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
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
It is well known that Landsat TM images are the most widely used remote sensing data in various fields.Usually,it has 7 different electromagnetic spectrum bands,among which the sixth one has much lower ground resoluti...It is well known that Landsat TM images are the most widely used remote sensing data in various fields.Usually,it has 7 different electromagnetic spectrum bands,among which the sixth one has much lower ground resolution compared with the other six bands.Nevertheless,it is useful in the study of rock spectrum reflection,geothermal resources exploration,etc.To improve the ground resolution of TM6 to the level as that of the other six bands is a problem .This paper presents an algorithm based on the combination of multivariate regression model with semivariogram function which can improve the ground resolution of TM6 by "fusing" the data of other six bands.It includes the following main steps: （1） testing the correlation between TM6 and one of TM15,7.If the correlation coefficient between TM6 and another one is greater than a given threshold value,then select the band to the regression analysis as an argument.（2） calculating the size of the template window within which some parameters needed by the regression model will be calculated; （3） replacing the original pixel values of TM6 by those obtained by regression analysis; （4） using image entropy as a measurement to evaluate the quality of the fused image of TM6.The basic mechanism of the algorithm is discussed and the V C ++ program for implementing this algorithm is also presented.A simple application example is given in the last part of this paper,showing the effectiveness of the algorithm.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
Void ratio measures compactness of ground soil in geotechnical engineering. When samples are collected in certain area for mapping void ratios, other relevant types of properties such as water content may be also anal...Void ratio measures compactness of ground soil in geotechnical engineering. When samples are collected in certain area for mapping void ratios, other relevant types of properties such as water content may be also analyzed. To map the spatial distribution of void ratio in the area based on these types of point, observation data interpolation is often needed. Owing to the variance of sampling density along the horizontal and vertical directions, special consideration is required to handle anisotropy of estimator. 3D property modeling aims at predicting the overall distribution of property values from limited samples, and geostatistical method can be employed naturally here because they help to minimize the mean square error of estimation. To construct 3D property model of void ratio, cokriging was used considering its mutual correlation with water content, which is another important soil parameter. Moreover, K-D tree was adopted to organize the samples to accelerate neighbor query in 3D space during the above modeling process. At last, spatial configuration of void ratio distribution in an engineering body was modeled through 3D visualization, which provides important information for civil engineering purpose.展开更多
In this study, the petrophysical parameters such as density, sonic, neutron, and porosity were investigated and presented in the 3D models. The 3D models were built using geostatistical method that is used to estimate...In this study, the petrophysical parameters such as density, sonic, neutron, and porosity were investigated and presented in the 3D models. The 3D models were built using geostatistical method that is used to estimate studied parameters in the entire reservoir. For this purpose, the variogram of each parameter was determined to specify spatial correlation of data. Resulted variograms were non-monotonic. That shows anisotropy of structure. The lithology and porosity parameters are the main causes of this anisotropy. The 3D models also show that petrophysical data has higher variation in north part of reservoir than south part. In addition to, the west limb of reservoir shows higher porosity than east limb. The variation of sonic and neutron data are similar whereas the density data has opposed variation.展开更多
This paper presents a three-dimensional geological reservoir model created using stochastic simulation. The oil field presented is an East African oil field formed by a structural trap. Data analysis and transformatio...This paper presents a three-dimensional geological reservoir model created using stochastic simulation. The oil field presented is an East African oil field formed by a structural trap. Data analysis and transformations were conducted on the properties before simulation. The variogram was used to measure the spatial correlation of cell-based facies modeling, and porosity and permeability modeling. Two main lithologies were modelled using sequential indicator simulation, sand and shale. Sand had a percentage of 26.8% and shale of 73.2%. There was a clear property distribution trend of sand and shale from the southwest to the northeastern part of a reservoir. The distribution trend of the facies resembled the proposed depositional model of the reservoir. Simulations show that average porosity and permeability of the reservoir are about 20% and 1004 mD, respectively. Average water saturation was 64%. STOIIP volume of 689.42 MMbbls was calculated. The results of simulation showed that the south eastern part of the reservoir holds higher volumes of oil. In conclusion, the model gave a better geological understanding of the geology of the area and can be used for decision making about the future development of the reservoir, prediction performance and uncertainty analysis.展开更多
Population is an important strategic resource for national development, a fundamental element of socio-economic development. The coordinated development of population and economy is an effective way to achieve rapid e...Population is an important strategic resource for national development, a fundamental element of socio-economic development. The coordinated development of population and economy is an effective way to achieve rapid economic growth. Based on the population statistics data of counties (districts) in Henan Province, China, from 2006 to 2021. The paper firstly uses the logistic population growth mathematical model to calculate the resident population growth rate of counties (districts), then utilizes the hotspot analysis and spatial semi-variogram analysis, to research the spatial distribution characteristics of the resident population growth rate in Henan Province. The research results show that the evolution of the regional resident population in the province basically conforms to the logistic natural growth model. The resident population growth rate shows the characteristics of high in the north and low in the south, high in the center and low in the surrounding regions. The resident population growth rate is positively correlated with the level of economic development;the urban built-up areas, especially the new regions in urban planning, have a fast growth rate of resident population, which has a significant siphon effect on the population of surrounding regions. The hotspots of resident population growth rate in the province are mainly distributed in the urban built-up areas and surrounding regions of Zhengzhou, Luoyang, and Xinxiang, accounting for about 3.51% of the total area of the province. The cold spots are mainly distributed in the eastern part of the province, forming zonal distribution, which spans across Shangqiu City, Zhoukou City, and Zhumadian City, accounting for about 8.61% of the total area of the province. The area with negative growth of resident population accounts for approximately 53.47% of the total province. The spatial distribution of the growth rate of the resident population in the whole province basically conforms to the spherical model, with a small dispersion degree and a short range. In the range, there is a high degree of variability in resident population growth rate.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.
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It is well known that Landsat TM images are the most widely used remote sensing data in various fields.Usually,it has 7 different electromagnetic spectrum bands,among which the sixth one has much lower ground resolution compared with the other six bands.Nevertheless,it is useful in the study of rock spectrum reflection,geothermal resources exploration,etc.To improve the ground resolution of TM6 to the level as that of the other six bands is a problem .This paper presents an algorithm based on the combination of multivariate regression model with semivariogram function which can improve the ground resolution of TM6 by "fusing" the data of other six bands.It includes the following main steps: （1） testing the correlation between TM6 and one of TM15,7.If the correlation coefficient between TM6 and another one is greater than a given threshold value,then select the band to the regression analysis as an argument.（2） calculating the size of the template window within which some parameters needed by the regression model will be calculated; （3） replacing the original pixel values of TM6 by those obtained by regression analysis; （4） using image entropy as a measurement to evaluate the quality of the fused image of TM6.The basic mechanism of the algorithm is discussed and the V C ++ program for implementing this algorithm is also presented.A simple application example is given in the last part of this paper,showing the effectiveness of the algorithm.
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.
基金supported by Beijing Multi-parameters 3D Geological Survey Program (No. 200313000045)
文摘Void ratio measures compactness of ground soil in geotechnical engineering. When samples are collected in certain area for mapping void ratios, other relevant types of properties such as water content may be also analyzed. To map the spatial distribution of void ratio in the area based on these types of point, observation data interpolation is often needed. Owing to the variance of sampling density along the horizontal and vertical directions, special consideration is required to handle anisotropy of estimator. 3D property modeling aims at predicting the overall distribution of property values from limited samples, and geostatistical method can be employed naturally here because they help to minimize the mean square error of estimation. To construct 3D property model of void ratio, cokriging was used considering its mutual correlation with water content, which is another important soil parameter. Moreover, K-D tree was adopted to organize the samples to accelerate neighbor query in 3D space during the above modeling process. At last, spatial configuration of void ratio distribution in an engineering body was modeled through 3D visualization, which provides important information for civil engineering purpose.
文摘In this study, the petrophysical parameters such as density, sonic, neutron, and porosity were investigated and presented in the 3D models. The 3D models were built using geostatistical method that is used to estimate studied parameters in the entire reservoir. For this purpose, the variogram of each parameter was determined to specify spatial correlation of data. Resulted variograms were non-monotonic. That shows anisotropy of structure. The lithology and porosity parameters are the main causes of this anisotropy. The 3D models also show that petrophysical data has higher variation in north part of reservoir than south part. In addition to, the west limb of reservoir shows higher porosity than east limb. The variation of sonic and neutron data are similar whereas the density data has opposed variation.
文摘This paper presents a three-dimensional geological reservoir model created using stochastic simulation. The oil field presented is an East African oil field formed by a structural trap. Data analysis and transformations were conducted on the properties before simulation. The variogram was used to measure the spatial correlation of cell-based facies modeling, and porosity and permeability modeling. Two main lithologies were modelled using sequential indicator simulation, sand and shale. Sand had a percentage of 26.8% and shale of 73.2%. There was a clear property distribution trend of sand and shale from the southwest to the northeastern part of a reservoir. The distribution trend of the facies resembled the proposed depositional model of the reservoir. Simulations show that average porosity and permeability of the reservoir are about 20% and 1004 mD, respectively. Average water saturation was 64%. STOIIP volume of 689.42 MMbbls was calculated. The results of simulation showed that the south eastern part of the reservoir holds higher volumes of oil. In conclusion, the model gave a better geological understanding of the geology of the area and can be used for decision making about the future development of the reservoir, prediction performance and uncertainty analysis.
文摘Population is an important strategic resource for national development, a fundamental element of socio-economic development. The coordinated development of population and economy is an effective way to achieve rapid economic growth. Based on the population statistics data of counties (districts) in Henan Province, China, from 2006 to 2021. The paper firstly uses the logistic population growth mathematical model to calculate the resident population growth rate of counties (districts), then utilizes the hotspot analysis and spatial semi-variogram analysis, to research the spatial distribution characteristics of the resident population growth rate in Henan Province. The research results show that the evolution of the regional resident population in the province basically conforms to the logistic natural growth model. The resident population growth rate shows the characteristics of high in the north and low in the south, high in the center and low in the surrounding regions. The resident population growth rate is positively correlated with the level of economic development;the urban built-up areas, especially the new regions in urban planning, have a fast growth rate of resident population, which has a significant siphon effect on the population of surrounding regions. The hotspots of resident population growth rate in the province are mainly distributed in the urban built-up areas and surrounding regions of Zhengzhou, Luoyang, and Xinxiang, accounting for about 3.51% of the total area of the province. The cold spots are mainly distributed in the eastern part of the province, forming zonal distribution, which spans across Shangqiu City, Zhoukou City, and Zhumadian City, accounting for about 8.61% of the total area of the province. The area with negative growth of resident population accounts for approximately 53.47% of the total province. The spatial distribution of the growth rate of the resident population in the whole province basically conforms to the spherical model, with a small dispersion degree and a short range. In the range, there is a high degree of variability in resident population growth rate.
