Analysis of variograms with various sample sizes from a multispectral image

Variogram plays a crucial role in remote sensing application and geostatistics.It is very important to estimate variogram reliably from sufficient data.In this study,the analysis of variograms computed on various sample sizes of remotely sensed data was conducted.A 100×100-pixel subset was chosen randomly from an aerial multispectral image which contains three wavebands,Green,Red and near-infrared(NIR).Green,Red,NIR and Normalized Difference Vegetation Index(NDVI)datasets were imported into R software for spatial analysis.Variograms of these four full image datasets and sub-samples with simple random sampling method were investigated.In this case,half size of the subset image data was enough to reliably estimate the variograms for NIR and Red wavebands.To map the variation on NDVI within the weed field,ground sampling interval should be smaller than 12 m.The information will be particularly important for Kriging and also give a good guide of field sampling on the weed field in the future study.

Key parameter optimization and analysis of stochastic seismic inversion

Stochastic seismic inversion is the combination of geostatistics and seismic inversion technology which integrates information from seismic records, well logs, and geostatistics into a posterior probability density function （PDF） of subsurface models. The Markov chain Monte Carlo （MCMC） method is used to sample the posterior PDF and the subsurface model characteristics can be inferred by analyzing a set of the posterior PDF samples. In this paper, we first introduce the stochastic seismic inversion theory, discuss and analyze the four key parameters： seismic data signal-to-noise ratio （S/N）, variogram, the posterior PDF sample number, and well density, and propose the optimum selection of these parameters. The analysis results show that seismic data S/N adjusts the compromise between the influence of the seismic data and geostatistics on the inversion results, the variogram controls the smoothness of the inversion results, the posterior PDF sample number determines the reliability of the statistical characteristics derived from the samples, and well density influences the inversion uncertainty. Finally, the comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more reliable information of the subsurface character.

Spatial variability of soil microbial indices in common alder COMMON ALDER(Alnus glutinosa) stands using a geostatistical approach in northern Iran

Microbial indices and their spatial patterns are strongly affected by environmental factors. Spatial variability of soil properties is one of the most important causes of variability in soil microbial indices. This research was conducted in the Caspian forest to assess spatial variabilities and frequency distributions of microbial properties.Ninety soil samples were taken using a grid sampling design 40 9 40 m. Microbial indices, organic carbon,nitrogen and pH were determined. Soil variable distributions showed that microbial indices had abnormal distributions. Logarithmic transformation produced normal distribution. Spatial continuity using geostatistical(variogram) was studied and maps obtained by point kriging.The variograms revealed the presence of spatial autocorrelation. The results indicate that spatial dependence of soil microbial indices was affected by non-intrinsic factors and forest management procedures. The maps show that soil microbial indices and soil properties have spatial variability. The spatial pattern of microbial indices was correlated to organic carbon and nitrogen.

The Geostatistical Framework for Spatial Prediction

Geostatistics provides a coherent framework for spatial prediction and uncertainty assessment, whereby spatial dependence, as quantified by variograms, is utilized for best linear unbiased estimation of a regionalized variable at unsampied locations. Geostatistics for prediction of continuous regionalized variables is reviewed, with key methods underlying the derivation of major variants of uni-vafiate Kriging described in an easy-to-follow manner. This paper will contribute to demysti- fication and, hence, popularization of geostatistics in geoinformatics communities.

VARIOGRAM无偏估计类探讨

Variogram是空间数据分析中的一个重要参数。本文给出了 VARIOGRAM的一个无偏估计类。用之和传统估计作比较 。

Three-Dimensional Reservoir Modeling Using Stochastic Simulation, a Case Study of an East African Oil Field

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.

The Neighborhood Scale Variability of Airborne Particulates

Airborne particulates play a central role in both the earth’s radiation balance and as a trigger for a wide range of health impacts. Air quality monitors are placed in networks across many cities glob-ally. Typically these provide at best a few recording locations per city. However, large spatial var-iability occurs on the neighborhood scale. This study sets out to comprehensively characterize a full size distribution from 0.25 - 32 μm of airborne particulates on a fine spatial scale (meters). The data are gathered on a near daily basis over the month of May, 2014 in a 100 km2 area encompassing parts of Richardson, and Garland, TX. Wind direction was determined to be the dominant factor in classifying the data. The highest mean PM2.5 concentration was 14.1 ± 5.7 μg·m-3 corresponding to periods when the wind was out of the south. The lowest PM2.5 concentrations were observed after several consecutive days of rainfall. The rainfall was found to not only “cleanse” the air, leaving a mean PM2.5 concentration as low as 3.0 ± 0.5 μg·m-3, but also leave the region with a more uniform PM2.5 concentration. Variograms were used to determine an appropriate spatial scale for future sensor placement to provide measurements on a neighborhood scale and found that the spatial scales varied, depending on the synoptic weather pattern, from 0.8 km to 5.2 km, with a typical length scale of 1.6 km.

A flexible lag definition for experimental variogram calculation

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.

Spatial heterogeneity of plant species on the windward slope of active sand dunes in a semi-arid region of China

Species richness and abundance are two important species diversity variables that have attracted particular attention because of their significance in determining present and future species composition conditions. This paper aims to explain the qualitative and quantitative relationships between species diversity pattern and grain size （i.e. size of the sampling unit）, and species diversity pattern and sampling area, and to analyze species diversity variability on active sand dunes in the Horqin Sandy Land, northeastern Inner Mongolia, China. A 50 mx50 m sampling plot was selected on the windward slope, where the dominant species was annual herb Agriophyllum squarrosum. Species composition and abundance at five grain sizes were recorded, and the species-area curves were produced for thirteen grain sizes. The range of values for species abundance tended to increase with in- creasing grain size in the study area, whereas, generally, species richness did not follow this rule because of poor species richness on the windward slope of active sand dunes. However, the homogeneity of species richness in- creased significantly. With the increase in sampling area, species abundance increased linearly, but richness in- creased logarithmically. Furthermore, variograms showed that species diversity on the windward slope of active sand dunes was weakly anisotropic and the distribution pattern was random, according to the Moran Coefficient. The results also showed that species richness was low, with a random distribution pattern. This conflicts with the results of previous studies that showed spatial aggregation in lower richness in a sampling area within a community and inferred that the physical processes play a more important role in species diversity than distribution pattern on active sand dunes. Further research into different diversity patterns and mechanisms between active sand dunes and interdune lowlands should be conducted to better understand biodiversity conservation in sand dune fields.

A Study of Spatial Variability on Aquifer Hydraulic Conductivity K

A structural analysis of K of an aquifer system in the study area is presented, and the main direction and degree of the variability of K are found by using the unstationary regionalized variable theory of geostatistics. Optimal estimation of K has been made by universal kriging method (U K M ). Both spatial variability distribution map and division map of K are given.

3D Property Modeling of Void Ratio by Cokriging

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.

Spatiotemporal interpolation of precipitation across Xinjiang, China using space-time CoKriging

In various environmental studies, geoscience variables not only have the characteristics of time and space, but also are influenced by other variables. Multivariate spatiotemporal variables can improve the accuracy of spatiotemporal estimation. Taking the monthly mean ground observation data of the period 1960–2013 precipitation in the Xinjiang Uygur Autonomous Region, China, the spatiotemporal distribution from January to December in 2013 was respectively estimated by space-time Kriging and space-time CoKriging. Modeling spatiotemporal direct variograms and a cross variogram was a key step in space-time CoKriging. Taking the monthly mean air relative humidity of the same site at the same time as the covariates, the spatiotemporal direct variograms and the spatiotemporal cross variogram of the monthly mean precipitation for the period 1960–2013 were modeled. The experimental results show that the space-time CoKriging reduces the mean square error by 31.46% compared with the space-time ordinary Kriging. The correlation coefficient between the estimated values and the observed values of the space-time CoKriging is 5.07% higher than the one of the space-time ordinary Kriging. Therefore, a space-time CoKriging interpolation with air humidity as a covariate improves the interpolation accuracy.

Extraction of Morphometric Bedform Characteristics from Profiling Sonar Datasets Recorded in Shallow Coastal Waters of China

The morphological characteristics of small-scale bedforms were measured by means of an acoustic profiling sonar on the Dafeng tidal flat, Jiangsu, in 2009, and in the Jiulong Estuary, Xiamen, in 2010, respectively. The ＂multi-threshold value＂ method was utilized to reveal the morphological undulations along which bedforms were present. Analyses of the datasets obtained show that： （1） sand ripples can have irregular shapes, and （2） changes in bedform morphology are small within a single tidal cycle but may be significant over several tidal cycles. Fractal and variogram analyses of the seabed roughness revealed the existence of a significant relationship between current speed and the fractal dimension of the seabed roughness. As current speed increases, seabed roughness increases with a trend of smaller-scale bottom structures being replaced by larger-scale structures. Furthermore, the surface of the larger-scale bottom structures can either become smooth due to the absence of smaller-scale features or become rougher due to the presence of superimposed smaller-scale structures.

The Application of Geostatistical Methods to Prepare the 3D Petrophysical Model of Oil Reservoir

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.

Sedimentary Facies Controls on the Upscaling of Petrophysical Properties from Core to Log Scales and Its Implications to Petroleum Exploration

The clastic sedimentary realm comprises a number of genetically distinct depositional systems, which are dominated by distinct depositional processes. A variogram and a Levy-stable probability distribution-based geostatistical method have been applied to analyze petrophysical properties from well logs and cores from a variety of depositional environments in sedimentary basins from Australia to quantify the heterogeneity and upscaling range of different depositional systems. Two reservoir sequences with contrasting sedimentary facies, depositional processes and a diagenetic history are investigated for their petrographic, petrophysical and log characters and their scaling behaviour. The microscopic derived petrophysical parameters, including visual porosity, grain size, sorting and amount of matrix, core plug measured porosity and permeability and log-derived V-shale, porosity and permeability, have been found to be well correlated (|R|=0.72 to 0.91) across all the scales for the reservoir sequence deposited under a single predominant depositional process and a gradational change of the energy regime (Bilyara-1). In contrast, for the reservoir sequence (East Swan-2), which was deposited in heterogeneous processes and underwent diagenetic alteration, the cross-correlation of the petrophysical properties derived from the three different scales is extremely poor (|R|=0.01-0.54). Log-derived porosity and permeability for a thinly bedded reservoir sequence with an individual bed thinner than one metre can therefore be affected by the intrinsic averaging effects of the logging tools.

Characterizing Landscape Spatial Heterogeneity in Multisensor Images with Variogram Models

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.

Impact of Rainfall Temporal Heterogeneity on Relationship between Curve Number and Rainfall Depth in the Zagros Mountain Region,Iran

The impact of temporal variation of rainfall on the relationship between rainfall and catchment response is investigated in a catchment with high temporally variable rainfalls and a high percentage of permeable soils in the southwest of Iran.Twenty-nine storm events are classified into two classes, High Temporal heterogeneous(HT) and Low Temporal heterogeneous(LT) events using the variogram technique and the storm events of each class are analyzed to detect the relationship between Curve Number(CN) and rainfall depth. It is found that there is not a similar correlation between CN values and rainfall depths for both temporally variable classes, and hence, two different responses can be observed in the catchment according to rainfall temporal heterogeneities. For HT events, a complacent behavior is detected in which the CNs decline as rainfall depth increases while a different response, violent behavior, is observed for LT events in which the CNs rise and asymptotically approach a constant value with increasing storm size. This considerable difference between CN-P relationships derived from the two temporally variable classes of rainfall is attributed to the provocation of different runoff generation mechanisms, infiltration-excess and saturation-excess caused by rainfall temporal heterogeneities. Moreover, the results support the validity of variogram technique to classify storm events into two LT and HT classes.

Abandoned land identification in karst mountain area based on time series SAR characteristics at geo-parcels scale

Mapping abandoned land is very important for accurate agricultural management.However,in karst mountainous areas,continuous high-resolution optical images are difficult to obtain in rainy weather,and the land is fragmented,which poses a great challenge for remote sensing monitoring of agriculture activities.In this study,a new method for identifying abandoned land is proposed:firstly,a few Google Earth images are used to transform arable land into accurate vectorized geo-parcels;secondly,a time-series data set was constructed using Sentinel-1A Alpha parameters for 2020 on each farmland geoparcel;thirdly,the semi-variation function(SVF)was used to analyze the spatial-temporal characteristics,then identify abandoned land.The results show:(1)On the basis of accurate spatial information and boundary of farmland land,the SAR time-series dataset reflects the structure and time-series response.abandoned land with an accuracy of 80.25%.The problem of remote sensing monitoring in rainy regions and complex surface areas is well-resolved.(2)The spatial heterogeneity of abandoned land is more obvious than that of cultivated land within geoparcels.The step size for significant changes in the SVF of abandoned land is shorter than that of cultivated land.(3)The SVF time sequence curve presented a strong peak feature when farmland was abandoned.This reveals that the internal spatial structure of abandoned land is more disordered and complex.It showed that time-series variations of spatial structure within cultivated land have broader applications in remote sensing monitoring of agriculture in complex imaging environments.

Joint Application of Geostatistics and Multifractals for Decision-Making System of Ore Prospection in a Mineral Deposit

The strategy of ore prospection is made on the basis of raw exploratory data which are the products of coupled geological processes and random natural reformation. This decision-making system is extraordinary risky and needs to be supported by various statistical sciences. In this paper, geostatistics and multifractals are jointly employed to delineate the complexity of mineralization and to provide important guidelines for future ore prospecting. The geostatistical analysis indicates the mineralization in granite domain is more homogenous than that in wallrocks, and the exploratory spacing in these two lithological units should be different when taking into consideration the range of variogram. The multifractal analysis shows the spatial variation of mineralization homogeneity. The mineralization in the southwest of this region is much more heterogeneous than that in the granite. The schemes of borehole design are specified based on the combination of abovementioned analytical results. The joint application of geostatistics and multifractal proposed in this study can excavate the exploratory data and output mathematic models in an intuitive and quantitative way, assisting in decision-making and risk avoidance of mining industry.

A Method to Integrate Geological Knowledge in Variogram Modeling of Facies: A Case Study of a Fluvial Deltaic Reservoir

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.