The objective of this study is to develop an advanced approach to variogram modelling by integrating genetic algorithms(GA)with machine learning-based linear regression,aiming to improve the accuracy and efficiency of...The objective of this study is to develop an advanced approach to variogram modelling by integrating genetic algorithms(GA)with machine learning-based linear regression,aiming to improve the accuracy and efficiency of geostatistical analysis,particularly in mineral exploration.The study combines GA and machine learning to optimise variogram parameters,including range,sill,and nugget,by minimising the root mean square error(RMSE)and maximising the coefficient of determination(R^(2)).The experimental variograms were computed and modelled using theoretical models,followed by optimisation via evolutionary algorithms.The method was applied to gravity data from the Ngoura-Batouri-Kette mining district in Eastern Cameroon,covering 141 data points.Sequential Gaussian Simulations(SGS)were employed for predictive mapping to validate simulated results against true values.Key findings show variograms with ranges between 24.71 km and 49.77 km,opti-mised RMSE and R^(2) values of 11.21 mGal^(2) and 0.969,respectively,after 42 generations of GA optimisation.Predictive mapping using SGS demonstrated that simulated values closely matched true values,with the simu-lated mean at 21.75 mGal compared to the true mean of 25.16 mGal,and variances of 465.70 mGal^(2) and 555.28 mGal^(2),respectively.The results confirmed spatial variability and anisotropies in the N170-N210 directions,consistent with prior studies.This work presents a novel integration of GA and machine learning for variogram modelling,offering an automated,efficient approach to parameter estimation.The methodology significantly enhances predictive geostatistical models,contributing to the advancement of mineral exploration and improving the precision and speed of decision-making in the petroleum and mining industries.展开更多
变异函数量化了空间2点地质属性的变异性,对地质统计分析至关重要。当地质数据随空间坐标呈现趋势变化时,正确选择和估计变异函数十分困难。为实现变异函数的模型选择和参数估计,提出了基于贝叶斯理论的变异函数选择方法,采用拉普拉斯...变异函数量化了空间2点地质属性的变异性,对地质统计分析至关重要。当地质数据随空间坐标呈现趋势变化时,正确选择和估计变异函数十分困难。为实现变异函数的模型选择和参数估计,提出了基于贝叶斯理论的变异函数选择方法,采用拉普拉斯近似方法将后验概率分布近似为高斯分布。首先计算出参数的后验概率分布,随后分别计算每个备选变异函数的贝叶斯模型证据,以确定最优模型。探讨了3种模型选择方法在变异函数选择中的适用性,包括贝叶斯模型证据(BME)、Akaike information criterion(AIC)识别准则和Bayesian information criterion(BIC)识别准则。通过实测静力触探试验的锥端阻力数据,说明了该方法,并从模型拟合度和复杂度罚值2个方面比较3种方法在变异函数模型选择中的差异性。研究表明,给定试验数据条件下,BME能够合理地考虑变异函数的拟合度和复杂性;而AIC和BIC识别准则在模型参数个数相同时,仅能反映不同变异函数的拟合度差异,因此,在这种情况下推荐采用BME选择变异函数。本研究方法能够在考虑趋势项参数条件下合理地选择地质统计学变异函数,所选最优变异函数与试验变异函数较一致,为地质统计学分析提供了有效的参考。展开更多
Inferring the experimental variogram used in geostatistics commonly relies on the method-of-moments approach.Ideally,the available data-set used for calculating the experimental variogram should be drawn from a regula...Inferring the experimental variogram used in geostatistics commonly relies on the method-of-moments approach.Ideally,the available data-set used for calculating the experimental variogram should be drawn from a regular pattern.However,in practice the available data-set is typically sampled over a sparse pattern at irregularly spaced locations.Hence,some binning of the variogram cloud is required to obtain fair estimates of the experimental variogram.Grouping of the variogram data pairs as a result of conventional binning depends on parameters such as the main anisotropic directions and a regular definition of the lag vectors.These parameters are not based on the configuration of the variogram data pairs in the variogram cloud but on a segment of it that is arbitrarily predefined.Therefore,the conventional experimental variogram estimation approach is biased because of the strict configuration of the bins over the variogram cloud.In this paper,a new method of estimating experimental variograms is proposed.Lag vectors and their tolerances are decided in the proposed method from information in the variogram cloud：they are not influenced by any predefined directions.The proposed methodology is a well-founded,practicable and easy-to-automate approach for experimental variogram calculation using an irregularly sampled data-set.Comparison of results from the new method to those from the traditional approach is very encouraging.展开更多
Variograms are important tools in the spatial distribution of facies and petrophysical properties. Due to the scarcity of subsurface well data, both spatially and quantity wise, variograms representing the data tend t...Variograms are important tools in the spatial distribution of facies and petrophysical properties. Due to the scarcity of subsurface well data, both spatially and quantity wise, variograms representing the data tend to have a lot of uncertainties. In order to reduce uncertainty in variograms, well data can be supplemented with the geological knowledge of the reservoir. This has been demonstrated by various authors in previous works. In their paper “Methodology to Incorporate Geological Knowledge in Variogram Modeling,” A. Bahar and M. Kelkar introduced a methodology to incorporate geological knowledge by studying the energy level of the depositional environment and grain texture. They used these two attributes to determine the relative distance of continuity of the lithofacies and incorporated it in the variogram modeling. In this paper, we introduce another attribute that determines the continuity of lithofacies;the accommodation or deposition space. For illustration purpose, two sets of facies models were constructed: The first using subsurface well data only and the second using well data and geological information of the reservoir. The two sets of models showed significant variation in the property distribution. The first set gave a more random appearance of the facies distribution while the second set gave a more realistic depiction of the depositional environment of the reservoir. We concluded that other than the grain size and the energy level of the depositional environment, another important determinant for continuity in variograms is the knowledge of the depositional space. Incorporating the knowledge of the depositional environment enabled a more accurate estimation of the variogram parameters. This resulted in an improvement in the accuracy of the model.展开更多
Most evaluation of the consistency of multisensor images have focused on Normalized Difference Vegetation Index （NDVI） products for natural landscapes, often neglecting less vegetated urban landscapes. This gap has ...Most evaluation of the consistency of multisensor images have focused on Normalized Difference Vegetation Index （NDVI） products for natural landscapes, often neglecting less vegetated urban landscapes. This gap has been filled through quantifying and evaluating spatial heterogeneity of urban and natural landscapes from QuickBird, Satellite pour l＇observation de la Terre （SPOT）, Ad- vanced Spacebome Thermal Emission and Reflection Radiometer （ASTER） and Landsat Thematic Mapper （TM） images with variogram analysis. Instead of a logarithmic relationship with pixel size observed in the corresponding aggregated images, the spatial variability decayed and the spatial structures decomposed more slowly and complexly with spatial resolution for real multisensor im- ages. As the spatial resolution increased, the proportion of spatial variability of the smaller spatial structure decreased quickly and only a larger spatial structure was observed at very coarse scales. Compared with visible band, greater spatial variability was observed in near infrared band for both densely and less densely vegetated landscapes. The influence of image size on spatial heterogeneity was highly dependent on whether the empirical sernivariogram reached its sill within the original image size. When the empirical semivariogram did not reach its sill at the original observation scale, spatial variability and mean characteristic length scale would increase with image size; otherwise they might decrease. This study could provide new insights into the knowledge of spatial heterogeneity in real multisen- sor images with consideration of their nominal spatial resolution, image size and spectral bands.展开更多
The objective of this research is to analyze variogram analyses of soil characters in Glacial Moraine Landscapes. The research site is located in sloping landscapes, Kuehren, North Germany. The survey method was detai...The objective of this research is to analyze variogram analyses of soil characters in Glacial Moraine Landscapes. The research site is located in sloping landscapes, Kuehren, North Germany. The survey method was detailed using maps with scales of 1：5,000. Soil sampling was performed by soil pits and borings and completely analyzed in laboratory. Collected data were evaluated by geostatistics program for spatial soil variability analyses. The variogram models show that spatial soil variability ranges between 70-120 m （mean： 85 m）. Effective distances of sampling are calculated at around 50 m. The range values of soil characters are proportional with the range of elevation （range： 70 m, effective distance： 40 m）. The relief determines mainly the spatial variability of soil characters.展开更多
Background: When applied to trabecular bone X-ray images, a method for analyzing trabecular bone texture based on the initial slope of variogram (ISV) was used to assess the trabecular bone health. Methodology: Data f...Background: When applied to trabecular bone X-ray images, a method for analyzing trabecular bone texture based on the initial slope of variogram (ISV) was used to assess the trabecular bone health. Methodology: Data from more than two hundred subjects were retrospectively studied. For each subject, a DXA (GE Lunar Prodigy) scan of the forearm was performed, and bone mineral density (BMD) value was measured at the location of ultra-distal radius, X-ray digital image of the same forearm was taken on the same day, and ISV value over the same location of ultra-distal radius was calculated. Pearson’s correlation coefficients were calculated to examine the correlation between BMD and ISV of the trabecular bones located at the same ultra-distal radius. ISV values changed with subjects’ age were also reported. Results: The results show that ISV value was highly correlated with the DXA-measured BMD of the same trabecular bone located at the ultra-distal radius. The correlation coefficient between ISV and BMD with the 95% confident was 0.79 ± 0.09. They also demonstrated that the age-related changes in trabecular bone health and differentiated age patterns in males and females, respectively. The results showed that the decrease in BMD was accompanied by a decrease in the initial slope of variogram (ISV). Conclusions: This study suggests that ISV might be used to quantitatively evaluate trabecular health for osteoporosis and bone disease diagnosis.展开更多
文摘The objective of this study is to develop an advanced approach to variogram modelling by integrating genetic algorithms(GA)with machine learning-based linear regression,aiming to improve the accuracy and efficiency of geostatistical analysis,particularly in mineral exploration.The study combines GA and machine learning to optimise variogram parameters,including range,sill,and nugget,by minimising the root mean square error(RMSE)and maximising the coefficient of determination(R^(2)).The experimental variograms were computed and modelled using theoretical models,followed by optimisation via evolutionary algorithms.The method was applied to gravity data from the Ngoura-Batouri-Kette mining district in Eastern Cameroon,covering 141 data points.Sequential Gaussian Simulations(SGS)were employed for predictive mapping to validate simulated results against true values.Key findings show variograms with ranges between 24.71 km and 49.77 km,opti-mised RMSE and R^(2) values of 11.21 mGal^(2) and 0.969,respectively,after 42 generations of GA optimisation.Predictive mapping using SGS demonstrated that simulated values closely matched true values,with the simu-lated mean at 21.75 mGal compared to the true mean of 25.16 mGal,and variances of 465.70 mGal^(2) and 555.28 mGal^(2),respectively.The results confirmed spatial variability and anisotropies in the N170-N210 directions,consistent with prior studies.This work presents a novel integration of GA and machine learning for variogram modelling,offering an automated,efficient approach to parameter estimation.The methodology significantly enhances predictive geostatistical models,contributing to the advancement of mineral exploration and improving the precision and speed of decision-making in the petroleum and mining industries.
文摘变异函数量化了空间2点地质属性的变异性,对地质统计分析至关重要。当地质数据随空间坐标呈现趋势变化时,正确选择和估计变异函数十分困难。为实现变异函数的模型选择和参数估计,提出了基于贝叶斯理论的变异函数选择方法,采用拉普拉斯近似方法将后验概率分布近似为高斯分布。首先计算出参数的后验概率分布,随后分别计算每个备选变异函数的贝叶斯模型证据,以确定最优模型。探讨了3种模型选择方法在变异函数选择中的适用性,包括贝叶斯模型证据(BME)、Akaike information criterion(AIC)识别准则和Bayesian information criterion(BIC)识别准则。通过实测静力触探试验的锥端阻力数据,说明了该方法,并从模型拟合度和复杂度罚值2个方面比较3种方法在变异函数模型选择中的差异性。研究表明,给定试验数据条件下,BME能够合理地考虑变异函数的拟合度和复杂性;而AIC和BIC识别准则在模型参数个数相同时,仅能反映不同变异函数的拟合度差异,因此,在这种情况下推荐采用BME选择变异函数。本研究方法能够在考虑趋势项参数条件下合理地选择地质统计学变异函数,所选最优变异函数与试验变异函数较一致,为地质统计学分析提供了有效的参考。
文摘Inferring the experimental variogram used in geostatistics commonly relies on the method-of-moments approach.Ideally,the available data-set used for calculating the experimental variogram should be drawn from a regular pattern.However,in practice the available data-set is typically sampled over a sparse pattern at irregularly spaced locations.Hence,some binning of the variogram cloud is required to obtain fair estimates of the experimental variogram.Grouping of the variogram data pairs as a result of conventional binning depends on parameters such as the main anisotropic directions and a regular definition of the lag vectors.These parameters are not based on the configuration of the variogram data pairs in the variogram cloud but on a segment of it that is arbitrarily predefined.Therefore,the conventional experimental variogram estimation approach is biased because of the strict configuration of the bins over the variogram cloud.In this paper,a new method of estimating experimental variograms is proposed.Lag vectors and their tolerances are decided in the proposed method from information in the variogram cloud：they are not influenced by any predefined directions.The proposed methodology is a well-founded,practicable and easy-to-automate approach for experimental variogram calculation using an irregularly sampled data-set.Comparison of results from the new method to those from the traditional approach is very encouraging.
文摘Variograms are important tools in the spatial distribution of facies and petrophysical properties. Due to the scarcity of subsurface well data, both spatially and quantity wise, variograms representing the data tend to have a lot of uncertainties. In order to reduce uncertainty in variograms, well data can be supplemented with the geological knowledge of the reservoir. This has been demonstrated by various authors in previous works. In their paper “Methodology to Incorporate Geological Knowledge in Variogram Modeling,” A. Bahar and M. Kelkar introduced a methodology to incorporate geological knowledge by studying the energy level of the depositional environment and grain texture. They used these two attributes to determine the relative distance of continuity of the lithofacies and incorporated it in the variogram modeling. In this paper, we introduce another attribute that determines the continuity of lithofacies;the accommodation or deposition space. For illustration purpose, two sets of facies models were constructed: The first using subsurface well data only and the second using well data and geological information of the reservoir. The two sets of models showed significant variation in the property distribution. The first set gave a more random appearance of the facies distribution while the second set gave a more realistic depiction of the depositional environment of the reservoir. We concluded that other than the grain size and the energy level of the depositional environment, another important determinant for continuity in variograms is the knowledge of the depositional space. Incorporating the knowledge of the depositional environment enabled a more accurate estimation of the variogram parameters. This resulted in an improvement in the accuracy of the model.
基金Under the auspices of National Natural Science Foundation of China(No.41071267,41001254)Natural Science Foundation of Fujian Province(No.2012I0005,2012J01167)
文摘Most evaluation of the consistency of multisensor images have focused on Normalized Difference Vegetation Index （NDVI） products for natural landscapes, often neglecting less vegetated urban landscapes. This gap has been filled through quantifying and evaluating spatial heterogeneity of urban and natural landscapes from QuickBird, Satellite pour l＇observation de la Terre （SPOT）, Ad- vanced Spacebome Thermal Emission and Reflection Radiometer （ASTER） and Landsat Thematic Mapper （TM） images with variogram analysis. Instead of a logarithmic relationship with pixel size observed in the corresponding aggregated images, the spatial variability decayed and the spatial structures decomposed more slowly and complexly with spatial resolution for real multisensor im- ages. As the spatial resolution increased, the proportion of spatial variability of the smaller spatial structure decreased quickly and only a larger spatial structure was observed at very coarse scales. Compared with visible band, greater spatial variability was observed in near infrared band for both densely and less densely vegetated landscapes. The influence of image size on spatial heterogeneity was highly dependent on whether the empirical sernivariogram reached its sill within the original image size. When the empirical semivariogram did not reach its sill at the original observation scale, spatial variability and mean characteristic length scale would increase with image size; otherwise they might decrease. This study could provide new insights into the knowledge of spatial heterogeneity in real multisen- sor images with consideration of their nominal spatial resolution, image size and spectral bands.
文摘The objective of this research is to analyze variogram analyses of soil characters in Glacial Moraine Landscapes. The research site is located in sloping landscapes, Kuehren, North Germany. The survey method was detailed using maps with scales of 1：5,000. Soil sampling was performed by soil pits and borings and completely analyzed in laboratory. Collected data were evaluated by geostatistics program for spatial soil variability analyses. The variogram models show that spatial soil variability ranges between 70-120 m （mean： 85 m）. Effective distances of sampling are calculated at around 50 m. The range values of soil characters are proportional with the range of elevation （range： 70 m, effective distance： 40 m）. The relief determines mainly the spatial variability of soil characters.
文摘Background: When applied to trabecular bone X-ray images, a method for analyzing trabecular bone texture based on the initial slope of variogram (ISV) was used to assess the trabecular bone health. Methodology: Data from more than two hundred subjects were retrospectively studied. For each subject, a DXA (GE Lunar Prodigy) scan of the forearm was performed, and bone mineral density (BMD) value was measured at the location of ultra-distal radius, X-ray digital image of the same forearm was taken on the same day, and ISV value over the same location of ultra-distal radius was calculated. Pearson’s correlation coefficients were calculated to examine the correlation between BMD and ISV of the trabecular bones located at the same ultra-distal radius. ISV values changed with subjects’ age were also reported. Results: The results show that ISV value was highly correlated with the DXA-measured BMD of the same trabecular bone located at the ultra-distal radius. The correlation coefficient between ISV and BMD with the 95% confident was 0.79 ± 0.09. They also demonstrated that the age-related changes in trabecular bone health and differentiated age patterns in males and females, respectively. The results showed that the decrease in BMD was accompanied by a decrease in the initial slope of variogram (ISV). Conclusions: This study suggests that ISV might be used to quantitatively evaluate trabecular health for osteoporosis and bone disease diagnosis.
