Efficiency of Ni Content in Laterite Nickel Deposits through The Least Square Method Approach on Semivariogram

Ordinary kriging is one of the geostatistical techniques used for spatial prediction on a spatially distributed random plane. Ordinary kriging is a linear unbiased estimator which is part of a semivariogram system of equations that minimizes errors of variance in estimating mineral resources. The semivariogram model shows optimal results in the estimation using the least square method, the effective minimization method smoothes the data points against the curve on a semivariogram graph, the least square makes the size error efficient in the semivariogram model and has been proven to be effective in reducing errors in the semivariogram model in the case of laterite nickel deposits. at PT. Vale Indonesia Tbk. Thus, conclusively the prediction of unsampled Ni content results is very accurate. This is indicated by the lowest root mean square error (RMSE) in limonite in the exponential model, saprolite in the spherical model, and bedrock in the gaussian model. The greatest value of Ni content in this study was in the saprolite layer.

Quality of surface geostatistical parameter reproduction for laser profilometers

The description of the surface topography of building structures is important for contact tasks, bond strength and rheological processes monitoring. The determination of surface parameters is carried out using increasingly sophisticated methods and techniques, such as laser profilometer, laser scanner, confocal microscope or short range photogrammetry. The research is aimed at evaluating the mobile surface test device for quality control and failure prevention, also the authors have addressed the possibility of using inexpensive profile measuring laser equipment to obtain a geostatistical description of the surface parametrics. It is the support of creation of new measurement apparatus that is the impetus for this work for the selection of optimal laser device. It is possible to deduce from the paper how the density of measurements taken and the accuracy of height estimation in the profile affect the parameters of the semivariogram model. With the proper choice of device it is easier correctly estimate the strength parameters of the joint of concrete or soil-concrete structures. The relevance of the correctly performed measurement is proved by the link between the strength parameters of the contact surfaces and its geostatistical description. In order to assess the quality of the mapping, a spherical theoretical model with a corresponding generated surface was used as a reference. The measuring laser devices with various mapping accuracy and depth measurement precision were tested, also for description fractal dimension of results. The measurement accuracy of the depth parameter has the greatest influence for determination of the remaining parameters of the surface roughness.

Semivariogram models for rice stem bug population densities estimated by ordinary kriging

Tibraca limbativentris is considered one of the main species of insect pests in irrigated rice. This species can be found in plants in the vegetative and reproductive stages. This study aimed to select semivariogram models to estimate rice stem bug population densities by ordinary kriging. Two fields were used to survey the T. limbativentris population in Oryza sativa. A grid of 30 x 30 m was drawn, which generated 143 and 385 sample units for the first and second fields, respectively. Seven evaluations of two hundred plants per sampling unit were performed during cultivation. From the insect counts, the results were input into circular, spherical, pentaspherical, exponential, Gaussian, rational quadratic, cardinal sine, K-Bessel, J-Bessel, and stable semivariogram models via ordinary kriging interpolation and the best model was selected via cross-validation. Each assessment had a particular spatial structure and semivariogram model that best fit the experimental data.

Mapping the probability of detecting Burkholderia pseudomallei in rural rice paddy soil based on indicator kriging and spatial soil factor analysis

Background Melioidosis is an infectious disease commonly found in Thailand. This infectious disease is caused by Burkholderia pseudomallei in soil. This study aims to analyze the association between spatial soil factors and B. pseudomallei detection, as well as to map the probability of B. pseudomallei contamination based on indicator kriging in paddy soil. Methods Seventy-eight soil samples were collected randomly on 22 April 2018 in various paddy fields. Oxidase, Gram staining and monoclonal antibody-based latex agglutination assays were performed to confirm the presence of B. pseudomallei in soil samples. The association between B. pseudomallei detection and spatial soil factors including soil temperature, soil pH, soil texture and soil drainage were analyzed by the Mann–Whitney U test and χ2 test. Subsequently, a semivariogram model and indicator kriging were used to map the probability of B. pseudomallei contamination. Results Of the 78 samples, B. pseudomallei was detected in 32 (41.03%). The presence or absence of B. pseudomallei was not significantly associated with spatial soil factors. The semivariogram model showed that the lag distance between positive B. pseudomallei samples was 90.51 m. Conclusion The empirical semivariogram and indicator kriging are an alternative option for predicting the spatial distribution of B. pseudomallei in soil.

COMPARAÇÃO ENTRE MÉTODOS DE INTERPOLAÇÃO ESPACIAL PARA A ESTIMATIVA DA DISTRIBUIÇÃO DE PRECIPITAÇÃO NO CEARÁ-BRASIL

COMPARAÇÃO ENTRE MÉTODOS DE INTERPOLAÇÃO ESPACIAL PARA A ESTIMATIVA DA DISTRIBUIÇÃO DE PRECIPITAÇÃO NO CEARÁ-BRASIL DANILO BATISTA NOGUEIRA1; ALEXSANDRO OLIVEIRA DA SILVA 2 E ANA PAULA NUNES DA SILVA 3 1 Departamento de Engenharia Agrícola, Universidade Federal do Ceará, Avenida Mister Hull, S/N-Campus do Pici, Centro de Ciências Agrárias, Bloco 804, CEP 60455-760, Fortaleza, Ceará, Brasil, [email protected] 2 Departamento de Engenharia Agrícola, Universidade Federal do Ceará, Avenida Mister Hull, S/N-Campus do Pici, Centro de Ciências Agrárias, Bloco 804, CEP 60455-760, Fortaleza, Ceará, Brasil, [email protected] 3 Departamento de Engenharia Agrícola, Universidade Estadual do Amapá, Avenida Presidente Vargas, N 650, Centro de Ciências Agrárias, CEP 68906-970, Macapá, Amapá, Brasil, [email protected] 1 RESUMO A distribuição espacial de precipitação ainda é largamente representada por métodos geoestatísticos de interpolação e em áreas de semiárido necessita de estudos recorrentes por conta de sua variabilidade temporal e espacial. Diante disto, visando o aperfeiçoamento dos métodos de interpolação e o desenvolvimento de mapas no estado do Ceará, o presente trabalho teve como objetivo analisar a acurácia de cinco métodos de interpolação: Inverso do Quadrado da Distância (IQD), Krigagem com um semivariograma esférico, Krigagem com um semivariograma exponencial, Vizinho natural e Spline regularizada. Para isto foram utilizados dados de precipitação média anual de um período de vinte anos (1991 a 2010) de 252 postos pluviométricos. Como forma de determinação do método mais adequado optou-se pela técnica de validação cruzada como critério de comparação, determinando o erro médio quadrático (RMSE), o coeficiente de determinação (r²), o coeficiente de correlação de Pearson (r), o índice de concordância (d) e o índice de desempenho (c) entre os dados estimados e os dados observados. Os resultados apontam que a interpolação por Krigagem exponencial apresentou critério de desempenho classificado como bom e um menor erro quadrático médio (164,09 mm), mostrando ser esse o interpolador de melhor representatividade espacial para o conjunto de dados. Keywords: geoestatística, postos pluviométricos, variáveis regionalizadas. NOGUEIRA, D. B.; SILVA, A. O.; SILVA, A. P. N. COMPARISON OF SPATIAL INTERPOLATION METHODS FOR THE ESTIMATION OF PRECIPITATION DISTRIBUTION IN CEARÁ -BRAZIL 2 ABSTRACT The spatial distribution of precipitation is still largely represented by geostatistical methods of interpolation and in semiarid areas it requires recurrent studies due to their temporal and spatial variability. Therefore, aiming at the improvement of interpolation methods and the improvement of rainfall maps in the state of Ceará, this study aimed to analyze the accuracy of five interpolation methods: Inverse of Square Distance (ISD), Kriging with a spherical semivariogram model, Kriging with a exponential semivariogram model, Natural neighbor and Spline regularized. For that, data of annual average rainfall of a period of twenty years (1991 to 2010) of 252 rain gauges were used. As a form of evaluation and determination of the most appropriate method, the technique of cross-validation was chosen as the criterion of comparison, determining the root mean square error (RMSE), coefficient of determination (r²), Pearson correlation coefficient (r), concordance index (d) and performance index (c) between the estimated data and the observed data. The results show that the interpolation by exponential Kriging method presented performance criterion classified as good and lower mean square error (164,09), showing that it is the interpolator of better spatial representation for the data set under study. Keywords: statistical, rain gauges, regionalized variables.

Comparison of Semivariogram Models in Rain Gauge Network Design

The well-known geostatistics method (variance-reduction method) is commonly used to determine the optimal rain gauge network. The main problem in geostatistics method to determine the best semivariogram model in order to be used in estimating the variance. An optimal choice of the semivariogram model is an important point for a good data evaluation process. Three different semivariogram models which are Spherical, Gaussian and Exponential are used and their performances are compared in this study. Cross validation technique is applied to compute the errors of the semivariograms. Rain-fall data for the period of 1975 – 2008 from the existing 84 rain gauge stations covering the state of Johor are used in this study. The result shows that the exponential model is the best semivariogram model and chosen to determine the optimal number and location of rain gauge station.

A Research on the Effect of Heterogeneities on Sandstone Matrix Acidizing Performance

Matrix acidizing is one of the common methods to enhance production in sandstone reservoirs. Conventional acidizing designs generally neglected the effect of heterogeneities of mineral and flow field distributions both in areal and vertical directions and assumed that the acid front propagates with a piston-like style. However, sandstone formations inevitably have small-scale heterogeneities of minerals and flow properties that may give rise to acid propagation in a manner much different from what is predicted based on homogeneous assumptions. In this paper, we conduct a research to numerically investigate how the heterogeneities affect acidizing performance under in situ conditions. Firstly, a heterogeneity model is built for mineral and porosity distributions by using the semivariogram model of geological statistics, based on which we generate spatially correlated porosity and mineral distributions. Next, a model of radial acid flooding is developed based on mass balance and the chemical reactions between the acids and minerals occurring during the acidizing process. The model is numerically solved to investigate the permeability response, acid distributions, precipitate distributions, and the effect of the heterogeneities on acidizing. The results show that the heterogeneities both in areal and vertical directions have a significant effect on acidizing. The flow field heterogeneities have a more serious impact than the mineral heterogeneities. In a plane, strong porosity heterogeneity can give rise to acid fingering and even channeling, which make the acid penetration distance longer than the homogeneous cases. The secondary precipitate has a significant effect when fast-reacting mineral content is high. Vertically, several-fold permeability contrast creates the acid break through the high-perm zone leaving the low-perm zone understimulated. Both flow field and mineral heterogeneities make it possible to create high-permeability channels during the acidizing process and to obtain a longer acid penetration distance.

Geostatistical mapping of land prices in Taiwan Case: an empirical comparison of ordinary kriging

<p><strong>Abstract.</strong> This study discusses the use of land price data to estimate the land price using the ordinary kriging method (OK). Moreover, compares the Gaussian and exponential semivariogram model by cross-validation and which one is more suitable for the ordinary kriging model also has a good Mean absolute percentage error (MAPE). The study area is in Tainan City, Taiwan. The data sample is a land transaction case from 2012 to 2018. The study adopts the inherent hypothesis that the difference between the random variables in different spatial locations is a random variable, and the expected value and the variance are only related to the distance between the random variables and the spatial position. The ordinary kriging method was used as a tool in the study. First, the data were randomly divided into experimental group (90%) and control group (10%) by spatial random sampling. A total of 10 pairs were combined to ensure the stability of the verification. The space autocorrelation distance (Moran's I) is taken as the influence range, and the semivariogram are verified by cross-validation method, and then verified by mean absolute percentage error (MAPE). The study found that under the same data sample, after cross-validation, the exponential semivariogram model has a better land price prediction effect, whether it is the verification result or the mean absolute percentage error.</p>

GEOESTATÍSTICA APLICADA NA ESTIMATIVA DE CHUVAS MÁXIMAS DIÁRIAS NO ESTADO DE MINAS GERAIS

O objetivo desse trabalho foi determinar os parâmetros α e β espacializados e, assim, possibilitar a estimativa de chuvas intensas em todo o estado de Minas Gerais com uma determinada probabilidade, e também para tempos de retorno diferentes dos tradicionais. A área de estudo considerada foi o Estado de Minas Gerais, foram utilizados dados de 96 estações pluviométricas presentes na região e aplicados testes de aderência da distribuição generalizada de valores extremos (GEV) e de tendência. Os resultados da avaliação da dependência espacial dos parâmetros α e β e seus respectivos intervalos de confiança, demonstram que o modelo de semivariograma exponencial foi o mais adequado para descrever a dependência espacial dos parâmetros da distribuição GEV, podendo ser aplicados os valores de precipitação máxima diária no Estado de Minas Gerais. Concluiu-se que os mapas gerados podem ser utilizados para determinação dos parâmetros α e β em qualquer localidade de Minas Gerais e, assim, a precipitação máxima diária pode ser obtida para quaisquer tempos de retorno desde que os intervalos de confiança de α e β sejam respeitados.Palavras-chave: eventos extremos, precipitação máxima, probabilidade. GEOSTATISTICS APPLIED IN THE ESTIMATION OF DAILY MAXIMUM RAINS IN THE STATE OF MINAS GERAIS ABSTRACT:The objective of this work is to determine the parameters α and β estimates of rainfall in the entire state of Minas Gerais with a certain probability, as well as our traditional return times. A study area of the State of Minas Gerais, with rainfall data of 96 rainfall stations present in the region and tested for generalized distribution of extreme values (GEV)adherence and trend. The results of the spatial dependence evaluation of the parameters and their confidence parameters demonstrate that the exponential semivariogram model was the most adequate to describe a spatial dependence of the parameters of the GEV distribution, being able to be applied to values of daily maximum non-state precipitation Minas Gerais. It was concluded that the generated maps can be used for the determination of the parameters and in any locality of Minas Gerais and, thus, a maximum daily precipitation, can be obtained by times of return since the confidence intervals of α and β are respected.Keywords: extreme events, maximum precipitation, probability.

The Application of Spatial Analysis and Time Series in Modeling the Frequency of Earthquake Events in Bengkulu Province

This study provides an overview in combining spatial analysis and time series analysis to model the frequency of earthquake. The aim of this research is to apply the spatial statistical analysis and time series analysis in estimating semivariogram parameters for the next four steps. The data in this study is secondary data that has been validated based on sources that publish parameters of earthquake events. Looking at the characteristics of the earthquake frequency frequency data, there are spatial and time elements. The method used in this research is interpolation kriging and Autoregressive Moving Average (ARMA) model. The semivariogram models used in kriging interpolation are: Spherical, Exponential, Gaussian, and Linear. The parameters of the semivariogram model are modeled using ARMA time series analysis adjusted to the model diagnostic results. To measure of fit model is used Mean Square Error (MSE). The result of research is a suitable semivariogram model to be applied in the modeling of earthquake events is the Spherical model. While each parameter is estimated using ARMA model (2,2) with different coefficient estimation value.