An exploratory spatial data analysis method(ESDA) was designed Apr.28,2002 for kriging monthly rainfall.Samples were monthly rainfall observed at 61 weather stations in eastern China over the period 1961-1998.Comparis...An exploratory spatial data analysis method(ESDA) was designed Apr.28,2002 for kriging monthly rainfall.Samples were monthly rainfall observed at 61 weather stations in eastern China over the period 1961-1998.Comparison of five semivariogram models(Spherical,Exponential,Linear,Gaussian and Rational Quadratic)indicated that kriging fulfills the objective of finding better ways to estimate interpolation weights and can provide error information for monthly rainfall interpolation.ESDA yielded the three most common forms of experimental semivariogram for monthly rainfall in the erea.All five models were appropriate for monthly rainflaa interpolation but under different circumstances.Spherical,Exponential and Linear models perform as smoothing interpolator of the data,whereas Gaussian and Rational Quadratic models serve as an exact interpolator.Spherical,Exponential and Linear models tend to underestimate the values,On the contrayr,Gaussian and Rational Quadratic models tend to overestimate the values.On the contrary,Gaussian and Rational Quadratic models tend to overestimate the values,Since the suitable model for a specific month usually is not unique and each model does not show any bias toward one or more specific months,an ESDA is recommended for a better interpolation result.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
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
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
The yield map is generated by fitting the yield surface shape of yield monitor data mainly using paraboloid cones on floating neighborhoods. Each yield map value is determined by the fit of such a cone on an elliptica...The yield map is generated by fitting the yield surface shape of yield monitor data mainly using paraboloid cones on floating neighborhoods. Each yield map value is determined by the fit of such a cone on an elliptical neighborhood that is wider across the harvest tracks than it is along them. The coefficients of regression for modeling the paraboloid cones and the scale parameter are estimated using robust weighted M-estimators where the weights decrease quadratically from 1 in the middle to zero at the border of the selected neighborhood. The robust way of estimating the model parameters supersedes a procedure for detecting outliers. For a given neighborhood shape, this yield mapping method is implemented by the Fortran program paraboloidmapping.exe, which can be downloaded from the web. The size of the selected neighborhood is considered appropriate if the variance of the yield map values equals the variance of the true yields, which is the difference between the variance of the raw yield data and the error variance of the yield monitor. It is estimated using a robust variogram on data that have not had the trend removed.展开更多
This paper studies electrical resistivity dataset acquired for a groundwater study in the Domail Plain in the northwestern Himalayan section of Pakistan. Through a combination of geostatistical analysis,geophysical in...This paper studies electrical resistivity dataset acquired for a groundwater study in the Domail Plain in the northwestern Himalayan section of Pakistan. Through a combination of geostatistical analysis,geophysical inversion and visualization techniques,it is possible to re-model and visualize the single dimension resistivity data into 2D and 3D space.The variogram models are utilized to extend the interpretation of the data and to distinguish individual lithologic units and the occurrence of saline water within the subsurface. The resistivity data has been calibrated with the lithological logs taken from the available boreholes. As such the alluvial system of the Domail Plain has formed during episodes of local tectonic activity with fluvial erosion and depositionyielding coarse sediments with high electrical resistivities near to the mountain ranges and finer sediments with medium to low electrical resistivities which tend to settle in the basin center. Thus a change is depositional setting happened from basin lacustrine environment to flash flooding during the Himalayan orogeny. The occurrence of rock salt in the northern mountains has imparted a great influence on the groundwater quality of the study area. The salt is dissolved by water which infiltrates into the subsurface through the water channels. Variogram aided gridding of resistivity data helps to identify the occurrence and distribution of saline water in the subsurface.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 bee...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), Advanced Spaceborne 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 images. 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 semivariogram 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 multisensor images with consideration of their nominal spatial resolution, image size and spectral bands.展开更多
文摘An exploratory spatial data analysis method(ESDA) was designed Apr.28,2002 for kriging monthly rainfall.Samples were monthly rainfall observed at 61 weather stations in eastern China over the period 1961-1998.Comparison of five semivariogram models(Spherical,Exponential,Linear,Gaussian and Rational Quadratic)indicated that kriging fulfills the objective of finding better ways to estimate interpolation weights and can provide error information for monthly rainfall interpolation.ESDA yielded the three most common forms of experimental semivariogram for monthly rainfall in the erea.All five models were appropriate for monthly rainflaa interpolation but under different circumstances.Spherical,Exponential and Linear models perform as smoothing interpolator of the data,whereas Gaussian and Rational Quadratic models serve as an exact interpolator.Spherical,Exponential and Linear models tend to underestimate the values,On the contrayr,Gaussian and Rational Quadratic models tend to overestimate the values.On the contrary,Gaussian and Rational Quadratic models tend to overestimate the values,Since the suitable model for a specific month usually is not unique and each model does not show any bias toward one or more specific months,an ESDA is recommended for a better interpolation result.
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.
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.
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The yield map is generated by fitting the yield surface shape of yield monitor data mainly using paraboloid cones on floating neighborhoods. Each yield map value is determined by the fit of such a cone on an elliptical neighborhood that is wider across the harvest tracks than it is along them. The coefficients of regression for modeling the paraboloid cones and the scale parameter are estimated using robust weighted M-estimators where the weights decrease quadratically from 1 in the middle to zero at the border of the selected neighborhood. The robust way of estimating the model parameters supersedes a procedure for detecting outliers. For a given neighborhood shape, this yield mapping method is implemented by the Fortran program paraboloidmapping.exe, which can be downloaded from the web. The size of the selected neighborhood is considered appropriate if the variance of the yield map values equals the variance of the true yields, which is the difference between the variance of the raw yield data and the error variance of the yield monitor. It is estimated using a robust variogram on data that have not had the trend removed.
基金Water and Power Development Authority(WAPDA)is hereby acknowledged for their support in th e present study.
文摘This paper studies electrical resistivity dataset acquired for a groundwater study in the Domail Plain in the northwestern Himalayan section of Pakistan. Through a combination of geostatistical analysis,geophysical inversion and visualization techniques,it is possible to re-model and visualize the single dimension resistivity data into 2D and 3D space.The variogram models are utilized to extend the interpretation of the data and to distinguish individual lithologic units and the occurrence of saline water within the subsurface. The resistivity data has been calibrated with the lithological logs taken from the available boreholes. As such the alluvial system of the Domail Plain has formed during episodes of local tectonic activity with fluvial erosion and depositionyielding coarse sediments with high electrical resistivities near to the mountain ranges and finer sediments with medium to low electrical resistivities which tend to settle in the basin center. Thus a change is depositional setting happened from basin lacustrine environment to flash flooding during the Himalayan orogeny. The occurrence of rock salt in the northern mountains has imparted a great influence on the groundwater quality of the study area. The salt is dissolved by water which infiltrates into the subsurface through the water channels. Variogram aided gridding of resistivity data helps to identify the occurrence and distribution of saline water in the subsurface.
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), Advanced Spaceborne 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 images. 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 semivariogram 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 multisensor images with consideration of their nominal spatial resolution, image size and spectral bands.