Sequential Gaussian Co-simulation Research Articles

Iran's comprehensive heat flow map generated by the Random Forest method and the Sequential Gaussian Simulation

The objective of this research is to present a comprehensive heat flow map for Iran by utilizing a novel approach that combines geostatistical distributions, machine learning algorithms, and deterministic calculations. In order to enhance the accuracy and quality of the initial geothermal map obtained from a recent study, a machine learning technique called the Random Forest method was employed in the mapping process, taking into consideration approximately 100 processed data points. To accomplish this, various geological features such as active faults, hot springs, geological domains, and hot spots were identified as effective attributes for generating a geology-based geothermal map. This geology-based map was then used as a trend to create a geostatistics-based geothermal gradient map. The sequential Gaussian co-simulation method was adopted for the geostatistical distribution, enabling the extension of the available geothermal gradient data points (which were calculated in a recent study) to cover the entire surface of Iran on a map. Consequently, an integrated geothermal gradient map was derived. Afterwards, thermal conductivity values corresponding to the prevalent lithology of each location in Iran were incorporated to calculate the heat flow values. This process resulted in the generation of a comprehensive heat flow map. The introduction of such an extensive map would greatly contribute to future geothermal-related explorations and complementing research in this field.

CoYangCZ: a new spatial interpolation method for nonstationary multivariate spatial processes

In multivariate spatial interpolation, the accuracy of a variable of interest can be improved using ancillary variables. Although geostatistical methods are widely used for multivariate spatial interpolation, these methods usually require second-order stationary assumption of spatial processes, which is difficult to satisfy in practice. We developed a new multivariate spatial interpolation method based on Yang-Chizhong filtering (CoYangCZ) to overcome this limitation. CoYangCZ does not solve the multivariate spatial interpolation problem from a purely statistical point of view but integrates geometry and statistics-based strategies. First, we used a weighted moving average method based on binomial coefficients (i.e. Yang-Chizhong filtering) to fit the spatial autocorrelation structure of each spatial variable from a geometric perspective. We then quantified the spatial autocorrelation of each spatial variable and the correlations between different spatial variables by analyzing the variances of different spatial variables. Finally, we obtain the best linear unbiased estimators at the unsampled locations. Experiments on air pollution and meteorological datasets show that CoYangCZ has a higher interpolation accuracy than cokriging, regression kriging, gradient plus-inverse distance squared, sequential Gaussian co-simulation, and the kriging convolutional network. CoYangCZ can adapt to second-order non-stationary spatial processes; therefore, it has a wider scope of application than purely statistical methods.

Sequential Gaussian co-simulation of tectono-geochemical anomaly for concealed ore deposit prediction

Tectono-geochemical data measured from tectonites host a wealth of information that is closely related to the accumulation and dispersion of ore-forming materials, while structure system is the only pathway to connect the deep orebody with the surficial tectono-geochemical anomaly, and both have correspondence and consistency. Based on the geological precondition that structure system and ore-forming process are closely associated with each other, the study proposed a method of sequential Gaussian co-simulation of tectono-geochemical anomaly, which integrates the tectono-geochemical anomaly with the ore-controlling structure system to solve two basic geological prospecting problems that are closely associated with ore-forming space and ore-forming material migration. A case study for concealed Pb–Zn prospecting based on tectono-geochemical data in the Huangzhuguang ore cluster (China) was employed to examine the potential applications of the proposed method. Firstly, centered logratio transformation was employed to remove the closure effect of tectono-geochemical data and to make the data conform to an approximate normal distribution. Secondly, sequential Gaussian co-simulation was applied to improve the simulation results of the tectono-geochemical anomaly by introducing the ore-controlling structure system. Thirdly, the probability distribution of tectono-geochemical anomalies was quantified by uncertainty modeling technique. The case study demonstrated that the proposed method can significantly improve the performance of the primary variable in predicting concealed ore deposits.

Assessing the spatial variability of saturated soil hydraulic conductivity at the watershed scale using the sequential Gaussian co-simulation method

Accurate spatial characterization of saturated soil hydraulic conductivity (KSat) is vital for modeling hydrological processes. An effective representation of KSat by field sampling is very difficult on a watershed scale, due the heterogeneity of landscape characteristics for wide land surfaces. To improve the estimation of spatial distributions of KSat at this scale, Sequential Gaussian Simulation (SGS) and Sequential Gaussian Co-Simulation (SGCS) algorithms were applied. The study was conducted in a 70 ha watershed, with 178 sampling points. In addition to KSat the database is composed of Bulk Density (BD), Total Porosity (TP), Macroporosity (Mac), Microporosity (Mic) and Organic Carbon (OC). The Land Use (LU) was also quantified as a regionalized variable. A principal component analysis generated additional two regionalized variables (PC1 and PC2). The simulations were evaluated by faithfully reproducing the stochastic and spatial characteristics of the KSat original data. To estimate the KSat, a univariate SGS was run first. The reproduction of the KSat histograms was satisfactory, while the semivariograms of the simulated fields underestimated the sill. The SGCS was run using five different secondary variables: BD; Mac; LU; PC1 and PC2. All SGCS satisfactorily represented the original KSat histogram, with a slight overestimation for some simulated fields. The semivariogram was very well reproduced for SGCS, being an indication that the process was quite efficient for all secondary variables. The smallest uncertainties were identified for the SGCS that used BD and Mac as secondary variables while the greatest uncertainties were associated with the SGS. The results of this study demonstrate that soil hydrological attributes as BD and Mac are a reliable auxiliary dataset to improve the spatial assessment of KSat by SGCS at watershed scale.

Multivariate simulation through minimum/maximum autocorrelation factors versus sequential Gaussian co-simulation: A case study on geochemical data from soil

Multivariate simulation through minimum/maximum autocorrelation factors versus sequential Gaussian co-simulation: A case study on geochemical data from soil

Multi-parameter pre-stack seismic inversion based on deep learning with sparse reflection coefficient constraints

In the field of seismic inversion, Convolutional Neural Network (CNN) has been extensively applied for their powerful capability of feature extraction and nonlinear fitting. However, the insufficient amount of labeled seismic inversion dataset impedes the application of CNN in seismic elastic inversion. Besides, the lack of effective geophysical constraints in conventional CNN will make the network prone to over-fitting, leading to unstable inversion results. In this paper, a workflow is developed for generating sufficient and diverse datasets for pre-stack seismic inversion with limited log and seismic data. The Sequential Gaussian Co-Simulation algorithm is used to simulate the changes in the reservoir space under the constraints of the low-frequency model. At the same time, the Elastic Distortion algorithm is used to simulate the complex geological structures. This can increase the diversity of the strata longitudinal combination by enriching the combination mode of stratigraphic parameters. Besides, the combination of a U-net and three fully connected networks (UCNN) is proposed to predict the elastic parameters from seismic data. In UCNN, the sparse reflection coefficient is used as a constraint to improve the accuracy of the network. The performance of this method was evaluated by synthetic and field data examples. The results show not only the effectiveness of the proposed method but also demonstrate its outperformance over the conventional deep learning method. The R2 scores of density, Vp and Vs are 0.94, 0.98, 0.98.

Improving correction quality for in-situ portable X-ray fluorescence (PXRF) using robust geographically weighted regression with categorical land-use types at a regional scale

Cost is a priority consideration in soil heavy metal investigation. For the correction of in-situ portable X-ray fluorescence (PXRF), traditionally-used linear regression (LR) is sensitive to outliers and cannot deal with the spatially varying influence of the relevant environmental factors. Moreover, each land-use type usually has a specific impact on the analysis quality of in-situ PXRF but was rarely incorporated into the correction model. This study first proposed robust geographically weighted regression with land-use types (RGWR-LUT) to correct in-situ PXRF Pb in an urban–rural transition area of Changzhou City, China. Next, its correction quality was compared with that of LR, LR with land-use types (LR-LUT), GWR, GWR with land-use types (GWR-LUT), and RGWR. Then, sequential Gaussian simulation with the corrected (by RGWR-LUT) in-situ PXRF as hard data (SGS-PXRF*) was proposed for spatial simulation of soil Pb. Finally, its spatial simulation quality was compared with that of SGS, SGS with the raw in-situ PXRF as hard data (SGS-PXRF), sequential Gaussian co-simulation with the raw in-situ PXRF as co-variable (CoSGS-PXRF), and CoSGS with the corrected (by RGWR-LUT) in-situ PXRF as co-variable (CoSGS-PXRF*). Results showed that: (i) spatially varying correction coefficient surface for in-situ PXRF Pb were obtained by RGWR-LUT; (ii) correction quality for in-situ PXRF Pb was in the order of RGWR-LUT (RI = 81.44%), GWR-LUT (RI = 72.1%), RGWR (RI = 67.83%), GWR (RI = 51.07%), LR-LUT (RI = 48.71%), and LR (RI = 22.72%); (iii) the corrected in-situ PXRF provided more information input than the raw in-situ PXRF for spatial simulation of soil Pb; (iv) SGS-PXRF* obtained the highest spatial simulation quality (RI = 62.5%). It is concluded that RGWR-LUT could effectively correct in-situ PXRF, and SGS-PXRF* could effectively incorporate the corrected in-situ PXRF for spatial simulation of soil heavy metals.

Additional sampling using in-situ portable X-ray fluorescence (PXRF) for rapid and high-precision investigation of soil heavy metals at a regional scale

Traditional soil heavy metal (HM) investigation usually costs a lot of human and material resources. In-situ portable X-ray fluorescence spectrometry (PXRF) is a cheap and rapid HM analysis method, but its analysis accuracy is usually affected by spatially non-stationary field environment factors. In this study, residual sequential Gaussian co-simulation (RCoSGS) was first proposed to incorporate both continuous and categorical auxiliary variables for spatial simulation of soil Cu. Next, additional in-situ PXRF sampling sites (n = 300) were allocated in the subareas with high, medium, and low conditional variances in the proportions of 50%, 33.33%, and 16.67%, respectively. Then, robust geographically weighted regression (RGWR) was established to correct the spatially non-stationary effects of field environmental factors on in-situ PXRF and further compared with the traditionally-used multiple linear regression (MLR) and basic GWR in correction accuracy. Finally, RCoSGS with the RGWR-corrected in-situ PXRF as part of hard data (RCoSGS-PXRF) was established and further compared with the model with one or multiple auxiliary variables in the spatial simulation accuracy. Results showed that (i) RCoSGS effectively incorporated both SOM and land-use types and obtained higher spatial simulation accuracy (RI = 37.52%) than residual sequential Gaussian simulation with land-use types (RI = 19.44%) and sequential Gaussian co-simulation with SOM (RI = 20.92%); (ii) RGWR significantly weakened the spatially non-stationary effects of field environmental factors on in-situ PXRF, and RGWR (RI = 58.96%) and GWR (RI = 39.61%) obtained higher correction accuracy than MLR; (iii) the RGWR-corrected in-situ PXRF (RI = 66.57%) brought higher spatial simulation accuracy than both land-use types and SOM (RI = 37.52%); (iv) RCoSGS-PXRF obtained the highest spatial simulation accuracies (RI = 83.74%). Therefore, the proposed method is cost-effective for the rapid and high-precision investigation of soil HMs at a regional scale.

Assessing heterotopic searching strategy in hierarchical cosimulation for modeling the variables with inequality constraints

A hierarchical sequential Gaussian cosimulation method is applied in this study for modeling the variables with an inequality constraint in the bivariate relationship. An algorithm is improved by embedding an inverse transform sampling technique in the second simulation to reproduce bivariate complexity and accelerate the process of cosimulation. A heterotopic simple cokriging (SCK) is also proposed, which introduces two moving neighborhoods: single and multiple searching strategies in both steps of the hierarchical process. The proposed algorithm is tested over a real case study from an iron deposit where iron and aluminum oxide shows a strong bivariate dependency as well as a sharp inequality constraint. The results showed that the proposed hierarchical cosimulation with a multiple searching strategy provides satisfying results compared to the case when a single searching strategy is employed. Moreover, the proposed algorithm is compared to the conventional hierarchical cosimulation, which does not implement the inverse transform sampling integrated into the second simulation. The proposed methodology successfully reproduces inequality constraint, while conventional hierarchical cosimulation fails in this regard. However, it is demonstrated that the proposed methodology requires further improvement for better reproduction of global statistics (i.e., mean and standard deviation).

Resampling with in situ field portable X-ray fluorescence spectrometry (FPXRF) to reduce the uncertainty in delineating the remediation area of soil heavy metals.

There must be some uncertainty in the remediation areas delineated based on limited sample points, and resampling in the high-uncertainty areas is particularly necessary. In situ field portable X-ray fluorescence spectrometry (FPXRF), a rapid and cheap analysis method for soil heavy metals, is strongly affected by many spatially non-stationary soil factors. This study first delineated the high-uncertainty area (threshold-exceeding probabilities (PTE) between 30% and 70%) of soil Pb based on the 1000 realizations produced by sequential Gaussian simulation (SGS) with 93 ICP-MS Pb concentrations measured in a peri-urban agriculture area, China. Next, in situ FPXRF was used to increase sample density in this high-uncertainty area. Then, robust geographically weighted regression (RGWR) was used to correct the in situ FPXRF Pb, and the correction accuracies of RGWR, basic GWR, and traditionally-used ordinary least squares regression (OLSR) were compared. Finally, to explore the best way to combine these corrected in situ FPXRF concentrations in delineating the remediation area, we compared the following spatial simulation methods: basic SGS, sequential Gaussian co-simulation (CoSGS) with the RGWR-corrected in situ FPXRF Pb as auxiliary soft data (CoSGS-CorFPXRF), and SGS with the RGWR-corrected in situ FPXRF Pb as part of hard data (SGS-CorFPXRF). Results showed that (i) RGWR produced higher correction accuracy (RI=71.5%) than GWR (RI=59.68%) and OLSR (RI=25.58%) for the in situ FPXRF Pb; (ii) SGS-CorFPXRF produced less uncertainty (G=0.97) than CoSGS-CorFPXRF (G=0.95) and SGS (G=0.91) in the spatial simulation; (iii) High-uncertainty area (30%<PTE<70%) was reduced from 36.55% to 8.7% of the whole study area. It is concluded that the recommended methods are cost-effective to reduce the uncertainty in delineating the remediation areas of soil heavy metals.

A hierarchical cosimulation algorithm integrated with an acceptance\u2013rejection method for the geostatistical modeling of variables with inequality constraints

This work addresses the problem of the cosimulation of cross-correlated variables with inequality constraints. A hierarchical sequential Gaussian cosimulation algorithm is proposed to address this problem, based on establishing a multicollocated cokriging paradigm; the integration of this algorithm with the acceptance–rejection sampling technique entails that the simulated values first reproduce the bivariate inequality constraint between the variables and then reproduce the original statistical parameters, such as the global distribution and variogram. In addition, a robust regression analysis is developed to derive the coefficients of the linear function that introduces the desired inequality constraint. The proposed algorithm is applied to cosimulate Silica and Iron in an Iron deposit, where the two variables exhibit different marginal distributions and a sharp inequality constraint in the bivariate relation. To investigate the benefits of the proposed approach, the Silica and Iron are cosimulated by other cosimulation algorithms, and the results are compared. It is shown that conventional cosimulation approaches are not able to take into account and reproduce the linearity constraint characteristics, which are part of the nature of the dataset. In contrast, the proposed hierarchical cosimulation algorithm perfectly reproduces these complex characteristics and is more suited to the actual dataset.

System reliability analysis for seismic site classification based on sequential Gaussian co-simulation: A case study in Shiraz, Iran

Seismic site classification plays a significant role in the estimation of site response and is carried out using average shear wave velocity through the top 30 m (VS30) soil layers. Meanwhile, at some sites with a number of boreholes, identification of the VS30 acquired from different boreholes does not lead to the classification of the site into one single category, and this makes the seismic classification of the site troublesome. This paper proposes a practical approach for obtaining the reliability index of the seismic site classification when not all VS30 calculated from the boreholes converge to that of a unique seismic class. For this purpose, the geostatistical method is combined with the system reliability approach. A real site with three boreholes, two of which fall into the ‘D' and the third into the ‘C' category based on the National Earthquake Hazards Reduction Program (NEHRP), is considered. The site is divided into 66 hypothetical soil columns. The shear wave velocity (VS) is estimated in depths of each column using the Sequential Gaussian Co-Simulation (SGCS) method based on sampled data determined nearby. Ten thousand realizations of VS with spatial distributions are generated via the SGCS method and are validated with the original data. In order for reliability analysis of the proposed classification approach, the reliability indices of the components are merged based on their corresponding correlation through the Sequential Compounding Method (SCM). The proposed method is proven to be consistent, fast, and the results are shown to be reliable.

Integrated receptor models and multivariate geostatistical simulation for source apportionment of potentially toxic elements in soils

Adequately understanding the source characteristic of potentially toxic elements (PTEs) in soils plays an important role in soil environmental protection and regulation. To improve the accuracy of quantifying source contributions, US-EPA positive matrix factorization (EPAPMF), weighted alternating least squares positive matrix factorization (WALSPMF), absolute principal component analysis/multiple linear regression (APCA/MLR), and UNMIX were applied and compared. Spatial distribution maps were delineated by using sequential Gaussian cosimulation (SGCS) with a linear model of coregionalization (LMC) fitting, and can be used to demarcate natural or polluted sources through superposing with auxiliary environmental data. Polluted area of PTEs exceeding a given threshold was determined using uncertainty analysis. The combination of receptor models and SGCS was used to a dataset consisting of As, Cd, Cr, Hg, Ni, Pb, and Zn as a case study. The four receptor models yielded three factors with comparable contributions to seven PTEs, but APCA/MLR produced some negative contributions. The average contributions were calculated based on EPAPMF, WALSPMF, and UNMIX. 85.3% of As, 81.3% of Cr, and 86.7% of Ni originated from natural source, and these three PTEs indicated consistent distributions with parent material map. Cd, Pb, and Zn were contributed by both industrial-traffic emissions and parent materials, with hotspots related to pollution sources and lacustrine deposits. Hg exhibited large-scale high value area around industrial sites, and exclusively derived from atmospheric deposition. A critical probability of 0.95 was adopted to determine polluted areas with PTE content exceeding 1.5 times its background. More than 40.0% of the total area was classified as contaminated for Hg, followed by Cd (3.1%) and Pb (2.9%). The combination of receptor models and SGCS proved to be an effective integrated approach for source apportionment.

Bernstein copula-based spatial cosimulation for petrophysical property prediction conditioned to elastic attributes

A new methodology for the simulation of spatially distributed petrophysical properties conditioned by elastic attributes as secondary variables is presented. The method, namely Bernstein copula-based spatial cosimulation (BCSCS), is based on Bernstein copula for the estimation of the joint probability function and simulated annealing for the spatial simulation. The proposed method can model complex non-linear relationships between variables in a fully nonparametric approach. The main advantage is that it does not require linear dependence between variables nor any distribution constraint. This method is first validated in a 1-dimensional case at the well-log scale and it is applied in a 2-dimensional case at the seismic scale to predict effective porosity conditioned to P-impedance in a marine hydrocarbon reservoir located offshore Mexico. The uncertainty quantification analysis shows that the BCSCS method significantly reduces the uncertainty compared to the traditional sequential Gaussian cosimulation method.

Geochemical modelling and mapping of Cu and Fe anomalies in soil using combining sequential Gaussian co-simulation and local singularity analysis: a case study from Dedeyazı (Malatya) region, SE Turkey

Mapping and modelling of the spatial distribution of geochemical anomalies is a key task for geochemical exploration. This case study explores mapping and modelling of Cu and Fe geochemical anomalies combining the Sequential Gaussian Co-simulation (SGCS) method and Local Singularity Analysis (LSA) in the Malatya region, SE Turkey. A total of 652 topsoil samples were collected on a regular grid design from the study area. A cell declustering technique was applied to the raw data. Both geometric and zonal anisotropy exist in the directional variogram of Cu and Fe. SGCS was applied to create maps representing an equally probable spatial distribution of Cu and Fe geochemical anomalies. SGCS results have been validated by a variety of tests including the reproduction of the variograms, histograms, descriptive statistics and contour plots. LSA is based on a sliding window estimation approach applied to the grid data created for SGCS realization. LSA was carried out and mapped via the results of the realization on the same grid layout. Critical anomaly threshold values of the variables were identified using the singularity and quantile plot. Integration of SGCS and LSA results provides quantification of the uncertainty of spatial distribution and determination of Cu and Fe critical thresholds.

Better assessment of the distribution of As and Pb in soils in a former smelting area, using ordinary co-kriging and sequential Gaussian co-simulation of portable X-ray fluorescence (PXRF) and ICP-AES data

To design an appropriate remediation plan at polluted sites, the spatial distribution of soil contaminants should be accurately assessed using geostatistical approaches such as co-kriging. In this study, we evaluated whether portable X-ray fluorescence (PXRF) spectroscopy can provide a reliable dataset to improve the spatial assessment of contaminated soils. For this purpose, soil samples were collected at a high density in a former smelting area (70 m by 65 m) that was highly polluted with arsenic (As) and lead (Pb). The samples were analyzed using inductively coupled plasma atomic emission spectroscopy (ICP-AES; n = 153). In addition, at the sampling locations, As and Pb levels were scanned in the field using PXRF spectroscopy (n = 156). As a result, PXRF measurements were highly correlated with ICP-AES data and seemed appropriate as a secondary variable for spatial evaluation with co-kriging. Thus, we conducted ordinary co-kriging (OCK) using a part of ICP-AES data (primary variable) and all PXRF data (auxiliary variable), and compared the interpolation result with that by ordinary kriging (OK) using the same number of ICP-AES data. We assumed that the ICP-AES data represented true values but were less effective in cost and analytical time. A best spatial map of As and Pb levels was constructed by OK using all the training ICP-AES data (n = 123) for performance comparison and the prediction errors were calculated using the test ICP-AES data (n = 30). Comparison results indicated that the spatial distribution of contamination levels estimated by OCK was more similar to the best spatial map than that by OK when the same number of ICP-AES data was used; OCK addressed the spatial heterogeneity despite the small number of training data, while OK lost the heterogeneity. OCK using PXRF data also improved the prediction of spatial distribution even with the cutting of the sample size of ICP-AES data; the number of samples that minimized errors was reduced by 40 and 50% for As and Pb, respectively, in OCK. As a last step, the uncertainty of the spatial extent of soil contamination for remedial action or additional investigation was addressed using sequential Gaussian co-simulation algorithms, which incorporated PXRF measurements as a secondary variable and provided the probability of exceeding the regulatory limits of a soil contaminant. The probability map can help risk-based decision making in contaminated sites within budget and time constraints. The results of this study demonstrate that PXRF provides a reliable auxiliary dataset to improve the spatial assessment of contaminated soils, with reducing the time and cost of investigations.

In-situ coal quality variability analysis by combining Gaussian co-simulation and a JavaScript

ABSTRACTThis study covers an in-situ analysis of simulated coal quality attribute variations of a power plant in Tufanbeyli/Adana, Turkey. Three main coal quality variables including calorific value, sulfur and ash content were simulated by Sequential Gaussian co-simulation method. The results were validated by a number of tests. A this-study-specific JavaScript is written to reveal the variations of coal qualities in a specific extraction route and capacity for both short and long-term production planning and scheduling. Results declared that the JavaScript successfully reflected the simulated variations in the candidate route and very adaptable to similar studies easily.

CO2 storage capacity estimation through static reservoir modelling: A case study of the lower Cretaceous Gage Sandstone reservoir in the offshore Vlaming Sub-basin, Perth Basin, Australia

The Lower Cretaceous Gage Sandstone is a deep saline aquifer which is overlain by the regionally extensive Lower Cretaceous South Perth Shale seal in the offshore Vlaming Sub-basin, Perth Basin, Australia. This paper is focused on the CO2 storage capacity estimation in the Gage Sandstone reservoir by integrating both the well and seismic data. After a 3D grid system was constructed, well log interpretations, depth converted interval velocity and seismic relative acoustic impedance data were imported into the 3D grids. The volume fraction of shale was first constructed combining the neural networks modelling and residual stochastic simulation from the well and seismic attributes data. Porosity was modelled using sequential Gaussian co-simulation with the volume fraction of shale model. The CO2 storage capacity was estimated using the total pore volume and storage coefficients in the US-DOE methodology. The best estimate (P50) of carbon storage capacity in the Gage Sandstone reservoir is 493 million tonnes based on the static reservoir modelling.

An integrated approach to identify quantitative sources and hazardous areas of heavy metals in soils

Identifying quantitative sources and hazardous areas of heavy metals is a crucial issue for soil management. For this purpose, an integrated approach composed of finite mixture distribution modeling (FMDM), positive matrix factorization (PMF) and sequential Gaussian co-simulation (SGCS) was proposed. FMDM was used to establish background standards and pollution thresholds. PMF supported by FMDM background standards was applied to estimate the source apportionment. Hazardous areas of single metals were delineated using SGCS with FMDM pollution thresholds and uncertainty analysis, and overall hazardous areas were defined by the presence of multiple metals. This integrated approach was applied to a dataset of seven metals as a case study. FMDM indicated that the distributions of Cr, Cu, Ni, and Zn were fitted to two-dimensional mixture distributions, representing a background distribution and a moderately polluted distribution. The distributions of Cd, Hg, and Pb were composed of a three-component lognormal mixture distribution, corresponding to the background, moderate, and high pollution distributions. Three sources were apportioned. Cr, Cu, Ni, and Zn were dominated by parent materials. Parent materials contributed 52.6%, 45.8%, and 81.9% of Cd, Hg, and Pb concentrations, respectively. Human emissions from coal combustion, industrial work and traffic had significant influences on Hg, Cd, and Pb, with contributions of 49.8%, 26.9%, and 15.6%, respectively. Agricultural practices were exclusively associated with 20.5% of Cd. Overall, hazardous areas exceeding moderate pollution thresholds covered 17.4% of the total area, corresponding to urban areas and industrial sites, whereas overall hazardous areas above high pollution thresholds were limited to 0.01% of the total area.

A geostatistical investigation of 3D magnetic inversion results using multi-Gaussian kriging and sequential Gaussian co-simulation

Inversion of magnetic data has a significant role in geophysical exploration and it can be utilized in the 3D (three-dimensional) modeling of subsurface bodies (e.g. geological structures, mineral deposits, etc.). In this study, Physical Property Distribution Method (PPDM) was utilized for the inversion of magnetic data and the reliability of the resultant model was later examined by means of the geostatistical methods. For magnetic anomalies, PPDM first divides the surface of interest into a large number of cells with constant dimensions and then calculates the susceptibility value for each cell. On the other hand, geostatistical methods can calculate the ore grade value at different depths of a mineral deposit. In this study, we have used Multi-Gaussian Kriging (MGK) method for estimation of iron grade (Fe %) in Darreh-Ziarat Iron Deposit. MGK is a powerful non-linear estimation method that first provides normal distribution of grade values using the plot variogram of these new values and then makes use of one of the linear estimation approaches to prepare the ore grade distribution of each block. Also, Sequential Gaussian Co-Simulation (SGCS), which is based on the normal distribution of the variables of interest, can simulate iron grade value of each block using a secondary value. Here, SGCS method was utilized as a simulation algorithm to determine the relationship between Fe and susceptibility variables. Considering the fact that magnetic susceptibility variables exist in all simulated blocks, SGCS results are highly dependent on inversion results. So, Iron grade values at different depths of Darreh-Ziarat Iron Ore deposit were calculated using MGK and SGCS methods in order to assess the correctness of inversion results. Finally, the results revealed a high degree of validity at shallower depths and a lower depth of confidence at deeper depths.