Evaluation of spatial interpolation methods for groundwater level in an arid inland oasis,northwest China

The Wuwei oasis, situated in the upper reaches of the Shiyang River basin in the arid inland of northwest China, is intensively cultivated using both groundwater and irrigation water originating from the Qilian Mountains. Groundwater levels are declining due to overuse of irrigation water. To estimate the decline over the entire Wuwei oasis, eight different interpolation methods were used for interpolating groundwater levels over 3 years, i.e. starting in 1983, followed by 1988 and ending with 1992. Cross-validation and orthogonal-validation were applied to evaluate the accuracy of the different methods. Root mean squared error and the correlation coefficient (R ²) were calculated for each of the interpolation methods and years. Three kriging methods (simply, ordinary, and universal) gave the best fit. Modified ordinary kriging was found better than simple and universal kriging methods with a smaller number of points having large differences (>50 m) between estimated and predicted values. Based on the groundwater surfaces determined by the ordinary kriging as modified by Yamamoto, the groundwater decline was found from 1983 to 1992 to be a modest 2.1 m in average.     

Geostatistical approach for identification of transmissivity structure at Dulliu area in Taiwan

 A thorough understanding of the characteristics of transmissivity makes groundwater deterministic models more accurate. These transmissivity data characteristics occasionally possess a complicated spatial variation over an investigated site. This study presents both geostatistical estimation and conditional simulation methods to generate spatial transmissivity maps. The measured transmissivity data from the Dulliu area in Yun-Lin county, Taiwan, is used as the case study. The spatial transmissivity maps are simulated by using sequential Gaussian simulation (SGS), and estimated by using natural log ordinary kriging and ordinary kriging. Estimation and simulation results indicate that SGS can reproduce the spatial structure of the investigated data. Furthermore, displaying a low spatial variability does not allow the ordinary kriging and natural log kriging estimates to fit the spatial structure and small-scale variation for the investigated data. The maps of kriging estimates are smoother than those of other simulations. A SGS with multiple realizations has significant advantages over ordinary kriging and even natural log kriging techniques at a site with a high variation in investigated data. These results are displayed in geographic information systems (GIS) as basic information for further groundwater study. Received: 27 August 1999 · Accepted: 22 February 2000     

Identifying groundwater arsenic contamination mechanisms in relation to arsenic concentrations in water and host rocks

Leaching and oxidation of high arsenic (As) host rocks tend to be induced by circulation of deep geothermal waters, which increase As concentration in shallow groundwater. The purpose of this study is to identify the mechanism of groundwater As contamination in relation to leaching and oxidation along the border between the South Minahasa and Bolaang Mongondow districts, North Sulawesi, Indonesia. This region contains Miocene sedimentary rock-hosted disseminated gold deposits associated with hydrothermal alteration in a fault zone. Abnormally high As concentrations were observed in hot and cold springs and in surrounding shallow groundwater for a total mineralization area of 8 × 10 km². Two methods were adopted in this study: (1) microscopic and spectroscopic analyses of rock samples for mineral identification and (2) geostatistics for spatial modeling of As concentrations in groundwater. Jarosite was identified as the chief fill mineral in rock defects (cracks and pores). The presence of this mineral may indicate release of As into the environment, as can occur as an alteration product derived from oxidation and leaching of pyrite, As-rich pyrite or sulfide minerals by geothermal waters. Moreover, As concentrations in groundwater were estimated using geostatistics for spatial modeling. The co-kriging map identified local anomalies in groundwater As concentrations over the permissible limit (10 ppb). Such anomalies did not appear through ordinary kriging. Integration of the results indicates that As contamination in shallow groundwater probably is controlled by heterogeneous distributions of jarosite and variations in intensity and extent of hydrothermal activities.     

Interpolation and mapping of probabilities for geochemical variables exhibiting spatial intermittency

In monitoring a minor geochemical element in groundwater or soils, a background population of values below the instrumental detection limit is frequently present. When those values are found in the monitoring process, they are assigned to the detection limit which, in some cases, generates a probability mass in the probability density function of the variable at that value (the minimum value that can be detected). Such background values could distort both the estimation of the variable at nonsampled locations and the inference of the spatial structure of variability of the variable. Two important problems are the delineation of areas where the variable is above the detection limit and the estimation of the magnitude of the variables inside those areas. The importance of these issues in geochemical prospecting or in environmental sciences, in general related with contamination and environmental monitoring, is obvious. In this paper the authors describe the two-step procedure of indicator kriging and ordinary kriging and compare it with empirical maximum likelihood kriging. The first approach consists of using a binary indicator variable for estimating the probability of a location being above the detection limit, plus ordinary kriging conditional to the location being above the detection limit. An estimation variance, however, is not available for that estimator. Empirical maximum likelihood kriging, which was designed to deal with skew distributions, can also deal with an atom at the origin of the distribution. The method uses a Bayesian approach to kriging and gives intermittency in the form of a probability map, its estimates providing a realistic assessment of their estimation variance. The pros and cons of each method are discussed and illustrated using a large dataset of As concentration in groundwater. The results of the two methods are compared by cross-validation.     

Spatial modelling of hazardous elements at waste dumps using geostatistical approach: a case study Sarcheshmeh copper mine,Iran

Mining activities and resulting wastes can be considered as one of the most important sources of hazardous elements in the environment. Knowledge of the spatial distribution of toxic elements in waste dump systems is necessary to assess environmental hazard and strategy. To achieve this goal, this paper investigates spatial distribution of toxic elements using statistical and geostatistical analysis. A total of 58 soil samples were collected, and the amount of As, Cd, Co, Cr, Cu, Mn, Mo, Ni, Pb and Zn was then determined at “Sarcheshmeh” copper mine waste dumps. In order to evaluate the presence of multivariate outliers, Mahalanobis distance technique (D ²) was applied and the multivariate outlier samples were removed. This resulted in an increase in correlation coefficient. To reduce dimension of data set, principal component analysis was applied and four principal components were determined which indicate 83.463% of the total variance of data set. Estimated PCs together with the toxic elements maps based on the ordinary kriging display aggregation of toxic elements in some parts, and validity of predictions was evaluated using the leave-one-out cross-validation method. The regression coefficients of estimated and observed values presented the reliability of the kriging estimates. Sequential Gaussian simulation method was applied for principal components due to similar results of estimated principal components and toxic elements. The results of simulation maps are almost identical to estimated outcomes.     

Metal mobilization from base-metal smelting slag dumps in Sierra Almagrera (Almería,Spain)

Smelting slags associated with base-metal vein deposits of the Sierra Almagrera area (SE Spain) show high concentrations of Ag (<5–180 ppm), As (12–750 ppm), Cu (45–183 ppm), Fe (3.2–29.8%), Pb (511–2150 ppm), Sb (22–620 ppm) and Zn (639–8600 ppm). The slags are mainly composed of quartz, fayalite, barite, melilite, celsian, pyrrhotite, magnetite, galena and Zn–Pb–Fe alloys. No glassy phases were detected. The following weathering-related secondary phases were found: jarosite–natrojarosite, cotunnite, cerussite, goethite, ferrihydrite, chalcanthite, copiapite, goslarite, halotrichite and szomolnokite. The weathering of slag dumps near the Mediterranean shoreline has contaminated the soils and groundwater, which has caused concentrations in groundwater to increase to 0.64 mg/L Cu, 40 mg/L Fe, 0.6 mg/L Mn, 7.6 mg/L Zn, 5.1 mg/L Pb and 19 μg/L As. The results of laboratory leach tests showed major solubilization of Al (0.89–12.6 mg/L), Cu (>2.0 mg/L), Fe (0.22–9.8 mg/L), Mn (0.85–40.2 mg/L), Ni (0.092–2.7 mg/L), Pb (>2.0 mg/L) and Zn (>2.5 mg/L), and mobilization of Ag (0.2–31 μg/L), As (5.2–31 μg/L), Cd (1.3–36.8 μg/L) and Hg (0.2–7 μg/L). The leachates were modeled using the numerical code PHREEQC. The results suggested the dissolution of fayalite, ferrihydrite, jarosite, pyrrhotite, goethite, anglesite, goslarite, chalcanthite and cotunnite. The presence of secondary phases in the slag dumps and contaminated soils may indicate the mobilization of metals and metalloids, and help to explain the sources of groundwater contamination.     

Spatial variation in arsenic and fluoride concentrations of shallow groundwater from the town of Shahai in the Hetao basin,Inner Mongolia

Twenty-nine wells were selected for groundwater sampling in the town of Shahai, in the Hetao basin, Inner Mongolia. Four multilevel samplers were installed for monitoring groundwater chemistry at depths of 2.5–20 m. Results show that groundwater As exhibits a large spatial variation, ranging between 0.96 and 720 μg/L, with 71% of samples exceeding the WHO drinking water guideline value (10 μg/L). Fluoride concentrations range between 0.30 and 2.57 mg/L. There is no significant correlation between As and F⁻ concentrations. Greater As concentrations were found with increasing well depth. However, F⁻ concentrations do not show a consistent trend with depth. Groundwater with relatively low Eh has high As concentrations, indicating that the reducing environment is the major factor controlling As mobilization. Low As concentrations (<10 μg/L) are found in groundwater at depths less than 10 m. High groundwater As concentration is associated with aquifers that have thick overlying clay layers. The clay layers, mainly occurring at depths <10 m, have low permeability and high organic C content. These strata restrict diffusion of atmospheric O₂ into the aquifers, and lead to reducing conditions that favor As release. Sediment composition is an additional factor in determining dissolved As concentrations. In aquifers composed of yellowish-brown fine sands at depths around 10 m, groundwater generally has low As concentrations which is attributed to the high As adsorption capacity of the yellow–brown Fe oxyhydroxide coatings. Fluoride concentration is positively correlated with pH and negatively correlated with Ca²⁺ concentration. All groundwater samples are over-saturated with respect to calcite and under-saturated with respect to fluorite. Dissolution and precipitation of Ca minerals (such as fluorite and calcite), and F⁻ adsorption–desorption are likely controlling the concentration of F⁻ in groundwater.     

Application of universal kriging for estimation of earthquake ground motion: Statistical significance of results

Universal kriging is compared with ordinary kriging for estimation of earthquake ground motion. Ordinary kriging is based on a stationary random function model; universal kriging is based on a nonstationary random function model representing first-order drift. Accuracy of universal kriging is compared with that for ordinary kriging; cross-validation is used as the basis for comparison. Hypothesis testing on these results shows that accuracy obtained using universal kriging is not significantly different from accuracy obtained using ordinary kriging. Tests based on normal distribution assumptions are applied to errors measured in the cross-validation procedure;t andF tests reveal no evidence to suggest universal and ordinary kriging are different for estimation of earthquake ground motion. Nonparametric hypothesis tests applied to these errors and jackknife statistics yield the same conclusion: universal and ordinary kriging are not significantly different for this application as determined by a cross-validation procedure. These results are based on application to four independent data sets (four different seismic events).     

Effects of desferrioxamine-B on the release of arsenic from volcanic rocks

Microorganisms play an important role in As mobilization into groundwater by directly influencing As speciation or indirectly inducing solubilisation from As-bearing phases, such as Fe, Mn and Al oxides. Iron oxide dissolution could also be induced by siderophores, small-molecule compounds produced by microorganisms to favour Fe uptake. Well waters exceeding the potable water limit of 10 μg As L⁻¹ (0.133 μM) have been widely reported in geothermal areas. Mechanisms responsible for these high As concentrations have not yet been thoroughly elucidated and the complexity of As mobilization in volcanic aquifers is still open to multiple interpretations. The present study was based on batch release experiments aimed at verifying and quantifying the effect of siderophores on As mobilization from volcanic rocks (lava, tuff, peperino and fallout deposit) at different pH and ligand concentration. In the experiments the siderophore trihydroxamate desferroxamine B (Dfob) was used and its effect on As release from volcanic rocks was manifest after the first days. The most favourable pH for As release was pH 6 while concentrations above 250 μM Dfob considerably enhanced As and Fe concentrations in solution. The As release from rocks was between 2.0–10% at pH 6 and 2.4–8.8% at pH 8. The As/Fe ratio in solution changed with time suggesting different release mechanisms and higher mobility of As compared to Fe during the first phase of the experiment. The presence of siderophore increased Fe dissolution rates up to 10 orders of magnitude. The As release correlated with Al, Mn, Fe, Si, V, Ga and Sb and the release of all these elements increased with increasing Dfob concentration. In alkaline environments also Cu, Zn and Pb were mobilized. The presence of siderophores represents a possible trigger for As mobilization from iron binding minerals to the water phase, with interesting implications for groundwater quality, plant uptake and bacterial communities.     

Application of geostatistics to identify gold-rich areas in the Finisterre-Fervenza region,NW Spain

Three univariate geostatistical methods of estimation are applied to a geochemical data set. The studied methods are: ordinary kriging (cross-validation), factorial kriging, and indicator kriging. These techniques use the probabilistic and spatial behaviour of geochemical variables, giving a tool for identifying potential anomalous areas to locate mineralization. Ordinary kriging is easy to apply and to interpret the results. It has the advantage of using the same experimental grid points for its estimates, and no additional grid points are needed. Factorial kriging decomposes the raw variable into as many components as there are identified structures in the variogram. This, however, is a complex method and its application is more difficult than that of ordinary or indicator kriging. The main advantages of indicator kriging are that data are used by their rank order, being more robust about outlier values, and that the presentation of results is simple. Nevertheless, indicator kriging is incapable of separating anomalous values and the high values from the background, which have a behaviour different to the anomaly. In this work, the results of the application of these 3 kriging methods to a set of mineral exploration data obtained from a geochemical survey carried out in NW Spain are presented. This area is characterised by the presence of Au mineral occurrences. The kriging methods were applied to As, considered as a pathfinder of Au in this area. Numerical treatment of Au is not applicable, because it presents most values equal to the detection limit, and a series of extreme values. The results of the application of ordinary kriging, factorial kriging and indicator kriging to As make possible the location of a series of rich values, sited along a N–S shear zone, considered a structure related to the presence of Au.     

Dissolved organic carbon from the traditional jute processing technique and its potential influence on arsenic enrichment in the Bengal Delta

Dissolved organic C (DOC) plays an important role in the mobilization of As from sediments. In West Bengal, the widely used technique for obtaining jute fiber involves retting of the jute plant in ponds (hereafter such ponds are termed jute decomposing ponds) for several weeks, which produces significant amounts of DOC in the ponds. These ponds thus act as point sources of DOC and supply huge quantities of organic C to the Bengal Delta sediments. This study has been carried out to investigate the role of such DOC in enriching the groundwater with As in the Bengal Delta. Data clearly show that due to the effect of DOC, As is mobilized from the upper 2.6 m of the sediment profile, and is fixed between 2.6 and 6.1 m, while the lower part (6.1–9 m) largely remains unaffected. The reducing conditions mainly developed due to the decay of the percolating DOC seem to help the mobilization and transportation of As and other redox sensitive elements (Fe, Mn), as well as elements (Cu, Zn) attached to oxy-hydroxides of those redox-sensitive elements. Experiments also indicate that if the DOC production at the surface continues for a longer period of time, the zone of As fixation (2.6–6.1 m) may get shifted further downwards and ultimately intercept the water table resulting in As enrichment of groundwater.     

Comparison of approaches to spatial estimation in a bivariate context

The problem of estimating a regionalized variable in the presence of other secondary variables is encountered in spatial investigations. Given a context in which the secondary variable is known everywhere (or can be estimated with great precision), different estimation methods are compared: regression, regression with residual simple kriging, kriging, simple kriging with a mean obtained by regression, kriging with an external drift, and cokriging. The study focuses on 19 pairs of regionalized variables from five different datasets representing different domains (geochemical, environmental, geotechnical). The methods are compared by cross-validation using the mean absolute error as criterion. For correlations between the principal and secondary variable under 0.4, similar results are obtained using kriging and cokriging, and these methods are superior slightly to the other approaches in terms of minimizing estimation error. For correlations greater than 0.4, cokriging generally performs better than other methods, with a reduction in mean absolute errors that can reach 46% when there is a high degree of correlation between the variables. Kriging with an external drift or kriging the residuals of a regression (SKR) are almost as precise as cokriging.     

Estimating groundwater residence time using multiple regression model based on fluoride dissolution: an exploration of possibilities

High levels of fluoride concentration were observed in deep groundwater of the Mizunami area in Central Japan. Fluoride occurs mainly due to the reaction between granitic basement rock and groundwater. Granites were collected, crushed to powder, and then allowed to react with purified water for 80 days. Water–rock interaction results showed that the major factor affecting fluoride concentration is the residence time of the groundwater. Coexisting ions have also some contribution toward fluoride concentration. The groundwater residence time in the Mizunami area was estimated by applying results of water–rock interaction to correspond with field data. A regression model relating fluoride concentration, residence time, and coexisting ions was developed. The parameters of the regression model were determined using the genetic algorithms technique. Residence time was estimated by extrapolating experimental data to correspond with filed data. Near the recharge area, residence times in the potential fluoride source rock varied between 1 and 2,000 years, whereas near the discharge area residence times were in excess of tens of thousands of years. The groundwater residence time was also estimated by the groundwater particle-tracking-flow model. The estimates of groundwater residence time based on geochemical regression model were often larger than estimates of groundwater residence time developed by particle-tracking analysis using a groundwater flow model. There were large uncertainties—on the order of 10–10,000 years—in the estimates based on geochemical data.     

Spatial analysis of land use and shallow groundwater vulnerability in the watershed adjacent to Assateague Island National Seashore,Maryland and Virginia,USA

Spatial relations between land use and groundwater quality in the watershed adjacent to Assateague Island National Seashore, Maryland and Virginia, USA were analyzed by the use of two spatial models. One model used a logit analysis and the other was based on geostatistics. The models were developed and compared on the basis of existing concentrations of nitrate as nitrogen in samples from 529 domestic wells. The models were applied to produce spatial probability maps that show areas in the watershed where concentrations of nitrate in groundwater are likely to exceed a predetermined management threshold value. Maps of the watershed generated by logistic regression and probability kriging analysis showing where the probability of nitrate concentrations would exceed 3 mg/L (>0.50) compared favorably. Logistic regression was less dependent on the spatial distribution of sampled wells, and identified an additional high probability area within the watershed that was missed by probability kriging. The spatial probability maps could be used to determine the natural or anthropogenic factors that best explain the occurrence and distribution of elevated concentrations of nitrate (or other constituents) in shallow groundwater. This information can be used by local land-use planners, ecologists, and managers to protect water supplies and identify land-use planning solutions and monitoring programs in vulnerable areas.     

The Use of Geographically Weighted Regression for Spatial Prediction: An Evaluation of Models Using Simulated Data Sets

Increasingly, the geographically weighted regression (GWR) model is being used for spatial prediction rather than for inference. Our study compares GWR as a predictor to (a) its global counterpart of multiple linear regression (MLR); (b) traditional geostatistical models such as ordinary kriging (OK) and universal kriging (UK), with MLR as a mean component; and (c) hybrids, where kriging models are specified with GWR as a mean component. For this purpose, we test the performance of each model on data simulated with differing levels of spatial heterogeneity (with respect to data relationships in the mean process) and spatial autocorrelation (in the residual process). Our results demonstrate that kriging (in a UK form) should be the preferred predictor, reflecting its optimal statistical properties. However the GWR-kriging hybrids perform with merit and, as such, a predictor of this form may provide a worthy alternative to UK for particular (non-stationary relationship) situations when UK models cannot be reliably calibrated. GWR predictors tend to perform more poorly than their more complex GWR-kriging counterparts, but both GWR-based models are useful in that they provide extra information on the spatial processes generating the data that are being predicted.     

Factors responsible for high arsenic concentrations in two groundwater catchments in Taiwan

High As contents in groundwater were found in two neighboring catchments – the Chianan plain and the southern Choushui river alluvial fan in Taiwan. The groundwater quality, the redox potential and the As distribution of the Chianan plain were characterized using factor analysis, redox zoning and a geochemical program. The results were compared with those of the southern Choushui river alluvial fan. Possible As release mechanisms are also elucidated. Factors 1 and 2 of the groundwater in the Chianan plain – the salinization factor and the As enrichment factor – are similar to those in the southern Choushui river alluvial fan. However, the spatial distribution of reductive tendency in the Chianan plain is different to that in the Choushui river alluvial fan, and yields spatially distinct hydrogeochemical environments in these two neighboring areas. The reduction potential in the Chianan plain is stronger than that in the Choushui river alluvial fan. The difference between the reduction potentials in these two vicinal areas influences the concentrations of As in groundwater. The reductive dissolution of As-rich Fe oxyhydroxide is suggested to be the major mechanism for release of As to the groundwater in the Chianan plain and the Choushui river alluvial fan of Taiwan.     

Using stable and radioactive isotopes for the investigation of contaminant metal mobilization in a metal mining district

Naturally occurring stable and radioactive isotopes were used as environmental tracers to investigate contaminant metal mobilization processes in a metal smelter dump mainly consisting of slag. Water emerging from the dump at a spring is heavily contaminated by metals. The smelter dump contains minor amounts of flue dust, a material which shows a high potential for metal mobilization. Nearby dumps mainly consist of low-grade ore. Concentration patterns of ²³⁸U, ²²⁶Ra and ²¹⁰Pb determined in sediment deposited close to the contaminated spring reveal the flue dust to be the major local metal source rather than the slag or the low-grade ore. Contamination pathways inside the dump were investigated using hydrological, chemical and isotopic data. Strong negative correlation between water discharge and metal concentration in the spring water suggests, besides short-term dilution of the metal concentration by direct rainwater runoff, distinct long-term dilution of the spring water by groundwater being discharged at a significantly increased rate as a result of heavy rains. δ¹⁸O and δD signatures of rain, local groundwater and spring water confirm the importance of groundwater derived from the local aquifer. Another hydrological component with importance for metal mobilization was found to be water that is recharged in the dump itself. Tritium analysis allowed an assessment of the probable residence time of that water component in the smelter dump. Since that water component seems to represent a major local contamination pathway the findings of the study are of substantial importance for site remediation planning. As a primary result it could be stated that covering the dump would not result in any noteworthy short-term improvement of the spring water quality. First significant effects would only be visible after 2–3 decades at the earliest.     

Spatial interpolation of severely skewed data with several peak values by the approach integrating kriging and triangular irregular network interpolation

It was not unusual in soil and environmental studies that the distribution of data is severely skewed with several high peak values, which causes the difficulty for Kriging with data transformation to make a satisfied prediction. This paper tested an approach that integrates kriging and triangular irregular network interpolation to make predictions. A data set consisting of total Copper (Cu) concentrations of 147 soil samples, with a skewness of 4.64 and several high peak values, from a copper smelting contaminated site in Zhejiang Province, China. The original data were partitioned into two parts. One represented the holistic spatial variability, followed by lognormal distribution, and then was interpolated by lognormal ordinary kriging. The other assumed to show the local variability of the area that near to high peak values, and triangular irregular network interpolation was applied. These two predictions were integrated into one map. This map was assessed by comparing with rank-order ordinary kriging and normal score ordinary kriging using another data set consisting of 54 soil samples of Cu in the same region. According to the mean error and root mean square error, the approach integrating lognormal ordinary kriging and triangular irregular network interpolation could make improved predictions over rank-order ordinary kriging and normal score ordinary kriging for the severely skewed data with several high peak values.     

Chemical treatments for mobilizing arsenic from contaminated aquifer solids to accelerate remediation

Arsenic is a prevalent contaminant at US Superfund sites where remediation by pump and treat systems is often complicated by slow desorption of As from Fe and Al (hydr)oxides in aquifer solids. Chemical amendments that either compete with As for sorption sites or dissolve Fe and Al (hydr)oxides can increase As mobility and improve pump and treat remediation efficiency. The goal of this work was to determine optimal amendments for improving pump and treat at As contaminated sites such as the Vineland Chemical Co. Superfund site in southern New Jersey. Extraction and column experiments were performed using As contaminated aquifer solids (81 ± 1 mg/kg), site groundwater, and either phosphate (NaH₂PO₄·H₂O) or oxalic acid (C₂H₂O₄·2H₂O). In extraction experiments, phosphate mobilized between 11% and 94% of As from the aquifer solids depending on phosphate concentration and extraction time (1 mM–1 M; 1–24 h) and oxalic acid mobilized between 38% and 102% depending on oxalic acid concentration and extraction time (1–400 mM; 1–24 h). In column experiments, phosphate additions induced more As mobilization in the first few pore volumes but oxalic acid was more effective at mobilizing As overall and at lower amendment concentrations. At the end of the laboratory column experiments, 48% of As had been mobilized from the aquifer sediments with 100 mM phosphate and 88% had been mobilized with 10 mM oxalic acid compared with 5% with ambient groundwater alone. Furthermore, simple extrapolations based on pore volumes suggest that chemical treatments could lower the time necessary for clean up at the Vineland site from 600 a with ambient groundwater alone to potentially as little as 4 a with 10 mM oxalic acid.     

Block size selection with the objective of minimizing the discrepancy in real and estimated block grade

The valuation of a mining project depends upon the accuracy of geological block model. Sampling density, estimation method, and proper block size mainly affect the accuracy of estimated block. This paper aims to answer three questions: (1) which estimation method is more accurate, (2) what is the relation between sampling density and block size, and (3) what the optimum block size is. Conditional Gaussian simulation (CGS) was used to generate a hypothetical deposit, considered as a real block model. A range of different block dimensions were estimated by ordinary kriging, inverse squared distance, and nearest neighbor methods based on tow-simulated drilling grids database. The comparison of estimated and real block grades reveals that increasing the sampling density results the similar outcomes of geostatistics and deterministic interpolation methods. Furthermore, it was deduced that sampling density could not be a viable alternative in choosing appropriate block dimension and the variogram rang a was suggested as an affective parameter in block size selection. Then a geometrical formula was developed to obtain the block size based on the variogram range. The increment in project value that a mine planner can expected from the additional information of the dense drilling grid was also calculated and it was concluded that the block size obtained based on the suggested formula results acceptable information value. Finally, the database of Chador Malu iron ore mine which is located in 180 km northeast of Yazd city in the central part of Iran were used to validate the suggested formula.