Factorial Kriging Research Articles

Sources and spatial variations of heavy metals in offshore sediments of the western Pearl River Estuary

The concentrations of six heavy metals (Cd, Cr, Cu, Pb, Zn, and As) in offshore surface sediments of western Pearl River Estuary were analyzed to investigate their sources and spatial variations using factorial kriging analysis. Three-scale spatial variations in heavy metal concentrations were identified and separated: nugget, local, and regional scale, which indicated sample errors, anthropogenic pollution and natural variation, respectively. Anthropogenic heavy metals varied sharply and heterogeneous at range of 60 km. Maoming Port, Hailing Bay and coastal area northeastern Hainan Island were potential polluted areas of Cd, Cr, Cu, Pb, Zn and As, also the Nandu River, Baoling River and Wanquan River estuaries were potential polluted areas of As. These polluted areas ranged up to 60 km in size and tended to extend with currents. The natural heavy metals varied continuously and relatively homogeneous at range of 180 km, which was dominated by riverine input and paleo-sea-level changes.

Environmental Controls to Soil Heavy Metal Pollution Vary at Multiple Scales in a Highly Urbanizing Region in Southern China.

Natural and anthropogenic activities affect soil heavy metal pollution at different spatial scales. Quantifying the spatial variability of soil pollution and its driving forces at different scales is essential for pollution mitigation opportunities. This study applied a multivariate factorial kriging technique to investigate the spatial variability of soil heavy metal pollution and its relationship with environmental factors at multiple scales in a highly urbanized area of Guangzhou, South China. We collected 318 topsoil samples and used five types of environmental factors for the attribution analysis. By factorial kriging, we decomposed the total variance of soil pollution into a nugget effect, a short-range (3 km) variance and a long-range (12 km) variance. The distribution of patches with a high soil pollution level was scattered in the eastern and northwestern parts of the study domain at a short-range scale, while they were more clustered at a long-range scale. The correlations between the soil pollution and environmental factors were either enhanced or counteracted across the three distinct scales. The predictors of soil heavy metal pollution changed from the soil physiochemical properties to anthropogenic dominated factors with the studied scale increase. Our study results suggest that the soil physiochemical properties were a good proxy to soil pollution across the scales. Improving the soil physiochemical properties such as increasing the soil organic matter is essentially effective across scales while restoring vegetation around pollutant sources as a nature-based solution at a large scale would be beneficial for alleviating local soil pollution.

FKgrain: A topography-based software tool for grain segmentation and sizing using factorial kriging

FKgrain: A topography-based software tool for grain segmentation and sizing using factorial kriging

Factorial kriging for estimating and mapping the geochemical background from in situ gamma dose rate measurements downstream of a former uranium mine

A geostatistical approach is applied for extracting the geochemical background from gamma dose rate data acquired downstream of a former French uranium mining area. The exploratory data analysis shows that the spatial structure of the gamma dose rate consists of two components: a short isotropic component (10 m-range) that corresponds to the geochemical background; and a long anisotropic component (30–60 m-range) that corresponds to the drainage network features previously fed by the mine discharge water. The gamma dose rate on the whole area of interest was estimated and simulated (to deal with uncertainties) through a kriging of the measured values. The spatial component related to the geochemical background was then extracted through factorial kriging. The proportion of the gamma dose rate explained by the geochemical background according to factorial kriging is consistent within uncertainties with geochemical analyses performed on soil and sediment samples. This study thus highlights the potential of such geostatistical approaches for better exploiting radiometric data.

Separation of geomagnetic anomalies in the Bashmaq area in northwestern Iran by factorial kriging

Geomagnetic measurements detect the superposition of both regional and residual anomalies. Regional anomalies are caused by deep geological structures, while the residual ones are due to shallow sources. The presence of regional anomalies complicates the interpretation of magnetic data; to this end, a variety of techniques have been proposed for regional-residual anomaly separation. Most of them are based on Fourier transforms. Although valid results can be obtained from these methods, they have some limitations, such as requiring basic knowledge on approximate cut-off frequencies. This study focuses on spatial filtering employing factorial kriging (FK) for geomagnetic anomaly separation. FK employs geostatistical filtering based on spatial dependencies of the data. In contrast to the upward continuation, which is a trial and error method and needs to be checked with different distances of continuations, the utilisation of FK on synthetic data revealed that FK could automatically perform the separation and also helps to find the optimum distance for the upward continuation method. Following experiments with a synthetic model, the method was applied to real magnetic data of Bashmaq in northwestern Iran. Applying FK on a complicated real case study showed that it could separate the regional and residual components satisfactorily. Furthermore, results from the proposed approach have been compared against the Gaussian Separation Method (GSM). The results are compared to borehole information. The lithological columns are presented as part of the geology investigation. As demonstrated in the case study, the FK method has proven to be an accurate tool to better determine the mineralisation zones compared to GSM, which, in turn, facilitates the interpretation.

Reliability estimation of jacket type offshore platforms against seismic and wave loadings applied in time domain

ABSTRACT A novel approach is proposed for the reliability estimation of jacket-type offshore platforms excited by dynamic loadings (wave and seismic) applied in time domain. The information on risk is extracted with the help of multiple finite element-based deterministic analyses. This feature is expected to be attractive to practitioners for routine applications without advanced expertise in the risk-based design concept. It will also be of interest to researchers since the proposed concept innovatively integrates several advanced mathematical concepts, including the extensively modified response surface method, advanced factorial design schemes, Kriging, and other techniques producing compounding beneficial effects. For verification, an operating platform is excited by multiple time histories of wave and seismic loadings generated using current design guidelines. The probabilities of failure of the platform are estimated for both the strength and serviceability performance functions using about 200 deterministic analyses. The results are successfully verified using 10,000 Monte Carlo simulations.

Hydrogeochemical and hydrodynamic features affecting redox processes in groundwater

This research deals with some hydrogeochemical and hydrodynamic features that affect redox processes in groundwater, presenting three different case studies and methodological approaches. This information is vital when characterizing contaminated sites, planning monitoring, selecting remedial techniques, and assessing health risks. In the San Pedro Sula site case study (Honduras), new insights and an advanced method for the aquifer redox zonation were provided. The Multi-Collocated Factorial Kriging, a multivariate geostatistical technique borrowed from agriculture and soil science, identified simultaneous redox processes, acting at different scales and mainly due to eutrophicated surface-water/groundwater interaction: at short-range, Mn oxihydroxide reductive dissolution and Fe oxi-hydroxide colloidal phase precipitation; at long-range, Fe mobilization. The obtained results are supported by the Principal Component Analysis and hydrogeochemical numerical modeling. The interaction among different contamination events in the VR site allowed to get a deeper insight into the competition for organic substrate among different redox processes. To this purpose, a 1-D Advective-Reactive- Dispersive transport numerical model was implemented, and its results highlighted that the reductive dechlorination is inhibited by the inorganic Terminal Electron Accepting Processes, enriching groundwater in highly toxic by-products of the reductive dechlorination (i.e. Vinyl Chloride). As a matter of fact, the bacteria using inorganic Terminal Electron Acceptors to oxidize the organic substrate are more efficient than the halo-respiring bacteria, that favor reductive dechlorination. The contaminated site of Bussi Officine case study allowed to clarify the hydrodynamic effect on the redox processes and the anoxic condition distribution. The comparison between dissolved chlorinated solvents and the inorganic Terminal Electron Acceptors distribution in the aquifer pointed out that dispersion inhibits all the redox processes because it dilutes the organic substrate concentration in groundwater. On the other hand, the lacustrine deposits rich organic matter (i.e. peat) can be considered as “chemical reactors”, that releases by back-diffusion toxic by-product of the reductive dichlorination in groundwater.

Advanced redox zonation of the San Pedro Sula alluvial aquifer (Honduras) using data fusion and multivariate geostatistics

The incorrect wastewater management and the land use distribution lead to severe environmental problems, creating heavy eutrophication condition in surface-water; when surface-water/groundwater relationships exist, the organic matter transferred to the aquifer oxidizes and triggers redox processes (i.e. Terminal Electron Accepting Processes, TEAPs), that provoke severe groundwater quality modifications and complicate its exploitation and management. For this reason, the definition of the redox zonation within an aquifer is an effective tool for the identification of the contamination sources and for the conceptual model refinement, when remediation strategies need to be planned. Although the redox processes are dynamic reactions, the aquifer redox zonation is generally aimed to identify homogenous zones, characterized by a predominant TEAP. To overcome this methodological approach, the Multi-Collocated Factorial Kriging (MCFK) was applied to redox-related physico-chemical parameters, which allowed identifying their spatial relationships at different scales, transferring this method from precision agriculture and soil science to hydrogeochemistry.The selected study area is the San Pedro Sula aquifer (Honduras), a multi-layer alluvial aquifer characterized by well-known surface-water/groundwater interactions and heavy eutrophicated streams. Here, high concentrations of Mn and Fe were found in the aquifer.The MCFK results identified a short-range (2300 m) factor, highlighting a strong relation between Mn concentrations and anoxic conditions, due to the organic matter transfer from eutrophicated surface-water into the aquifer. Simultaneously, the relationship between Fe and turbidity is related to a fine Fe(III) oxi-hydroxide colloidal phase, developed when different redox conditions of groundwater mix up in the wells. The long-range (6000 m) factor points out that Fe is related to redox processes at a wider scale, especially in the northern San Pedro Sula alluvial plain. These results are supported by both the Principal Component Analysis and the hydrogeochemical numerical modeling. As a result, different TEAPs occur simultaneously in contaminated areas, acting at multiple scales.

Variogram modeling of broadband artifacts of a seafloor map for filtering with Factorial Kriging

Accurate seafloor maps are critical in offshore petroleum projects. Almost all subsurface modeling workflows use these maps: for example, pore pressure models and reservoir geomechanics. These studies generally involve sums of properties along the vertical, consequently, noise or acquisition artifacts at the seafloor map tend to propagate and even amplify in the subsequent models. Seafloor maps are normally acquired by sound-sensing technology and related procedures, which expectedly introduce noise and artifacts. Moving window filters, such as average and median filters, are easy to use and fast to compute, hence they are used very often by interpreters to make geologically sound horizons. However such filters are unable to discern noise, artifacts and signal, resulting in the compromise of actual information. Filtering in the frequency domain can pose difficulties when noise, artifacts and geological information overlap in the frequency domain, as the total energy tend to concentrate in the lowest frequencies. Factorial kriging (FK) is a spatial filter that yields separate estimations, each corresponding to a variogram nested structure. FK relies on the principle that structurally complex information is a sum of independent information components while the variogram is a clear and reliable way to select the frequency ranges of each component. Hence, this method can effectively separate acquisition artifacts from seafloor information based on their different spatial structures modeled with variograms. This work investigates an application of FK for filtering of hard-edged (broadband) artifacts in post-processed interpreted seismic data. Differently from random noise, artifacts are spatially correlated information components mixed with actual geologic information. Initially, removal of the bathymetric trend makes the case stationary for a high-resolution variogram map computed in the frequency domain via fast Fourier transform (FFT), which enables a full 2D variogram modeling. Theoretical variogram surfaces are fit to the experimental variogram map, enabling the identification and modeling of a set of nested variograms. The authors envisaged search strategies to select a small number of informative samples to reduce kriging runtime and, at the same time, cover the necessary spatially correlated variability. A workflow on a large seismic-derived seafloor 2D map is demonstrated, detailing each step with emphasis on the sensitive variogram modeling step, followed by search strategy definition and choice of the geology-bearing factors for seafloor restoration. Filtering in frequency domain was performed for comparison. Results showed that broadband artifacts require a non-traditional approach to variogram modeling, which was performed in a second FK run with a wholly new variogram model. The filtering operations revealed seafloor features, which were previously unseen in the original map, and the final result was similar to that obtained with FFT. FK is a lossless filtering technique that is a highly effective method to remove acquisition footprints in final grids and volumes in which acquisition geometry information is not available. 11FFT – fast Fourier transform22FK – Factorial Kriging33KT – Kriging with a trend44TCL – Tool Command Language

Factorial kriging analysis leverages soil physical properties and exhaustive data to predict distinguished zones of hydraulic properties

Measurement of unsaturated hydraulic properties of soil is a time-consuming endeavor which limits the scale of studies. A stratified sampling scheme could enable more efficient use of samples but some information about the strata is needed a priori. The aim of this study is to define zones of soil hydraulic properties using remotely sensed and soil physical inputs. Samples were collected from 50 locations at 4 depth intervals in a 20.8 ha field located along the margin of the Venice Lagoon, Italy, and characterized by paleo-channel structures and highly heterogeneous soils. Water retention curves (WRC) and unsaturated hydraulic conductivity curves (UHC) were determined via inversion of measurements taken in the lab using the Wind method. Factorial kriging analysis (FKA) was applied separately to hydraulic parameters and soil physical properties and the 4 depths treated as independent samples. The mapped principal components (PCs) were used in a fuzzy-c means algorithm to define zones of like properties. To examine the physical significance of these zones, curve parameters and hydraulic curves were investigated. Zonation was able to distinguish between θs (saturated water content), n (shape parameter) and α (inverse of air entry), while θr (residual water content) and Ks (saturated conductivity) were not statistically different between the groups. For curve comparisons, WRCs were found to be significantly different between zones at all tensions while effective saturation curves (Se) differ for the majority of tensions (except at 28 cm), and UHCs did not differ. The spatial relevance of the zones was examined by overlaying hydraulic zones with zones defined using the FKA and fuzzy-c means approach from soil physical properties such as texture and bulk density. The hydraulic zones overlaid the physical property zones with an areal accuracy ranging from 46.66% to 92.41%. The similarity between these zone sets suggests that there is a potential to predict hydraulic zones from zones defined from soil physical properties. This work illustrates the potential to incorporate geospatial statistics in a stratified sampling scheme for hydraulic properties.

Identification of shallow geohazard channels based on discontinuity seismic attributes in the South Caspian Sea

Identification of geomorphological features in seismic data is a key element of seismic interpretation. Channels in the shallow subsurface are potential geohazards. At deeper levels, they can be the actual targets for (horizontal) drilling. Either way, it is important to optimally delineate these features prior to well location positioning and drilling. We have studied a poststack 3D seismic data from the South Caspian Sea featuring shallow channels that are considered potential geohazards for drilling operations. In the first step, we attenuate the acquisition footprints along the inline direction using a geostatistics approach based on factorial kriging. To better visualize channels in the presence of stratigraphic dips, we create a dense set of horizons using an inversion-based flattening algorithm. In the next step, we compare various discontinuity attributes such as semblance, similarity, curvature, and the relatively new attribute based on the multiscale and multidirectional shearlet transformation to determine which one best images our features of interest. Curvature attributes clearly image channel levies (positive curvature) and channel centers (negative curvature). Lateral changes in the curvature magnitude infer sedimentation from the north. Similarity, semblance, and shearlet transform attributes also successfully delineate channel edges, but these attributes do not contain additional geologic information. In the final step, we qualitatively analyze channel thickness variations by the red-green-blue blending of three spectral components based on short window Fourier transforms.

Quantifying the scales of spatial variation in gravel beds using terrestrial and airborne laser scanning data

Abstract Previous studies measured gravel bed surfaces by terrestrial laser scanning (TLS) and close-range photogrammetry suggested the presence of at least two different scales of spatial variation in gravel bed surfaces. This study investigated the spatial variation of airborne laser scanning (ALS) point clouds acquired in gravel bed. Due to the large footprint of ALS systems, a smoother surface is expected, but there exists some uncertainty over the precise scale of ALS measurement (hereafter referred to as the spatial support). As a result, we applied the regularization method, which is a variogram upscaling approach, to investigate the true support of ALS data. The regularization results suggested that the gravel bed surface described by the ALS is much smoother than expected in terms of the ALS reported measurement scale. Moreover, we applied the factorial kriging (FK) method, which allows mapping of different scales of variation present in the data separately (different from ordinary kriging which produces a single map), to obtain the river bed topography at each scale of spatial variation. We found that the short-range and long-range FK maps of the TLS-derived DSMs were able to highlight the edges of gravels and clusters of gravels, respectively. The long-range FK maps of the ALS data shows a pattern of gravel-bed clusters and aggregations of gravels. However, the short-range FK maps of the ALS data produced noisy maps, due to the smoothing effect. This analysis, thus, shows clearly that ALS data may be insufficient for geomorphological and hydraulic engineering applications that require the resolution of individual gravels.

Multi-scale analysis of heavy metals sources in soils of Jiangsu Coast, Eastern China

Since the development of Jiangsu Coast was proposed as a national strategy by the Chinese Government in 2009, Jiangsu Coast has been experiencing rapid and intensive development in industry and tidal flat reclamation, which has inevitably led to the accumulation of heavy metals in its soils. A total of 239 samples (0–20 cm) were collected from topsoils of Jiangsu Coast, and their concentrations of Cd, Cr, Cu, Hg, Ni, Pb, and Zn were determined. Factorial kriging was applied to examine the scale-dependent correlations between heavy metals and to generate the spatial components at multiple scales, and multivariate stepwise regression was used to explore the relationships between the spatial multi-scale components of heavy metals and environmental factors. Linear model of co-regionalization (LMC) fitting indicated that the multi-scale variation comprised a nugget effect, an exponential structure with a range of 15 km (local scale), and a spherical structure with a range of 135 km (regional scale). The spatial correlations of seven heavy metals depended on their spatial scales, and their correlations increased with the increasing scales. Spatial variations in Cr and Ni were associated with natural geochemical sources on both local and regional scales. Parent material influenced the basic spatial variations in Cd, Cu, Pb and Zn on both local and regional scales, but human activity also contributed to the spatial variations in these four metals. The human inputs of Cd, Cu, Pb, and Zn differed on these two scales. Hg was dominated by industrial emissions and agricultural practices on both scales.

Delineation of gravel-bed clusters via factorial kriging

Gravel-bed clusters are the most prevalent microforms that affect local flows and sediment transport. A growing consensus is that the practice of cluster delineation should be based primarily on bed topography rather than grain sizes. Here we present a novel approach for cluster delineation using patch-scale high-resolution digital elevation models (DEMs). We use a geostatistical interpolation method, i.e., factorial kriging, to decompose the short- and long-range (grain- and microform-scale) DEMs. The required parameters are determined directly from the scales of the nested variograms. The short-range DEM exhibits a flat bed topography, yet individual grains are sharply outlined, making the short-range DEM a useful aid for grain segmentation. The long-range DEM exhibits a smoother topography than the original full DEM, yet groupings of particles emerge as small-scale bedforms, making the contour percentile levels of the long-range DEM a useful tool for cluster identification. Individual clusters are delineated using the segmented grains and identified clusters via a range of contour percentile levels. Our results reveal that the density and total area of delineated clusters decrease with increasing contour percentile level, while the mean grain size of clusters and average size of anchor clast (i.e., the largest particle in a cluster) increase with the contour percentile level. These results support the interpretation that larger particles group as clusters and protrude higher above the bed than other smaller grains. A striking feature of the delineated clusters is that anchor clasts are invariably greater than the D90 of the grain sizes even though a threshold anchor size was not adopted herein. The average areal fractal dimensions (Hausdorff-Besicovich dimensions of the projected areas) of individual clusters, however, demonstrate that clusters delineated with different contour percentile levels exhibit similar planform morphologies. Comparisons with a compilation of existing field data show consistency with the cluster properties documented in a wide variety of settings. This study thus points toward a promising, alternative DEM-based approach to characterizing sediment structures in gravel-bed rivers.

Spatial multi-scale relationships of ecosystem services: A case study using a geostatistical methodology

Adequately understanding the spatial multi-scale relationships of ecosystem services (ES) is an important step for environmental management decision-making. Here, we used spatially explicit methods to estimate five critical ES (nitrogen and phosphorous purifications, crop production, water supply and soil retention) related to non-point source (NPS) pollution in the Taihu Basin region of eastern China. Then a factorial kriging analysis and stepwise multiple regression were performed to identify the spatial multi-scale relationships of ES and their dominant factors at each scale. The spatial variations in ES were characterized at the 12 km and 83 km scales and the result indicated that the relationships of these services were scale dependent. It was inferred that at the 12 km scale, ES were controlled by anthropogenic activities and their relationships were dependent on socio-economic factors. At the 83 km scale, we suggested that ES were primarily dominated by the physical environment. Moreover, the policy implications of ES relationships and their dominant factors were discussed for the multi-level governance of NPS pollution. Overall, this study presents an optimized approach to identifying ES relationships at multiple spatial scales and illustrates how appropriate information can help guide water management.

A multivariate approach to study the geochemistry of urban topsoil in the city of Tampere, Finland

Risk assessment of potentially toxic elements (PTEs) requires to separate their geogenic soil enrichment and anthropogenic pollution since they are two processes acting together and causing elevated concentrations of PTEs in urban topsoil. The study was aimed to analyse and compare the concentrations of various potentially harmful geochemical elements in the urban soils of the city of Tampere (Finland) to determine their spatial relations by modelling their coregionalization to isolate and display sources of variation acting at different spatial scales and define potential spatial anomalies based on the correlation structure associated at the different spatial scales. Principal Component Analysis (PCA) and Factorial Kriging Analysis (FKA) were used to analyse the geochemical data set. Principal Component Analysis (PCA) allowed to identify two groups of geochemical elements whereas FKA enabled to distinguish the correlation structure of the multivariate data at different spatial scales and to summarize the main features of the data at each spatial scale and to take into account different sources of geochemical elements concentrations. Such concentrations in topsoil of the Tampere city were explained by both geogenic and anthropogenic sources.

Factorial kriging analysis and pollution evaluation of potentially toxic elements in soils in a phosphorus-rich area, South Central China

Identifying spatial variations of potentially toxic elements at different spatial scales and their contamination conditions is important for soil management and remediation. Utilizing a 1km×1km sampling grid, a total of 615 soil samples were collected from a phosphorus-rich area of South Central China and determined for arsenic (As), cadmium (Cd), cobalt (Co), chromium (Cr), copper (Cu), nickel (Ni), lead (Pb), vanadium (V), and zinc (Zn) concentrations. Factorial kriging analysis (FKA), enrichment factor (EF), and potential ecological risk (RI) were used to examine scale-dependent correlations between the elements, identify factors of multi-scale spatial variations, and assess pollution status, respectively. The results indicate that only the mean concentrations of As, Cd, and Pb exceeded the background levels. Based on EF method, the pollution levels of As, Cd, and Pb were assessed as middle or high, and according to the RI values, 11.2% of the study area was under considerable potential ecological risk. Through linear model of co-regionalization (LMC) fitting, spatial multi-scale variations of elements could be modeled as the sum of a nugget effect, an exponential structure (3km), and a spherical structure (15km). At the short-range scale, spatial variations of Co, Cr, Cu, Ni, and V were controlled by parent materials, whereas that of As, Pb, Cd, and Zn were related to human influence, such as phosphorus-related industrial activities and river pollution. At the long-range scale, parent materials were the dominant factors regulating the spatial variations of all elements.

Interpretative filtering

Industry already acknowledges the power of dip-steered median filters to clean-up seismic data volume in which coherent events are enhanced and random noise is reduced. By combining two powerful technologies, this paper presents a dip-steered geostatistical filtering solution, called interpretative filtering (IF), which gives remarkable results for removing random and organised noise from seismic volumes. It defines a new generation of spatial filters useful for processing and interpretation. The IF solution is based on a 3D non-stationary factorial kriging technique (M-GS technology) driven by a high-resolution interpretation of the seismic volume coming from a Relative Geological Time model. This new technique enables some non-stationary noise to be dealt with. For example acquisition footprints are well known to be non-stationary noises, with varying orientation, width and intensity as a function of the position in the volume. IF opens the way to refine filtering operations of seismic volumes even in complex structural environments. For this paper, the solution is applied to an open-file 3D marine seismic dataset (HCA2000A 3D) covering the Exmouth sub-basin, North West Shelf, Australia. This survey presents a dense fault system, mostly intersecting the Jurassic and the Cretaceous. Results show a great improvement on reducing the acquisition footprint and random noise without compromising the definition of the subtle geological features.

Estimation of transit trip production using Factorial Kriging with External Drift: an aggregated data case study

Studies in transportation planning routinely use data in which location attributes are an important source of information. Thus, using spatial attributes in urban travel forecasting models seems reasonable. The main objective of this paper is to estimate transit trip production using Factorial Kriging with External Drift (FKED) through an aggregated data case study of Traffic Analysis Zones in São Paulo city, Brazil. The method consists of a sequential application of Principal Components Analysis (PCA) and Kriging with External Drift (KED). The traditional Linear Regression (LR) model was adopted with the aim of validating the proposed method. The results show that PCA summarizes and combines 23 socioeconomic variables using 4 components. The first component is introduced in KED, as secondary information, to estimate transit trip production by public transport in geographic coordinates where there is no prior knowledge of the values. Cross-validation for the FKED model presented high values of the correlation coefficient between estimated and observed values. Moreover, low error values were observed. The accuracy of the LR model was similar to FKED. However, the proposed method is able to map the transit trip production in several geographical coordinates of non-sampled values.

Factorial Kriging analysis and sources of heavy metals in soils of different land-use types in the Yangtze River Delta of Eastern China.

The objectives of this study are to analyse the pollution status and spatial correlation of soil heavy metals and identify natural and anthropogenic sources of these heavy metals at different spatial scales. Two hundred and twenty-four soil samples (0-20cm) were collected and analysed for eight heavy metals (Cd, Hg, As, Cu, Pb, Cr, Zn and Ni) in soils of different land-use types in the Yangtze River Delta of Eastern China. The multivariate methods and factorial Kriging analysis were used to achieve the research objectives. The results indicated that the human and natural effects of different land-use types on the contents of soil heavy metals were different. The Cd, Hg, Cu, Pb and Zn in soils of industrial area were affected by human activities, and the pollution level of these heavy metals in this area was moderate. The Pb in soils of traffic area was affected by human activities, and eight heavy metals in soils of residential area and farmland area were affected by natural factor. The ecological risk status of eight heavy metals in soils of the whole study area was light. The heavy metals in soils showed three spatial scales (nugget effect, short range and long range). At the nugget effect and short range scales, the Cd, Hg, Cu, Pb and Zn in soils were affected by human and natural factors. At three spatial scales, the As, Cr and Ni in soils were affected by soil parent materials.