Calculation of Variograms and spatial continuity is one of the first and most important processes in geostatistical modeling, which is a long and experience-oriented process. Due to the complexities of calculating experimental Variograms, interpretation and fitting the appropriate model are always the main challenges in this field. This article presents an intelligent Variogram modeling method using deep learning that can increase the speed of Variogram modeling and also prevent common errors in manual Variogram model fitting. In this method, two convolutional neural networks are used. The first CNN network converts the initial data into a 2D simulated map based on various Variogram models. For this purpose, it is necessary to train the first network with initial data and their corresponding simulations. The output of this model is entered into the second convolutional neural network as input, and the Variogram parameters (including range, azimuth, ratio, and nugget effect) are predicted. In this article, the proposed algorithm is implemented on synthetic 2D data and the parameters of the CNN models are optimized. The accuracy of the proposed model was 97 %, and then the proposed algorithm was used for Variogram modeling of Nouchon area geochemical data, which included the elements Cu, Zn, and Pb. the accuracy of the obtained model compared to manual fitting was 90%.

An important problem in spatial data analysis is Variogram modeling to specify the correlation structure of data. Usually the values of a Variogram estimator at different lags are used for Variogram modeling. Since the number of lags affects the accuracy of the model fitted to the Variogram estimates, finding an optimal value for the number of lags plays an important role in Variogram modeling. In this paper a simulation study is carried out to find the optimal value of the number of lags for data generated from a Gaussian random field. The result has been used in a real practical example to fit an exponential Variogram model to the Variogram estimates. Then, the Variogram is used in kriging to predict tuberculosis disease incidence rates in some cities of Iran.    

The evaluation of potential human and economic losses arising from earthquakes, which may affect urban infrastructures that are spatially extended over an area, is important for national authorities, local municipalities, and the insurance and reinsurance industries. However, seismic-risk analysis of distributed systems and infrastructures need to apply a different approach with respect to the classical site-specific hazard and risk analysis. Ground motion intensity measures (IMs) and resulting structural responses are correlated in neighborhood sites. The correlation value depends on the distance between the adjacent sites and the natural vibration period of structures. In particular, when a lifeline system is of concern, classical site-specific hazard tools, which consider IMs at different locations independently, may not be accurate enough to assess the seismic risk. In fact, modeling of ground motion as a random field, which consists of assigning a spatial correlation to the IM of interest, is required. It is very common in the seismic design of spatially distributed structures and lifelines to include the correlation of the nearby earthquake records, through empirical semi-Variogram functions. In this study, the semi-Variogram of vertical components as a function of inter-site separation distance with respect to the ground motion prediction equations for the Iranian acceleration data (vertical peak ground acceleration (PGA) and vertical pseudo spectral acceleration (PSA)) are presented for the first time using acceleration data from 220 earthquakes. The calculations were carried out for five natural vibration periods in the range of 0 to 3 seconds and using ground motion prediction equations for vertical component. The selected ground motion prediction equation is the local model proposed by Soghrat & Ziaeifar (2017). For estimation of empirical semi-Variogram, two classical and robust estimators, and to fit the data, the exponential and Goda models are used. For the ground motion prediction equation by Soghrat & Zyiaeifar (2017), the values of the range (b) in the exponential model and the values of a and b in the model of Goda (i.e. a continuous function fitted to experimental values in order to deduce semiVariogram values for any possible site separation distance, Goda & Hong, 2008) are estimated. It is observed that the correlation trend range generally increases with period.

The spatial analysis became very important in various fields of landscape archeology and statistical analysis. Spatial relationships of archaeological data, patterns created by human activities, their implications for the interior space of archaeological sites as well as their surroundings are studied by spatial archeology. The main purpose of the study is the geometric analysis and clustering of three archaeological periods of Khonj County. The central question of this research is,“, What patterns do the spatial distribution of the archaeological sites of the Khonj plain follow based on periodic clustering (prehistoric, historical-Islamic, Islamic) and what factors have played a role in locating these sites? ”,The present study is a descriptive-analytical. Through field studies, initially, 192 archaeological sites were recorded in three periods of classification and their location (latitude and longitude). By studying the research literature, then, to extract 8 effective indicators (distance from the river, altitude, slope, direction of slope, climatic conditions, vegetation, precipitation, distance from villages) in the distribution of centers and ancient sites in the Khonj County were extracted at the level of 4 identified villages using Delphi technique. The final status of the points was analyzed using the SemiVariogram tool in the Geostatistical analyst section with ArcGIS software. Research results show,more than 45% of the areas are scattered at an altitude of 1100-900 meters and on a slope of 5 to 10%, their climate with an average precipitation of less than 100 to 150 mm, temperate climate, and pastures around them can be irrigated. The average area is more than 1 hectare and the average distance from the villages is 3000 meters. On average, the distance from water sources is more than 3 km,the areas are concentrated in the eastern half and partly in the southeastern part of the county.

To enhance the certainty of the grade block model, it is necessary to increase the number of exploratory drillholes and collect more data from the deposit. The inputs of the process of locating these additional drillholes include the Variogram model parameters, locations of the samples taken from the initial drillholes, and the geological block model. The uncertainties of these inputs will lead to uncertainties in the optimal locations of additional drillholes. Meanwhile, the locations of the initial data are crisp, but the Variogram model parameters and the geological model have uncertainties due to the limitation of the number of initial data. In this paper, effort has been made to consider the effects of Variogram uncertainties on the optimal location of additional drillholes using the fuzzy kriging and solve the locating problem with the genetic algorithm (GA) optimization method. A bauxite deposit case study has shown the efficiency of the proposed model.

In spatial analysis, the Variogram function that determines the spatial correlation structure of the data is usually unknown and it should be estimated by observations. Although there are several estimation methods for Variogram parameters, limited number of observations produces in much uncertainty in Variogram parameter estimates and finally non-precision of the spatial prediction. In this paper, precision measures of the weighted least squares estimates of Variogram parameters are determined by separate block bootstrap method. Next, these estimates are corrected using precision measures. Then, it is shown by cross-validation method that using a Variogram with corrected parameter estimates with result in increasing spatial prediction precision.

Accurate modeling of omni-directional assay Variograms for a deposit, plays a very significant role in the results of 3-D assay estimation and therefore its distribution within the estimation blocks. The high grade variations in uranium deposits render the significance of accurate Variogram modeling. By this research, some models have been fitted to the experimental Variograms with 0.5 meter composited uranium assay data, resulted from chemical analysis of drill core samples, from a uranium deposit. Reciprocal validation test has been applied for selection and evaluating the effect of suitable results, from multi-structural models in compare with other proper types of models. Validity study of the models is conducted through the reciprocal validation test, based on a series of criteria such as the average of differences and the difference of estimated values and raw data, in order to determine the validity accuracy of the fitted model. It is concluded that the dual-structure spherical model has a higher validity and furthermore reveals the significance of minor structures in Variogram modeling, specifically for uranium deposits.

Background and Objectives: Accuracy of spatial estimation of soil properties such as clay, organic matter and calcium carbonate equivalent is very important in plant nutrition and environmental planning. The most important step before statistical analysis and using geostatistical estimators is data check. In addition to investigation of outlier data and data distribution, another important action in geostatistical studies is trend surface analysis. Analyzing trend surface can evaluate the role of factors such as stone kin, climate, topography and generally regional anomalies. The objective of this study was trend-surface analysis and its effects on Variogram modeling and mapping of clay, organic matter and calcium carbonate equivalent.Materials and Methods: For this purpose, 100 surface soil samples in 0-15 cm depth were selected randomly based on different classes area slope from 41353 ha area in Selin plain farmland located in Kaleibar region, East-Azerbaijan. Soil properties such as clay, calcium carbonate equivalent and organic matter were measured by hydrometer, return titration and wet oxidation method, respectively. For analyzing trend surface used multiple regression models which its independent variables was geographical coordinate and dependent variable was soil properties. For zoning clay, organic matter and calcium carbonate equivalent and residuals of removing trend ordinary kriging was used. The effect of removing trend surface in Variogram modeling and kriging estimating were evaluated by cross-validation method with indexes mean error (ME), root mean square error (RMSE) and determination coefficient (R2).Results: Trend surface analysis showed that the best regression models for trend determination of clay, calcium carbonate equivalent and organic matter were first order, first order and quadratic, respectively. Removing the detected trend led to decrease in sill but the nugget effect did not change. However, no significant difference was observed between accuracy of kriging estimator in presence and removal of trend. This can be attributed to both abnormal manner of environment and activations of human. So that, the regression models of the trends were 35, 18 and 21% of clay, organic matter and calcium carbonate equivalent variations, respectively. However, removing the detected trend led to increase 9.1, 2.7 and 6.6% of R2 for clay, organic matter and calcium carbonate equivalent, respectively.Conclusion: Generally, investigation of trend surface is recommended in soil studies dealing with spatial data, because the trend depends on the location and conditions of the study area as well as the source of the creating trend.

Converting point data to continuous one is the first step in order to use them in scorpan flowchart. For this purpose, different geostatistic methods are available which at present research regression kriging with local Variogram, kriging and co-kriging was applied. For mapping apparent electrical conductivity at the area covering 72000ha located in Ardakan region, 700 readings in horizontal and vertical modes were carried out by electromagnetic induction. Auxiliary data used in this study to represent predictive soil forming factors were terrain attributes, Landsat 7 ETM+ data and a geomorphologic surfaces map. At first, the relationship between independent variables (i.e. auxiliary data) and dependent variable (i.e. apparent electrical conductivity) was calculated by regression tree. Then, the residuals, derived from regression tree, were mapped by using kriging with local Variogram. Finally, the residual and ECa maps were aggregated in order to produce the final maps. Results showed some auxiliary variables had more influence on predictive apparent electrical conductivity model which included: wetness index, geomorphology map and the first principal component analysis. Also, results showed that model predicted ECah with determination of coefficient, root mean square error and mean error were 0.48, 29.64 and -2.23, respectively. This founding confirmed that regression kriging with local Variogram had high performance; however, RK decreases the error of prediction in comparison with OK and CK up to 21% and 28%. Thus, using of regression kriging with local Variogram for digital mapping of soil properties in future studies is suggested.