (Zn) dataset from thousands of irregular drill hole patterns from a porphyritic system associated with skarn orebodies for the case study.
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Cook, S. E., and N. A. Coles. "A comparison of soil survey methods in relation to catchment hydrology." Soil Research 35, no. 6 (1997): 1379. http://dx.doi.org/10.1071/s95029.
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Eight primary catchments within the Western Australian wheatbelt were surveyed in detail to examine the abilities of conventional soil classification and geostatistical analysis to provide detailed information of soil spatial variation for catchment-scale hydrologic modelling. Nine soil physical properties were measured. The results illustrate potential diculties with both methods. Classification by using the Factual Key was unable to describe the major component of soil property variation. The relative variance accounted for by soil classes was usually <10%. Only the yellow duplex soils appeared distinct from other soil classes. Potential diculties with geostatistical analysis also arose because of fluctuations in the variogram models. Contrasts occurred between variograms for the same property over different catchments and for different properties over the same catchment. Within the areas studied, nugget and linear (unbounded) variogram models were more common than spherical or exponential models. It is proposed that the surveyor would have to select a survey method on the basis of prior knowledge about which model of variation is more likely to be successful for the scale and location of survey.
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Mälicke, Mirko. "SciKit-GStat 1.0: a SciPy-flavored geostatistical variogram estimation toolbox written in Python." Geoscientific Model Development 15, no. 6 (March 25, 2022): 2505–32. http://dx.doi.org/10.5194/gmd-15-2505-2022.
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Abstract. Geostatistical methods are widely used in almost all geoscientific disciplines, i.e., for interpolation, rescaling, data assimilation or modeling. At its core, geostatistics aims to detect, quantify, describe, analyze and model spatial covariance of observations. The variogram, a tool to describe this spatial covariance in a formalized way, is at the heart of every such method. Unfortunately, many applications of geostatistics focus on the interpolation method or the result rather than the quality of the estimated variogram. Not least because estimating a variogram is commonly left as a task for computers, and some software implementations do not even show a variogram to the user. This is a miss, because the quality of the variogram largely determines whether the application of geostatistics makes sense at all. Furthermore, the Python programming language was missing a mature, well-established and tested package for variogram estimation a couple of years ago. Here I present SciKit-GStat, an open-source Python package for variogram estimation that fits well into established frameworks for scientific computing and puts the focus on the variogram before more sophisticated methods are about to be applied. SciKit-GStat is written in a mutable, object-oriented way that mimics the typical geostatistical analysis workflow. Its main strength is the ease of use and interactivity, and it is therefore usable with only a little or even no knowledge of Python. During the last few years, other libraries covering geostatistics for Python developed along with SciKit-GStat. Today, the most important ones can be interfaced by SciKit-GStat. Additionally, established data structures for scientific computing are reused internally, to keep the user from learning complex data models, just for using SciKit-GStat. Common data structures along with powerful interfaces enable the user to use SciKit-GStat along with other packages in established workflows rather than forcing the user to stick to the author's programming paradigms. SciKit-GStat ships with a large number of predefined procedures, algorithms and models, such as variogram estimators, theoretical spatial models or binning algorithms. Common approaches to estimate variograms are covered and can be used out of the box. At the same time, the base class is very flexible and can be adjusted to less common problems, as well. Last but not least, it was made sure that a user is aided in implementing new procedures or even extending the core functionality as much as possible, to extend SciKit-GStat to uncovered use cases. With broad documentation, a user guide, tutorials and good unit-test coverage, SciKit-GStat enables the user to focus on variogram estimation rather than implementation details.
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Barange, Manuel, Janet C. Coetzee, and Nandipha M. Twatwa. "Strategies of space occupation by anchovy and sardine in the southern Benguela: the role of stock size and intra-species competition." ICES Journal of Marine Science 62, no. 4 (January 1, 2005): 645–54. http://dx.doi.org/10.1016/j.icesjms.2004.12.019.
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Abstract Strategies of space occupation by anchovy and sardine populations in the southern Benguela during cruises in 1994 (low biomass) and 2001 (high biomass) are investigated using geostatistical tools. The spatial expansion of anchovy and sardine during the high-density year resulted in an increase in the number and density of hotspots and, in the case of anchovy, a relative increase in the contribution of mid- to high-density intervals to the overall survey biomass. Variogram autocorrelation ranges were larger in the high-biomass year. Otherwise, similarities and differences in the strategies of space occupation between anchovy and sardine are consistent between years of low and high biomass, and are therefore density-independent. Variograms of indicator variables revealed comparable structures for both species and years, with autocorrelation ranges of 30 nautical miles for the smallest indicator (0.1 g m−2) and 10 miles for the largest (100 g m−2), reflecting intrinsic spatial structures independent of stock size. The ideal survey inter-transect distance, defined as the autocorrelation range of the highest density indicator, was not influenced by the expanded distribution of both species. Cumulative frequency distributions and cross-variograms revealed differences in space occupancy between both species. Despite the areal expansion, and in contrast to anchovy, a significant portion of the sardine biomass continued to be contributed by a few very high-density areas with little spatial structure, as indicated by large nugget effects in the variograms and lack of transitions in the cross-variograms. Both species were spatially segregated in the low-biomass year, but overlapped extensively in the high-biomass year.
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Entz, T., and C. Chang. "Evaluation of soil sampling schemes for geostatistical analyses: A case study for soil bulk density." Canadian Journal of Soil Science 71, no. 2 (May 1, 1991): 165–76. http://dx.doi.org/10.4141/cjss91-016.
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Sixteen soil sampling schemes were evaluated in a case study using geostatistical analyses to determine their impact on directional sample variograms and kriging. Soil bulk density measurements for each sampling scheme were obtained from an intensively sampled grid, and kriging was used to estimate the bulk densities not included in the sampling scheme. The kriged bulk density estimates for all sampling schemes were verified using a minimum of 6168 observed values. Grid sampling for this study required more samples than stratified random sampling and the stratified-grid sampling schemes, but the accuracy of the kriged estimates was comparable for all sampling schemes. Key words: Kriging, variogram, soil density
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Poultney, R., J. Riley, and R. Webster. "Optimizing plot size and shape for field experiments on terraces." Experimental Agriculture 33, no. 01 (January 1997): 51–64. http://dx.doi.org/10.1017/s0014479797000161.
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Two methods, namely combined plot analysis and integration of variograms, have been applied to investigate and compare plot-to-plot yields of intercropped millet (mean yield of about 1.9 t ha−1) and maize (mean yield 4.25 t ha−1) on terraces in Nepal. Combining plots diminishing the residual variance of millet from 0.52 (t/ha)2 of the original 1 m×1 m units to 0.08 (t/ha)2 for 4 m×4 m plots, the largest for which reliable estimates could be derived. The residual variance of maize declined from 4.91 (t/ha)2 of the original units to 0.61 (t/ha)2 for 4 m×4 m plots. Orientation was immaterial. The variogram for millet was isotropic and bounded with a range of approximately 4 m. Within-plot variance calculated from the variogram increased, and experimental error decreased, as the size of plots increased to this value, beyond which there was little gain. The variogram for maize was unbounded, and so gave no ‘natural' upper limit for plot size, that is, over the range studied, up to 6 m×6 m. It was also anisotropic with larger gradient in the direction from front to back of the terrace than along the contour. The reduction in residual variance was greatest for narrow plots elongated in this direction. Formulae are provided from which to calculate from the variogram approximate residual variances for experiments of given area and size, shape, and orientation of plots. Its application gave similar results to those from the combined plot analysis. Overall, the results from the two methods were consistent.
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van de Beek, C. Z., H. Leijnse, P. J. J. F. Torfs, and R. Uijlenhoet. "Climatology of daily rainfall semivariance in The Netherlands." Hydrology and Earth System Sciences Discussions 7, no. 2 (March 24, 2010): 2085–120. http://dx.doi.org/10.5194/hessd-7-2085-2010.
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Abstract. Rain gauges can offer high quality rainfall measurements at their location. Networks of rain gauges can offer better insight into the space-time variability of rainfall, but they tend to be too widely spaced for accurate estimates between points. While remote sensing systems, such as radars and networks of microwave links, can offer good insight in the spatial variability of rainfall they tend to have more problems in identifying the correct rain amounts at the ground. A way to estimate the variability of rainfall between gauge points is to interpolate between them using fitted variograms. If a dense rain gauge network is lacking it is difficult to estimate accurate variograms. In this paper a 30-year dataset of daily rain accumulations gathered at 29 automatic weather stations operated by KNMI and a one-year dataset of 10 gauges in a network with a radius of 5 km around CESAR (Cabauw Experimental Site for Atmospheric Research) are employed to estimate variograms. Fitted variogram parameters are shown to vary according to season, closely following simple cosine functions allowing for applications in catchment hydrology and rainfall field generation. Semivariances at short ranges during winter and spring tend to be underestimated, but summer and autumn are well predicted. This climatological semivariance can be employed to estimate the accuracy of the rainfall input to a hydrological model even with only few gauges in a given catchment area.
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Laun, S., N. Rösch, M. Breunig, and M. Al Doori. "IMPLEMENTATION OF KRIGING METHODS IN MOBILE GIS TO ESTIMATE DAMAGE TO BUILDINGS IN CRISIS SCENARIOS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B2 (June 7, 2016): 211–16. http://dx.doi.org/10.5194/isprs-archives-xli-b2-211-2016.
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In the paper an example for the application of kriging methods to estimate damage to buildings in crisis scenarios is introduced. Furthermore, the Java implementations for Ordinary and Universal Kriging on mobile GIS are presented. As variogram models an exponential, a Gaussian and a spherical variogram are tested in detail. Different test constellations are introduced with various information densities. As test data set, public data from the analysis of the 2010 Haiti earthquake by satellite images are pre-processed and visualized in a Geographic Information System. As buildings, topography and other external influences cannot be seen as being constant for the whole area under investigation, semi variograms are calculated by consulting neighboured classified buildings using the so called moving window method. The evaluation of the methods shows that the underlying variogram model is the determining factor for the quality of the interpolation rather than the choice of the kriging method or increasing the information density of a random sample. The implementation is completely realized with the programming language Java. Thereafter, the implemented software component is integrated into GeoTech Mobile, a mobile GIS Android application based on the processing of standardized spatial data representations defined by the Open Geospatial Consortium (OGC). As a result the implemented methods can be used on mobile devices, i.e. they may be transferred to other application fields. That is why we finally point out further research with new applications in the Dubai region.
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Laun, S., N. Rösch, M. Breunig, and M. Al Doori. "IMPLEMENTATION OF KRIGING METHODS IN MOBILE GIS TO ESTIMATE DAMAGE TO BUILDINGS IN CRISIS SCENARIOS." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLI-B2 (June 7, 2016): 211–16. http://dx.doi.org/10.5194/isprsarchives-xli-b2-211-2016.
Full textAbstract:
In the paper an example for the application of kriging methods to estimate damage to buildings in crisis scenarios is introduced. Furthermore, the Java implementations for Ordinary and Universal Kriging on mobile GIS are presented. As variogram models an exponential, a Gaussian and a spherical variogram are tested in detail. Different test constellations are introduced with various information densities. As test data set, public data from the analysis of the 2010 Haiti earthquake by satellite images are pre-processed and visualized in a Geographic Information System. As buildings, topography and other external influences cannot be seen as being constant for the whole area under investigation, semi variograms are calculated by consulting neighboured classified buildings using the so called moving window method. The evaluation of the methods shows that the underlying variogram model is the determining factor for the quality of the interpolation rather than the choice of the kriging method or increasing the information density of a random sample. The implementation is completely realized with the programming language Java. Thereafter, the implemented software component is integrated into GeoTech Mobile, a mobile GIS Android application based on the processing of standardized spatial data representations defined by the Open Geospatial Consortium (OGC). As a result the implemented methods can be used on mobile devices, i.e. they may be transferred to other application fields. That is why we finally point out further research with new applications in the Dubai region.
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Deems, Jeffrey S., Steven R. Fassnacht, and Kelly J. Elder. "Interannual Consistency in Fractal Snow Depth Patterns at Two Colorado Mountain Sites." Journal of Hydrometeorology 9, no. 5 (October 1, 2008): 977–88. http://dx.doi.org/10.1175/2008jhm901.1.
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Abstract Fractal dimensions derived from log–log variograms are useful for characterizing spatial structure and scaling behavior in snow depth distributions. This study examines the temporal consistency of snow depth scaling features at two sites using snow depth distributions derived from lidar datasets collected in 2003 and 2005. The temporal snow accumulation patterns in these two years were substantially different, but both years represent nearly average 1 April accumulation depths for these sites, with consistent statistical distributions. Two distinct fractal regions are observed in each log–log variogram, separated by a scale break, which indicates a length scale at which a substantial change in the driving processes exists. The lag distance of the scale break is 15 m at the Walton Creek site and 40 m at the Alpine site. The datasets show consistent fractal dimensions and scale break distances between the two years, suggesting that the scaling features observed in spatial snow depth distributions are largely determined by physiography and vegetation characteristics and are relatively insensitive to annual variations in snowfall. Directional variograms also show consistent patterns between years, with smaller fractal dimensions aligned with the dominant wind direction at each site.
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Wickramathilaka, N., and U. Ujang. "3D Kriging interpolation for traffic noise visualization: designing noise observation points and valuation of spatial interpolation accuracy." IOP Conference Series: Earth and Environmental Science 1274, no. 1 (December 1, 2023): 012001. http://dx.doi.org/10.1088/1755-1315/1274/1/012001.
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Abstract Identifying the risk of traffic noise is vital in minimizing traffic noise pollution in urban areas. As noise travels in every direction, 3D visualization of traffic noise is essential, which involves visualising traffic noise along the facades of buildings. A standard traffic noise model is necessary to calculate traffic noise levels, as several factors affect traffic noise. Moreover, designing noise observation points in 3D and spatial interpolation play significant roles in 3D noise visualisation. Therefore, this study demonstrates the results by elaborating on the spatial interpolation and designing noise observation points. A noise observation point consists of four parameters in 3D space. Generally, Inverse Distance Weighted (IDW), Triangular Irregular Network (TIN), and Kriging do not support the interpolation of four parameters in 3D. However, 3D Kriging in Empirical Bayesian Kriging provides significant opportunities to interpolate noise levels in 3D. However, the elements of the function of spatial interpolations are vital for accuracy. The 3D Kriging uses different variograms according to semivariance. This variogram directly impacts the weighting factor of 3D Kriging. Therefore, this study develops a comparison to identify the impact of different variograms on the accuracy of 3D Kriging interpolation on traffic noise.
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Gireesh, Midhula, Jhalendra P. Rijal, and Shimat V. Joseph. "Spatial Distribution of Hunting Billbugs (Coleoptera: Curculionidae) in Sod Farms." Insects 12, no. 5 (April 30, 2021): 402. http://dx.doi.org/10.3390/insects12050402.
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The hunting billbug, Sphenophorus venatus vestitus Chittenden (Coleoptera: Curculionidae), is an important turfgrass pest, especially in sod farms. S. venatus vestitus larvae feed on the stems and roots of turfgrass. Damaged turfgrass is loosely held together and poses a challenge for machine harvesting. Additionally, the normal growth of turfgrass is affected, especially after winter dormancy. Because S. venatus vestitus larvae are hidden inside the stems or under the soil, larval management is challenging. To improve sampling and management, the spatial distribution patterns of S. venatus vestitus larvae and adults were assessed at four sod farm sites with a history of S. venatus vestitus infestation in central Georgia (USA). The larvae were sampled by soil cores using a hole cutter, whereas adults were collected using pitfall traps for 7 d. The spatial distributions of larvae and adults was analyzed using SADIE and variograms. The SADIE and variogram analyses revealed a significant aggregation pattern for adults, whereas aggregated distributions were detected for larvae with variogram analyses. The average ranges of spatial dependence for larval and adult samples were 3.9 m and 5.4 m, respectively. Interpolated distribution maps were created to visually depict S. venatus vestitus infestation hotspots within the sod farms.
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Benavides-Bravo, Francisco Gerardo, Roberto Soto-Villalobos, José Roberto Cantú-González, Mario A. Aguirre-López, and Ángela Gabriela Benavides-Ríos. "A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series." Mathematics 9, no. 19 (October 3, 2021): 2466. http://dx.doi.org/10.3390/math9192466.
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Variogram models are a valuable tool used to analyze the variability of a time series; such variability usually entails a spherical or exponential behavior, and so, models based on such functions are commonly used to fit and explain a time series. Variograms have a quasi-periodic structure for rainfall cases, and some extra steps are required to analyze their entire behavior. In this work, we detailed a procedure for a complete analysis of rainfall time series, from the construction of the experimental variogram to curve fitting with well-known spherical and exponential models, and finally proposed a novel model: quadratic–exponential. Our model was developed based on the analysis of 6 out of 30 rainfall stations from our case study: the Río Bravo–San Juan basin, and was constructed from the exponential model while introducing a quadratic behavior near to the origin and taking into account the fact that the maximal variability of the process is known. Considering a sample with diverse Hurst exponents, the stations were selected. The results obtained show robustness in our proposed model, reaching a good fit with and without the nugget effect for different Hurst exponents. This contrasts to previous models, which show good outcomes only without the nugget effect.
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Marzban, Caren, and Scott Sandgathe. "Verification with Variograms." Weather and Forecasting 24, no. 4 (August 1, 2009): 1102–20. http://dx.doi.org/10.1175/2009waf2222122.1.
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Abstract The verification of a gridded forecast field, for example, one produced by numerical weather prediction (NWP) models, cannot be performed on a gridpoint-by-gridpoint basis; that type of approach would ignore the spatial structures present in both forecast and observation fields, leading to misinformative or noninformative verification results. A variety of methods have been proposed to acknowledge the spatial structure of the fields. Here, a method is examined that compares the two fields in terms of their variograms. Two types of variograms are examined: one examines correlation on different spatial scales and is a measure of texture; the other type of variogram is additionally sensitive to the size and location of objects in a field and can assess size and location errors. Using these variograms, the forecasts of three NWP model formulations are compared with observations/analysis, on a dataset consisting of 30 days in spring 2005. It is found that within statistical uncertainty the three formulations are comparable with one another in terms of forecasting the spatial structure of observed reflectivity fields. None, however, produce the observed structure across all scales, and all tend to overforecast the spatial extent and also forecast a smoother precipitation (reflectivity) field. A finer comparison suggests that the University of Oklahoma 2-km resolution Advanced Research Weather Research and Forecasting (WRF-ARW) model and the National Center for Atmospheric Research (NCAR) 4-km resolution WRF-ARW slightly outperform the 4.5-km WRF-Nonhydrostatic Mesoscale Model (NMM), developed by the National Oceanic and Atmospheric Administration/National Centers for Environmental Prediction (NOAA/NCEP), in terms of producing forecasts whose spatial structures are closer to that of the observed field.
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Caers, J. K., S. Srinivasan, and A. G. Journel. "Geostatistical Quantification of Geological Information for a Fluvial-Type North Sea Reservoir." SPE Reservoir Evaluation & Engineering 3, no. 05 (October 1, 2000): 457–67. http://dx.doi.org/10.2118/66310-pa.
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Summary Accurate prediction of petroleum reservoir performance requires reliable models of the often complex reservoir heterogeneity. Geostatistical simulation techniques generate multiple realizations of the reservoir model, all equally likely to be drawn. Traditional to geostatistics, geological continuity is represented through the variogram. The variogram is limited in describing complex geological structures as it measures correlation between rock properties at two locations only: it is a two-point statistic. Reservoir analogs such as outcrops can serve as training images depicting the interpreted geological structure. Due to scarcity of well data, the variogram models are often borrowed from such training sets. However, the same training images could be utilized to extract more complex information in the form of multiple-point statistics measuring the joint dependency between multiple locations. This paper compares a traditional variogram-based geostatistical model vs. a novel geostatistical method utilizing multiple-point statistics borrowed from training images. The comparison is made on the basis of flow performance for a typical North Sea reservoir. To obtain such comparison a "true" reference reservoir is generated using object-based simulation that depicts the complex intertwining of fluvial channels. Next, a different but similar reservoir is generated, termed the "training reservoir." The latter is used to extract the necessary structural information, be it variograms or multiple-point statistics, to build multiple geostatistical models of the true reservoir conditioned to sparse well data. A waterflood flow scenario with an inverted five-spot pattern is simulated using ECLIPSE on the true reference and the various geostatistical models. Water breakthrough characteristics and water saturation distributions are used for comparison. Introduction Typically, geostatistical reservoir characterization must address two important issues. First, a structural model needs to be established that provides an adequate description of the underlying geology. In geostatistics, the structural model describes the spatial continuity of geology in all directions. Traditional to geostatistics is to take variogram(s) as the basis for that prior to the structural model. Second, the structural model needs to be conditioned to all available hard and soft data. The intent of this paper is to compare two approaches to reservoir modeling: a traditional variogram-based technique and a novel training image-based simulation method. In traditional geostatistics, one models the variogram from well data, then one produces simulation models that honor or reflect the variogram model. This seems a highly objective procedure: the variogram model, which conditions the pattern generated from the reservoir model originates from data from the same reservoir. However, the practice of geostatistics has shown that it is difficult to model variograms from the limited well data and the variogram is often borrowed from ancillary information such as outcrops. Moreover, it is by now understood that the variogram is a very limited measure for quantifying spatial patterns. Every simulation algorithm that is variogram based implicitly needs to assume higher-order statistics (e.g., Gaussian simulation methods1). Essentially, any simulation algorithm imposes higher-order statistics beyond the control of the reservoir modeler. These imposed higher-order statistics, termed multiple-point statistics, might conflict with the actual understanding of the reservoir geology. The novel approach presented is based on the fact that outcrop or any other source of ancillary geological information allows us to borrow spatial structures beyond the variogram, which is only a two-point correlation measure. These patterns are borrowed in the form of multiple-point statistics from so-called training images, allowing a better description of the complex reservoir geology. Such training images could be as simple as a series of hand-drawn sketches by the geologist or a compilation of outcrop data (there may be several at different scales). If enough ancillary geological information is present, it should be possible to construct three-dimensional (3D) training images. If not enough geological information is present one can resort back to the traditional variogram-based method. Although the proposed methodology is general, this paper shows the application of the novel approach to a North Sea reservoir dataset and attempts to make comparisons with the variogram-based methodology. The comparison is based on the flow performance of a set of reservoir models generated with each geostatistical technique. The geology of many North Sea reservoirs is very heterogeneous due to the presence of high-permeability fluvial channels.2 The amount of hard data available along wells is typically sparse and the soft data (seismic) show a low correlation with petrophysical or facies properties within the reservoir. Hence, the construction of a representative prior structural model, accurately representing the reservoir geology, is of crucial importance. Data Sets The reservoir under study is a Triassic fluvial reservoir typical of a large number of fields in the North Sea. The fluvial channel formation was deposited by streams that range from braided to low-moderate sinuosity. The reservoir is made up of complex patterns of sand intercalated in a silty mudstone matrix. The reservoir is characterized by a trend of upward increasing sandiness. Well-defined fluvial channels of sandstones embedded in a mudstone matrix occur towards the base, while interstratified channels occur towards the top. For more-detailed information about the geology of such reservoirs refer to Ref. 2 and 3. True Reservoir. The purpose of this study is to evaluate the impact of alternative geostatistical reservoir models on the result of a flow simulation in a setting approaching a real case. To provide a common reference, a true reservoir, whose properties are exhaustively known at each gridblock, must be established. In order to keep the number of variables limited and be able to make a conclusive comparison, the reservoir is described by two facies only: channel sand and mudstone facies. For the true reservoir, a Boolean (object-based) simulation of channels was constructed from a detailed geological description of the channeling in actual North Sea reservoirs. For more details on the Boolean algorithm used, see Ref. 4. Selected slices of the true reservoir are shown in Fig. 1. The reservoir has the following general characteristics:The reservoir is discretized into 37×66×15 gridblocks in the x, y, and z vertical directions, respectively.
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Salsabila Nur Fitriana and Sutawanir Darwis. "Ordinary Kriging Magnitude dan Nilai B-Value Gutenberg-Richterpada Katalog Gempa Bumi Jawa Barat." Bandung Conference Series: Statistics 3, no. 2 (August 2, 2023): 466–75. http://dx.doi.org/10.29313/bcss.v3i2.8385.
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Abstract. Earthquake is a natural phenomenon that is not known when it will occur because measurements are not made in all locations. With these limitations, we need a method that can predict the level of earthquake strength at several points where measurements are not carried out, for example by the spatial interpolation method. There are several methods used to perform spatial interpolation, one of which is the ordinary kriging method. Ordinary kriging (OK) utilizes spatial values at sample locations and variograms that show correlations between spatial points to predict values at non-sample locations where the predicted value depends on their proximity to the sample locations. This thesis discusses the development of the ordinary kriging method on regional earthquake magnitudes and the b-value Gutenberg Richter variable using the West Java earthquake catalog. Regional magnitude variables and b-values were used to model the spatial correlation via a spherical variogram. Variogram parameters were estimated using the least squares method. The results of the Ordinary Kriging assessment of an area show that the level of rock fragility (b-value) is quite high, namely 6.523 which illustrates that the area has low stress accumulation or it can be said that a high b-value has experienced a large-scale earthquake so that only energy left that is capable of producing small earthquakes.
Abstrak. Gempa bumi merupakan fenomena alam yang tidak seorang pun mengetahui kapan terjadinya karena pengukuran tidak dilakukan di semua lokasi. Dengan keterbatasan tersebut, diperlukan suatu metode yang dapat memprediksi tingkat kekuatan gempa di beberapa titik yang tidak dilakukan pengukuran, misalnya dengan metode interpolasi spasial. Terdapat beberapa metode yang digunakan untuk melakukan interpolasi spasial, salah satunya metode ordinary kriging. Ordinary kriging (OK) memanfaatkan nilai spasial pada lokasi tersampel dan variogram yang menunjukkan korelasi antar titik spasial untuk memprediksi nilai pada lokasi yang tidak tersampel yang mana nilai prediksi tersebut tergantung pada kedekatannya terhadap lokasi tersampel. Skripsi ini membahas pengembangan metode ordinary kriging pada peubah teregioanal magnitude gempa dan b-value Gutenberg Richter menggunakan katalog gempa Jawa Barat. Peubah teregional magnitude dan nilai-b digunakan untuk memodelkan korelasi spasial melalui variogram spherical. Parameter variogram diestimasi menggunakan metode kuadrat terkecil. Hasil dari penaksiran Ordinary Kriging dari suatu wilayah menunjukkan bahwa nilai tingkat kerapuhan batuan (b-value) cukup tinggi yaitu sebesar 6.523, menggambarkan bahwa daerah tersebut memiliki akumulasi stress yang rendah atau dapat dikatakan nilai b-value yang tinggi pernah terjadi gempa bumi dengan skala besar sehingga hanya tersisa energi yang mampu menghasilkan gempa kecil.
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Ahmed, Waqas, Khan Muhammad, Hylke Jan Glass, Snehamoy Chatterjee, Asif Khan, and Abid Hussain. "Novel MLR-RF-Based Geospatial Techniques: A Comparison with OK." ISPRS International Journal of Geo-Information 11, no. 7 (July 1, 2022): 371. http://dx.doi.org/10.3390/ijgi11070371.
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Geostatistical estimation methods rely on experimental variograms that are mostly erratic, leading to subjective model fitting and assuming normal distribution during conditional simulations. In contrast, Machine Learning Algorithms (MLA) are (1) free of such limitations, (2) can incorporate information from multiple sources and therefore emerge with increasing interest in real-time resource estimation and automation. However, MLAs need to be explored for robust learning of phenomena, better accuracy, and computational efficiency. This paper compares MLAs, i.e., Multiple Linear Regression (MLR) and Random Forest (RF), with Ordinary Kriging (OK). The techniques were applied to the publicly available Walkerlake dataset, while the exhaustive Walker Lake dataset was validated. The results of MLR were significant (p < 10 × 10−5), with correlation coefficients of 0.81 (R-square = 0.65) compared to 0.79 (R-square = 0.62) from the RF and OK methods. Additionally, MLR was automated (free from an intermediary step of variogram modelling as in OK), produced unbiased estimates, identified key samples representing different zones, and had higher computational efficiency.