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.

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.

Locally varying geostatistical machine learning for spatial prediction

Machine learning methods dealing with the spatial auto-correlation of the response variable have garnered significant attention in the context of spatial prediction.Nonetheless,under these methods,the relationship between the response variable and explanatory variables is assumed to be homogeneous throughout the entire study area.This assumption,known as spatial stationarity,is very questionable in real-world situations due to the influence of contextual factors.Therefore,allowing the relationship between the target variable and predictor variables to vary spatially within the study region is more reasonable.However,existing machine learning techniques accounting for the spatially varying relationship between the dependent variable and the predictor variables do not capture the spatial auto-correlation of the dependent variable itself.Moreover,under these techniques,local machine learning models are effectively built using only fewer observations,which can lead to well-known issues such as over-fitting and the curse of dimensionality.This paper introduces a novel geostatistical machine learning approach where both the spatial auto-correlation of the response variable and the spatial non-stationarity of the regression relationship between the response and predictor variables are explicitly considered.The basic idea consists of relying on the local stationarity assumption to build a collection of local machine learning models while leveraging on the local spatial auto-correlation of the response variable to locally augment the training dataset.The proposed method’s effectiveness is showcased via experiments conducted on synthetic spatial data with known characteristics as well as real-world spatial data.In the synthetic(resp.real)case study,the proposed method’s predictive accuracy,as indicated by the Root Mean Square Error(RMSE)on the test set,is 17%(resp.7%)better than that of popular machine learning methods dealing with the response variable’s spatial auto-correlation.Additionally,this method is not only valuable for spatial prediction but also offers a deeper understanding of how the relationship between the target and predictor variables varies across space,and it can even be used to investigate the local significance of predictor variables.

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.

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.

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.

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.

基于Geostatistical Analyst的喀斯特地区土壤养分空间变异研究

基于ARCGIS平台Geostatistical Analyst模块对喀斯特地区土壤养分空间变异特征进行研究,以贵州省黔西县韦寨村为研究区,首先对研究区内耕地土壤进行取样,深度为0～ 20cm,并将研究区划分为两片,采样方式分别为25m＊ 25m和50m＊ 50m.通过实验得出土壤中全氮、有效磷、速效钾、有机质含量和pH值.采用GIS地统计分析和常规统计方法对土壤pH值及养分（全氮、有效磷、速效钾、有机质）的空间变异分析和合理采样数目研究.结果表明,研究区内全氮、有效磷、速效钾、pH、有机质均呈对数正态分布;全氮、有效磷、速效钾、pH、有机质均为中等变异强度;研究区内最优采样方式为50m＊ 50m.

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.

Implementing geostatistical analysis to study spatio-temporal distribution patterns of swimming crabs(Portunus trituberculatus)

This study attempted to compare the performance of local polynomial interpolation,inverse distance weighted interpolation,and ordinary kriging in studying distribution patterns of swimming crabs.Cross-validation was used to select the optimum method to get distribution results,and kriging was used for making spatial variability analysis.Data were collected from 87 sampling stations in November of 2015(autumn)and February(winter),May(spring)and August(summer)of 2016.Results indicate that swimming crabs widely distributed in autumn and summer:in the summer,they were more spatially independent,and resources in each sampling station varied a lot;in the winter and spring,the abundance of crabs was much lower,but the individual crab size was bigger,and they showed the patchy and more concentrative distribution pattern,which means they were more spatially dependent.Distribution patterns were in accordance with ecological migration features of swimming crabs,which were affected by the changing marine environment.This study could infer that it is applicable to study crab fishery or even other crustacean species using geostatistical analysis.It not only helps practitioners have a better understanding of how swimming crabs migrate from season to season,but also assists researchers in carrying out a more comprehensive assessment of the fishery.Therefore,it may facilitate advancing the implementation in the pilot quota management program of swimming crabs in northern Zhejiang fishing grounds.

Geostatistical Modeling of Uncertainty for the Risk Analysis of a Contaminated Site

This work is a study of multivariate simulations of pollutants to assess the sampling uncertainty for the risk analysis of a contaminated site. The study started from data collected for a remediation project of a steel- works in northern Italy. The soil samples were taken from boreholes excavated a few years ago and analyzed by a chemical laboratory. The data set comprises concentrations of several pollutants, from which a subset of ten organic and inorganic compounds were selected. The first part of study is a univariate and bivariate sta- tistical analysis of the data. All data were spatially analyzed and transformed to the Gaussian space so as to reduce the effects of extreme high values due to contaminant hot spots and the requirements of Gaussian simulation procedures. The variography analysis quantified spatial correlation and cross-correlations, which led to a hypothesized linear model of coregionalization for all variables. Geostatistical simulation methods were applied to assess the uncertainty. Two types of simulations were performed: correlation correction of univariate sequential Gaussian simulations (SGS), and sequential Gaussian co-simulations (SGCOS). The outputs from the correlation correction simulations and SGCOS were analyzed and grade-tonnage curves were produced to assess basic environmental risk.

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.

Geostatistical Approach for Site Suitability Mapping of Degraded Mangrove Forest in the Mahakam Delta, Indonesia

As part of operational guidance of mangrove forest rehabilitation in the Mahakam delta, Indonesia, site suitability mapping for 14 species of mangrove was modelled by combining 4 underlying factors—clay, sand, salinity and tidal inundation. Semivariogram analysis and a geographic information system (GIS) were used to apply a site-suitability model, while kriging interpolation generated surface layers, based on sample point data collection. The tidal inundation map was derived from a tide table and a digital elevation model from topographic maps. The final site-suitability maps were produced using spatial analysis technique, by overlaying all surface layers. We used a Gaussian model to adjust a semivariogram graph in order to help to understand the variation of sample data values, and create a natural surface layer of data distribution over the area of study. By examining the statistical value and the visual inspection of surface layers, we saw that the models were consistent with the expected data behavior;therefore, we assumed that interpolation has been carried out appropriately. Our site-suitability map showed that Avicennia species was the most suitable species and matched with 50% of the study area, followed by Nypa fruticans, which occupied about 42%. These results were actually consistent with the mangrove zoning pattern in the region prior to deforestation and conversion.

Using GIS and Geostatistical Techniques for Mapping Piezometry and Groundwater Quality of the Albian Aquifer of the M’zab Region, Algerian Sahara

The M’zab region is subject to an arid Saharan climate where surface and sub-surface waters are of little importance. The Albian Aquifer, commonly called Continental Intercalary (CI), main component of North Western Sahara Aquifer System (NWSAS/SASS), constitutes the most extensive aquifer formation of the region. In our study area, the CI is identified, as a regional subset, as the Albian Aquifer of M’zab Region (AAMR). Its groundwater resources are considered the only source available to meet the growing needs of drinking water supply, agriculture and industry. This aquifer is heavily exploited by a very large number of wells (more than 750). Its supply is very low, so it is a very low renewable layer. This requires periodic monitoring and control of its piezometric level and its physico- chemical quality. The objective of our study is to know the current state of this aquifer, while studying the variation of its piezometry for the period 2010-2018, and also the chemical quality of its groundwater by analyzing more than 90 samples over the entire study area. The application of geostatistics by kriging and the steps of analysis, modelling and calculation of semivariogram have enabled us to draw up maps of the various hydrogeological and hydrochemical parameters. As a result, twelve thematic maps were gridded using Geostatistical tools of ArcGIS software. The water-level-change map showed a significant drop in the groundwater level over the entire M’zab region and especially around the major cities (Ghardaïa, Berriane, Metlili and Zelfana) with more than 8 meters. Chemical analyses of the Albian groundwater in the study area show the dominance of evaporite facies (Cl--Na+-Ca2+) with low concentrations than the Algerian Standards for Drinking (ASD). All the water quality indices (WQI) that have been mapped reveal that the groundwater samples were suitable for drinking and irrigation with a high quality of water located in the south of the study area.

Multivariate Geostatistical Model for Groundwater Constituents in Texas

Although many studies have explored the quality of Texas groundwater, very few have investigated the concurrent distributions of more than one pollutant, which provides insight on the temporal and spatial behavior of constituents within and between aquifers. The purpose of this research is to study the multivariate spatial patterns of seven health-related Texas groundwater constituents, which are calcium (Ca), chloride (Cl), nitrate (NO3), sodium (Na), magnesium (Mg), sulfate (SO4), and potassium (K). Data is extracted from Texas Water Development Board’s database including nine years: 2000 through 2008. A multivariate geostatistical model was developed to examine the interactions between the constituents. The model had seven dependent variables—one for each of the constituents, and five independent variables: altitude, latitude, longitude, major aquifer and water level. Exploratory analyses show that the data has no temporal patterns, but hold spatial patterns as well as intrinsic correlation. The intrinsic correlation allowed for the use of a Kronecker form for the covariance matrix. The model was validated with a split-sample. Estimates of iteratively re-weighted generalized least squares converged after four iterations. Matern covariance function estimates are zero nugget, practical range is 44 miles, 0.8340 variance and kappa was fixed at 2. To show that our assumptions are reasonable and the choice of the model is appropriate, we perform residual validation and universal kriging. Moreover, prediction maps for the seven constituents are estimated from new locations data. The results point to an alarmingly increasing levels of these constituents’ concentrations, which calls for more intensive monitoring and groundwater management.

Predicting the Seasonal NDVI Change by GIS Geostatistical Analyst and Study on Driver Factors of NDVI Change in Hainan Island, China

As Hainan Island belonged to tropical monsoon influenced region, vegetation coverage was high. It is accessible to acquire the vegetation index information from remote sensing images, but predicting the average vegetation index in spatial distributing trend is not available. Under the condition that the average vegetation index values of observed stations in different seasons were known, it was possible to qualify the vegetation index values in study area and predict the NDVI (Normal Different Vegetation Index) change trend. In order to learn the variance trend of NDVI and the relationships between NDVI and temperature, precipitation, and land cover in Hainan Island, in this paper, the average seasonal NDVI values of 18 representative stations in Hainan Island were derived by a standard 10-day composite NDVI generated from MODIS imagery. ArcGIS Geostatistical Analyst was applied to predict the seasonal NDVI change trend by the Kriging method in Hainan Island. The correlation of temperature, precipitation, and land cover with NDVI change was analyzed by correlation analysis method. The results showed that the Kriging method of ARCGIS Geostatistical Analyst was a good way to predict the NDVI change trend. Temperature has the primary influence on NDVI, followed by precipitation and land-cover in Hainan Island.

Geostatistical Analysis of the Colorada and Quimichule Canyons Located in Popocatépetl Volcano (Mexico) for the Prevention of Natural Disasters

This paper aims to contribute to the prevention of natural disasters and generate a complement to other similar studies. The Popocatépetl volcano has showed significant and constant activity since 1994. The Colorada and Quimichule canyons are located within its geologic structure;due to their topographic features, ejected volcanic material and torrential rains in the past recent years, they put nearby communities at risk. This work presents a geostatistical analysis to obtain the gravity acceleration, slope by the distance-elevation relation, height-gravity and the fluid force on the canyons. The conversion of UTM to geographical coordinates was made with the use of the program Traninv applying the ITRF2008 epoch 2010.0 Datum and the 14 Zone;the local gravity was calculated with the use of International Organization of Legal Metrology (OIML) and the statistical analysis was obtained with the use of the Geostatistical Environmental Assessment. The structural modeling was performed using Surfer, and the spending and force were calculated using hydrological models. The correlation analysis concluded that Quimichule has the greatest gravity and that it would transport lahars faster. Mapping, geomorphological and statistical techniques and models were applied in accordance with the study to obtain the results presented here.

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.