Geostatistical seismic inversion and 3D modelling of metric flow units,porosity and permeability in Brazilian presalt reservoir

Flow units(FU)rock typing is a common technique for characterizing reservoir flow behavior,producing reliable porosity and permeability estimation even in complex geological settings.However,the lateral extrapolation of FU away from the well into the whole reservoir grid is commonly a difficult task and using the seismic data as constraints is rarely a subject of study.This paper proposes a workflow to generate numerous possible 3D volumes of flow units,porosity and permeability below the seismic resolution limit,respecting the available seismic data at larger scales.The methodology is used in the Mero Field,a Brazilian presalt carbonate reservoir located in the Santos Basin,who presents a complex and heterogenic geological setting with different sedimentological processes and diagenetic history.We generated metric flow units using the conventional core analysis and transposed to the well log data.Then,given a Markov chain Monte Carlo algorithm,the seismic data and the well log statistics,we simulated acoustic impedance,decametric flow units(DFU),metric flow units(MFU),porosity and permeability volumes in the metric scale.The aim is to estimate a minimum amount of MFU able to calculate realistic scenarios porosity and permeability scenarios,without losing the seismic lateral control.In other words,every porosity and permeability volume simulated produces a synthetic seismic that match the real seismic of the area,even in the metric scale.The achieved 3D results represent a high-resolution fluid flow reservoir modelling considering the lateral control of the seismic during the process and can be directly incorporated in the dynamic characterization workflow.

Structural Controls and Predictive Mapping of Tin, Niobium and Tantalum Mineralization Associated with the Mayo Darlé Stanniferous Granitoids;Contributions of Geostatistics

The aim of this study of the spatial dispersion of tin, niobium and tantalum mineralization associated with the Mayo Darlé granitoids was to produce prospecting guides through predictive maps of Sn, Nb and Ta in the region. It was based on a database (in appendix) obtained after analysis of rock samples (greisens and quartz veins) collected in the field, using a portable X-ray fluorescence (XRF) spectrometer. Two approaches were used: 1) structural studies in the field using the directions of veins and fractures 2) the use of variographic maps, an essential element in geostatistics for determining directional anisotropies. A joint synthesis of the modelling results shows that tin, tantalum and niobium mineralization at Mayo Darlé is concentrated along strike intervals N315E to N320E, with mineralization also occurring along strike N35E for high-grade Sn, medium-grade Ta and low-grade Nb. In short, mineral concentrations disperse progressively in space: positively from east to west for tantalum and niobium, and inversely for tin.

Spatial-temporal difference between nitrate in groundwater and nitrogen in soil based on geostatistical analysis

The study of temporal and spatial variations of nitrate in groundwater under different soil nitrogen environments is helpful to the security of groundwater resources in agricultural areas.In this paper,based on 320 groups of soil and groundwater samples collected at the same time,geostatistical analysis and multiple regression analysis were comprehensively used to conduct the evaluation of nitrogen contents in both groundwater and soil.From May to August,as the nitrification of groundwater is dominant,the average concentration of nitrate nitrogen is 34.80 mg/L;The variation of soil ammonia nitrogen and nitrate nitrogen is moderate from May to July,and the variation coefficient decreased sharply and then increased in August.There is a high correlation between the nitrate nitrogen in groundwater and soil in July,and there is a high correlation between the nitrate nitrogen in groundwater and ammonium nitrogen in soil in August and nitrate nitrogen in soil in July.From May to August,the area of low groundwater nitrate nitrogen in 0-5 mg/L and 5-10 mg/L decreased from 10.97%to 0,and the proportion of high-value area(greater than 70 mg/L)increased from 21.19%to 27.29%.Nitrate nitrogen is the main factor affecting the quality of groundwater.The correlation analysis of nitrate nitrogen in groundwater,nitrate nitrogen in soil and ammonium nitrogen shows that they have a certain period of delay.The areas with high concentration of nitrate in groundwater are mainly concentrated in the western part of the study area,which has a high consistency with the high value areas of soil nitrate distribution from July to August,and a high difference with the spatial position of soil ammonia nitrogen distribution in August.

An Assessment and Geostatistics of Land-Use and Selected Physico-Chemical Properties of Soils in the Mount Cameroon Area

This work investigated the land-use/land-cover and some physico-chemical properties of the soils of Mt Cameroon and presented same in maps. ArcGIS Pro mapping software, Landsat images, Global Positioning Systems (GPS) coordinates collected from the field combined with updated shape files from competent services were used to produce the location and land-use/land-cover maps. Sixteen topsoil samples (0 - 20 cm) were collected, 4 from each land use/cover category: farmland, forest, plantation and settlement, and analysed for soil pH, cation exchange capacity (CEC), bulk density, moisture content and soil texture, in the laboratory using standard analytical procedures. This data was used to produce spatial distribution maps using ordinary kriging, in ArcGIS Pro. The main terrestrial land use/cover categories comprised of the forest (mangrove, lowland, montane and sub-montane), agroforestry, plantations, grassland, settlement, cropland, shrubby savannah, and bare lava. Bulk density showed the highest values in settlement areas and least values under forest land-use categories. Soil moisture content exhibited a reverse trend compared to that of soil bulk density. Forest soils were the sandiest while soils in plantation agricultural land were the most clayey. The soils were slightly acidic to neutral with soils from agricultural land being more acidic (pH(water) = 5.43). It is discernible from the results that the conversion from forest to other land use/cover classes enhances soil degradation and that soil physico-chemical properties adequately serve as indicators of soil quality in the Mt Cameroon area.

Simultaneous inversion of petrophysical parameters based on geostatistical a priori information

The high-resolution nonlinear simultaneous inversion of petrophysical parameters is based on Bayesian statistics and combines petrophysics with geostatistical a priori information. We used the fast Fourier transform–moving average（FFT–MA） and gradual deformation method（GDM） to obtain a reasonable variogram by using structural analysis and geostatistical a priori information of petrophysical parameters. Subsequently, we constructed the likelihood function according to the statistical petrophysical model. Finally, we used the Metropolis algorithm to sample the posteriori probability density and complete the inversion of the petrophysical parameters. We used the proposed method to process data from an oil fi eld in China and found good match between inversion and real data with high-resolution. In addition, the direct inversion of petrophysical parameters avoids the error accumulation and decreases the uncertainty, and increases the computational effi ciency.

Geostatistical Analysis on Spatial Patterns of Eggs and Larvae of Kytorhinus immixtus

[ Objective ] The paper was to study the spatial distribution pattern and spatial correlation of eggs and larvae of Kytorhinus immixtus. [ Method ] By using geostatistical principles and methods, the number of eggs and larvae ofK. immixtus was investigated, and the obtained data were analyzed. [Result]The cir- cular model was the best fitting model for eggs and larvae of/C immixtus, and the spatial distribution pattern was aggregated distribution with a spatial correlation, and their variation ranges were 18.899 -62.922 and 13.464 -47.455. The distribution pattern of eggs and larvae of K.immistus was simulated by using ordinary Kriging method, and the result showed that their distributions had obvious agitated character, the aggregated intensity in the core area of patch was significantly higher than that in the edge. There was anisotropy of aggregation intensity, the aggregation intensity from northeast to southwest direction was significantly higher than that from northwest to southeast direction. [ Conclusion] The spatial distribution pattern of eggs and larvae of K. immixtus was aggregated distribution, and the increase of plant distance and fragmentation of patch had a certain control effect on the occurrence of K. immixtus population.

Geostatistical Analysis of Soil Nutrients Based on GIS and Geostatistics in the Typical Plain and Hilly-Ground Area of Zhongxiang, Hubei Province

Techniques of geostatistics are used to perform traditional statistical analysis and spatial structural analysis with ArcGIS, geostatistical software GS+ and statistical software SPSS in order to obtain the knowledge of characteristics of distribution and spatial variability of soil nutrients in different parts of Zhongxiang, Hubei Province. Some skewed values appeared during the analyses. To decrease the influence of those skewed values, domain processing and Box-Cox transformation were used. The results indicated spatial variability of Total N, Avail. P, rapidly-available potassium (R-Avail. K) and effective zinc (Effect. Zn) was strong, that of organic carbon (Org. C), effective molybdenum (Effect. Mo) and effective copper (Effect. Cu) was medium while that of others was weak. Fitted model of Total N, R-Avail. K and Effect. Mo was spherical model, that of Org. C and Effect. Zn was exponential model, while fitted model of Avail. P and Effect. Cu was Gaussian model. Ratio of variability caused by random factors to overall variability was large. What’s more, the ranges of spatial autocorrelation of soil nutrients had much difference. The smallest value was 3600 m in Effect. Zn while the largest was 77970 m in Org. C. Other characteristics were also included. The study is helpful to soil sampling design, to make people realize the influence of Han River to spatial variability of soil nutrients in this area, and to spatial interpolation and mapping.

The application of geostatistics in grain size trend analysis： A case study of eastern Beibu Gulf

There are 71 surface sediment samples collected from the eastern Beibu Gulf. The moment parameters （i.e. mean size, sorting and skewness） were obtained after applying grain size analysis. The geostatistical analysis was then applied to study the spatial autocorrelation for these parameters; while range, a parameter in the semivariogram that meters the scale of spatial autocorrelation, was estimated. The results indicated that the range for sorting coefficient was physically meaningful. The trend vectors calculated from grain size trend analysis model were consistent with the annual ocean circulation patterns and sediment transport rates according to previous studies. Therefore the range derived from the semivariogram of mean size can be used as the characteristic distance in the grain size trend analysis, which may remove the bias caused by the traditional way of basing on experiences or testing methods to get the characteristic distance. Hence the results from geostatistical analysis can also offer useful information for the determination of sediment sampling density in the future field work.

Sediment distribution pattern mapped from the combination of objective analysis and geostatistics in the large shallow Taihu Lake, China

Investigation was made into sediment depth at 723 irregularly scattered measurement points which cover all the regions in Taihu Lake, China. The combination of successive correction scheme and geostatistical method was used to get all the values of recent sediment thickness at the 69×69 grids in the whole lake. The results showed that there is the significant difference in sediment depth between the eastern area and the western region, and most of the sediments are located in the western shore-line and northern regimes but just a little in the center and eastern parts. The notable exception is the patch between the center and Xishan Island where the maximum sediment depth is more than 4.0 m. This sediment distribution pattern is more than likely related to the current circulation pattern induced by the prevailing wind-forcing in Taihu Lake. The numerical simulation of hydrodynamics can strong support the conclusion. Sediment effects on water quality was also studied and the results showed that the concentrations of TP, TN and SS in the western part are obviously larger than those in the eastern regime, which suggested that more nutrients can be released from thicker sediment areas.

Using Multivariate Statistical and Geostatistical Methods to Identify Spatial Variability of Trace Elements in Agricultural Soils in Dongguan City,Guangdong,China

Dongguan （东莞） City, located in the Pearl River Delta, South China, is famous for its rapid industrialization in the past 30 years. A total of 90 topsoil samples have been collected from agricultural fields, including vegetable and orchard soils in the city, and eight heavy metals （As, Cu, Cd, Cr, Hg, Ni, Pb, and Zn） and other items （pH values and organic matter） have been analyzed, to evaluate the influence of anthropic activities on the environmental quality of agricultural soils and to identify the spatial distribution of trace elements and possible sources of trace elements. The elements Hg, Pb, and Cd have accumulated remarkably here, incomparison with the soil background content of elements in Guangdong （广东） Province. Pollution is more serious in the western plain and the central region, which are heavily distributed with industries and rivers. Multivariate and geostatistical methods have been applied to differentiate the influences of natural processes and human activities on the pollution of heavy metals in topsoils in the study area. The results of cluster analysis （CA） and factor analysis （FA） show that Ni, Cr, Cu, Zn, and As are grouped in factor F1, Pb in F2, and Cd and Hg in F3, respectively. The spatial pattern of the three factors may be well demonstrated by geostatistical analysis. It is shown that the first factor could be considered as a natural source controlled by parent rocks. The second factor could be referred to as ＂industrial and traffic pollution sources＂. The source of the third factor is mainly controlled by long-term anthropic activities, as a consequence of agricultural activities, fossil fuel consumption, and atmospheric deposition.

Groundwater quality assessment using multivariate analysis,geostatistical modeling, and water quality index(WQI): a case of study in the Boumerzoug-El Khroub valley of Northeast Algeria

In this study,the analytical data set of 26 groundwater samples from the alluvial aquifer of Boumerzoug-E1 khroub valley has been processed simultaneously with Multivariate analysis,geostatistical modeling,WQI,and geochemical modeling.Cluster analysis identified three main water types based on the major ion contents,where mineralization increased from group 1 to group 3.These groups were confirmed by FA/PCA,which demonstrated that groundwater quality is influenced by geochemical processes(water-rock interaction)and human practice(irrigation).The exponential semivariogram model WQI.Groundwater chemistry has a strong spatial structure for Mg,Na,Cl,and NO3,and a moderate spatial structure for EC,Ca,K,HCO3,and SO4.Water quality maps generated using ordinary Kriging are consistent with the HCA and PCA results.All water groups are supersaturated with respect to carbonate minerals,and dissolution of kaolinite and Ca-smectite is one of the processes responsible for hydrochemical evolution in the area.

Integration of Tracer Test Data to Refine Geostatistical Hydraulic Conductivity Fields Using Sequential Self-Calibration Method

On the basis of local measurements of hydraulic conductivity, geostatistical methods have been found to be useful in heterogeneity characterization of a hydraulic conductivity field on a regional scale. However, the methods are not suited to directly integrate dynamic production data, such as, hydraulic head and solute concentration, into the study of conductivity distribution. These data, which record the flow and transport processes in the medium, are closely related to the spatial distribution of hydraulic conductivity. In this study, a three-dimensional gradient-based inverse method--the sequential self-calibration （SSC） method--is developed to calibrate a hydraulic conductivity field, initially generated by a geostatistical simulation method, conditioned on tracer test results. The SSC method can honor both local hydraulic conductivity measurements and tracer test data. The mismatch between the simulated hydraulic conductivity field and the reference true one, measured by its mean square error （MSE）, is reduced through the SSC conditional study. In comparison with the unconditional results, the SSC conditional study creates the mean breakthrough curve much closer to the reference true curve, and significantly reduces the prediction uncertainty of the solute transport in the observed locations. Further, the reduction of uncertainty is spatially dependent, which indicates that good locations, geological structure, and boundary conditions will affect the efficiency of the SSC study results.

Spatial analysis of carbon storage density of mid-subtropical forests using geostatistics： a case study in Jiangle County, southeast China

The mid-subtropical forest is one of the biggest sections of subtropical forest in China and plays a vital role in mitigating climate change by sequestering carbon.Studies have examined carbon storage density(CSD) distribution in temperate forests. However, our knowledge of CSD in subtropical forests is limited. In this study, Jiangle County was selected as a study case to explore geographic variation in CSD. A spatial heterogeneity analysis by semivariogram revealed that CSD varied at less than the mesoscale(approximately 2000–3000 m). CSD distribution mapped using Kriging regression revealed an increasing trend in CSD from west to east of the study area.Global spatial autocorrelation analysis indicated that CSD was clustered at the village level(at 5% significance).Some areas with local spatial autocorrelation were detected by Anselin Local Moran's I and Getis-Ord G*. A geographically weighted regression model showed different impacts on the different areas for each determinant. Generally, diameter at breast height, tree height, and stand density had positive correlation with CSD in Jiangle County, but varied substantially in magnitude by location.In contrast, coefficients of elevation and slope ranged from negative to positive. Based on these results, we propose certain measures to increase forest carbon storage,including increasing forested area, improving the quality of the current forests, and promoting reasonable forest management decisions and harvesting strategies. The established CSD model emphasizes the important role of midsubtropical forest in carbon sequestration and provides useful information for quantifying mid-subtropical forest carbon storage.

A comparative study of geometric and geostatistical methods for qualitative reserve estimation of limestone deposit

Mining projects especially relating to limestone deposits require an accurate knowledge of tonnage and grade,for both short and long-term planning.This is often difficult to establish as detailed exploration operations,which are required to get the accurate description of the deposit,are costly and time consuming.Geologists and mining engineers usually make use of geometric and geostatistical methods,for estimating the tonnage and grade of ore reserves.However,explicit assessments into the differences between these methods have not been reported in literature.To bridge this research gap,a comparative study is carried out to compare the qualitative reserve of Oyo-Iwa limestone deposit located in Nigeria,using geometric and geostatistical methods.The geometric method computes the reserve of the limestone deposit as 74,536,820 t(mean calcite,CaO grade=52.15)and 99,674,793 t(mean calcite,CaO grade=52.32),for the Northern and Southern zones of the deposit,respectively.On the other hand,the geostatistical method calculates the reserve as 81,626,729.65 t(mean calcite,CaO grade=53.36)and 100,098,697.46 t(mean calcite,CaO grade=52.96),for the two zones,respectively.The small relative difference in tonnage estimation between the two methods(i.e.,9.51%and 0.43%),proves that the geometric method is effective for tonnage estimation.In contrast,the relative difference in grade estimation between the two methods(i.e.,2.32%and 1.26%)is not negligible,and could be crucial in maintaining the profitability of the project.The geostatistical method is,therefore,more suitable,reliable and preferable for grade estimation,since it involves the use of spatial modelling and cross-validated interpolation.In addition,the geostatistical method is used to produce quality maps and three-dimensional(3-D)perspective view of the limestone deposit.The quality maps and 3-D view of the limestone deposit reveal the variability of the limestone grade within the deposit,and it is useful for operational management of the limestone raw materials.The qualitative mapping of the limestone deposit is key to effective production scheduling and accurate projection of raw materials for cement production.

Geostatistical Assessment of the Spatial Distribution of Some Chemical Properties in Calcareous Soils

Spatial patterns of soil fertility parameters and other extrinsic factors need to be identified to develop farming practices that match agricultural inputs with local crop needs. Little is known about the spatial structure of nutrition in Iran. The present study was conducted in a 132-ha field located in central Iran. Soil samples were collected at 0-30 cm depth and were then analyzed for total nitrogen （N）, available phosphorus （P）, available potassium （K）, available copper （Cu）, available zinc （Zn）, available iron （Fe） and available manganese （Mn）. The results showed that the contents of soil organic matter, Cu and Zn in Marvdasht＇s farms were low. The spatial distribution model and spatial dependence level for soil chemical properties varied in the field. N, K, carbonate calcium equivalent （CaCO3） and electrical conductivity （EC） data indicated the existence of moderate spatial dependence. The variograms for other variables revealed stronger spatial structure. The results showed a longer range value for available P （480 m）, followed by total N （429 m）. The value of other chemical properties values showed a shorter range （128 to 174 m）. Clear patchy distribution of N, P, K, Fe, Mn, Cu and Zn were found from their spatial distribution maps. This proved that sampling strategy for estimating variability should be adapted to the different soil chemical properties and field management. Therefore, the spatial variability of soil chemical properties with strong spatial dependence could be readily managed and a site-specific fertilization scheme for precision farming could be easily developed.

Geostatistical Analyst for Deciding Optimal Interpolation Strategies for Delineating Compact Zones

Variability maps of Hydraulic conductivity (K) were generated by using geo statistical analyst extension of ARC GIS for delineating compact zones in a farm. In the initial exploratory spatial data analysis, K data for 0 - 15 and 15 - 30 cm soil layers showed spatial dependence, anisotropy, normality on log transformation and linear trend. Outliers present in both layers were also removed. In the next step, cross validation statistics of different combinations of kriging (Ordinary, simple and universal), data transformations (none and logarithmic) and trends (none and linear) were compared. Combination of no data transformation and linear trend removal was the best choice as it resulted in more accurate and unbiased prediction. It thus, confirmed that for generating prediction maps by kriging, data need not be normal. Ordinary kriging is appropriate when trend is linear. Among various available anisotropic semivariogram models, spherical model for 0 - 15 cm and tetra spherical model for 15 - 30 cm were found to be the best with major and minor ranges between 273 - 410 m and 98 - 213 m. The kriging was superior to other interpolation techniques as the slope of the best fit line of scatter plot of predicted vs. measured data points was more (0.76) in kriging than in inverse distance weighted interpolation (0.61) and global polynomial interpolation (0.56). In the generated prediction maps, areas where K was <12 cm?day–1 were delineated as compact zone. Hence, it can be concluded that geostatistical analyst is a complete package for preprocessing of data and for choosing the optimal interpolation strategies.

Reserve estimation of the high phosphorous stockpile at the Choghart iron mine of Iran using geostatistical modeling

An attempt to estimate the reserves in the High Phosphorous stockpile （HP） at the Choghart Iron mine of Iran was carded out using geostatistical modeling. Grade and tonnage estimates of ore stockpiles can help convert them into a valuable ore reserve. This is valuable in consideration of increasing metal demand, and the depletion of in situ ore reserves, around the world. Estimation of reserves in stockpiles is difficult partly because of geological and grade discontinuities created during the dumping of the ore piles. Data input for the HP stockpile at Choghart was performed based upon pre-existing information gathered during extraction from the various mining benches. After establishing the input data files the reserve estimates were found using geostatistical methods aided by the international mining software SURPAC. The stockpile was divided in to three domains and the reserves in each domain were estimated separately. A grade block model was used to compute the reserve. Fe% and P% were estimated using the Ordinary Kriging method. The results showed that the total tonnage of the HP stockpile is 4.5 million tons with an average zrade of 55% Fe and 1.03% P.

Geostatistical Analysis on the Temporal Patterns of the Yellow Rice Borer, Tryporyza incertulas

In order to comprehend temporal pattern of the larvae population of the yellow rice borer, Tryporyza incertulas, and provide valuable information for its forecast model, the data series of the population for each generation and the over-wintered larvae from 1960 to 1990 in Dingcheng District, Changde City, Hunan Province, were analyzed with geostatistics. The data series of total number, the 1st generation, the 3rd generation and the over-wintered larvae year to year displayed rather better autocorrelation and prediction. The data series of generation to generation, the 2nd generation and the 4th generation year to year, however, demonstrated poor autocorrelation, especially for the 4th generation, whose autocorrelation degree was zero. The population dynamics of the yellow rice borer was obviously intermittent. A remarkable cycle of four generations, one year, was observed in the population of generation to generation. Omitting the certain generation or interposing the over-wintered larvae only resulted in a less or slight change of autocorrelation of the whole data series generation to generation. Crop system, food, climate and natural enemies, therefore, played more important roles in regulating the population dynamics than base number of the larvae. The basic techniques of geostatistics applied in analyzing temporal population dynamics were outlined.

Geostatistical Studies and Anomalous Elements Detection, Bardaskan Area, Iran

The aim of this study is geostatistical analysis and detection of anomalous elements in the Bardaskan area (in geological map of Bardaskan on scale 1:100,000 which is provided by the GSI organization). The study area is located in Khorasan province of Iran. Due to the availability of lithogeochemical regular data in the region as well as the importance of exploration of metal minerals in order to simplify and summarize the geochemical map, geostatistical methods were used to identify the mineralization potential of the region. Initially, using single-variable and multivariate statistical methods, anomalous elements were separated. Then, the thresholds (various communities) for the titanium element that was most likely to be anomalous were identified. Using these limits, the discriminant analysis was applied to the elements. Titanium, iron and magnesium elements were identified as the main mineral elements in the region. These elements indicate mineralization in the mafic bed rocks. Finally the map of the concentration of titanium element was mapped across the region with Kriging interpolation method. As a result, two anomalies of the titanium element in the region were identified.

Geostatistical Analysis of Spatial Distribution and Dynamics of Dead Heart of Sugarcane Seedlings Caused by Borer

Dead heart of sugarcane is an important symptom caused by borer attack. In the present study, the spatial distribution and dynamics of dead heart of sugarcane in the field were investigated based on geostatistical analysis, and semivariograms were computed in four separate directions(0°, 45°, 90° and 135°) and fitted with various theoretical models to determine the best fitted one. The Ordinary Kriging was used to interpolate spatial data. The results revealed that the density of dead hearts of sugarcane increased in a single-peak pattern, and the degree of spatial aggregation and random variation both decreased with the increase in the density of dead heart. In addition, dead heart of sugarcane caused by borer exhibited spatial aggregation.With the increase in the density of dead heart, the degree of spatial aggregation decreased, while the correlation increased. Kriging interpolation indicated that the correlation between the spatial patches was weak in early seedling stage, and became strong in middle and late seedling stage.