NPGNonlinear Processes in GeophysicsNPGNonlin. Processes Geophys.1607-7946Copernicus PublicationsGöttingen, Germany10.5194/npg-23-331-2016Comparison of the multifractal characteristics of heavy metals in soils
within two areas of contrasting economic activities in ChinaLiXiaohuiLiXianglingYuanFengyf_hfut@163.comJowittSimon M.https://orcid.org/0000-0003-0989-7910ZhouTaofaYangKuiZhouJieHuXunyuLiYangSchool of Resources and Environmental Engineering, Hefei University of Technology, Hefei 230009, ChinaXinjiang Research Centre for Mineral Resources, Xinjiang Institute of Ecology and Geography,
Chinese Academy of Sciences, Urumqi, Xinjiang 830011, ChinaSchool of Earth, Atmosphere and Environment, Monash University,
Wellington Road, Clayton, VIC 3800, AustraliaDepartment of Geoscience, University of Nevada Las Vegas, 4505 S. Maryland Parkway, Las Vegas, NV 89154-4010, USAFeng Yuan (yf_hfut@163.com)6September201623533133926January201625February20162August20163August2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://npg.copernicus.org/articles/23/331/2016/npg-23-331-2016.htmlThe full text article is available as a PDF file from https://npg.copernicus.org/articles/23/331/2016/npg-23-331-2016.pdf
Industrial and agricultural activities can generate heavy metal pollution
that can cause a number of negative environmental and health impacts. This
means that evaluating heavy metal pollution and identifying the sources of
these pollutants, especially in urban or developed areas, is an important
first step in mitigating the effects of these contaminating but necessary
economic activities. Here, we present the results of a heavy metal (Cu, Pb,
Zn, Cd, As, and Hg) soil geochemical survey in Hefei city. We used a
multifractal spectral technique to identify and compare the multifractality
of heavy metal concentrations of soils within the industrial Daxing and
agricultural Yicheng areas. This paper uses three multifractal parameters
(Δα, Δf(α), and τ′′(1)) to indicate the
overall amount of multifractality within the soil geochemical data. The
results show all of the elements barring Hg have larger Δα,
Δf(α), and τ′′(1) values in the Daxing area compared to
the Yicheng area. The degree of multifractality suggests that the differing
economic activities in Daxing and Yicheng generate very different heavy metal
pollution loads. In addition, the industrial Daxing area contains significant
Pb and Cd soil contamination, whereas Hg is the main heavy metal present in
soils within the Yicheng area, indicating that differing clean-up procedures
and approaches to remediating these polluted areas are needed. The results
also indicate that multifractal modelling and the associated generation of
multifractal parameters can be a useful approach in the evaluation of heavy
metal pollution in soils.
Introduction and overview of the study area
Heavy metal
pollution within soil poses a serious risk for human health and the
environment, and thus soil pollution caused by anthropogenic activities
(including industry and agriculture) has been the focus of a significant
amount of research (e.g. Leyval et al., 1997; Thomas and Stefan, 2002;
McGrath et al., 2004; Wang et al., 2007; Luo et al., 2011). Analysing soil
geochemistry and pollution using multifractal techniques may allow for
assessing many of the problems of non-linear variability which commonly arise
when dealing with pollutants, as well as enabling the identification of
non-linear characteristics within data sets. This approach can yield new
information that can be used to understand the factors controlling the
distribution of key elements within the objects or data being studied
(Salvadori, 1997; Gonçalves, 2000; Zuo et al., 2012). This in turn means
that determining the multifractal characteristics of the distribution of
heavy metals in soils can improve our understanding of any heavy metal
pollution that is associated with these differing anthropogenic activities.
Multifractal techniques include singularity mapping and multifractal
interpolation that enable more detailed analysis of the spatial distribution
of heavy metals, concentration-area modelling that can be used to define
threshold values between background (i.e. geological) and anthropogenic
anomalies (Lima et al., 2003), spectral density-area modelling that can be
used to define thresholds to separate anomalies (i.e. anthropogenically
derived heavy metal concentrations in this case) from background
concentrations (i.e. geologically derived heavy metal concentrations; Cheng,
2001), and multifractal spectra that highlight non-linear characteristics
and identify anomalous behaviour that reflects the characteristics of some
multifractal sets (Gonçalves, 2000; Albanese et al., 2007; Guillén et
al., 2011), such as the presence of porous structures and spatial variations
in soil properties (Caniego et al., 2005; Dathe et al., 2006). This means
that multifractal techniques can be useful tools for the analysis of heavy
metal pollution within soils (e.g. Salvadori et al., 1997; Lima et
al., 2003; Albanese et al., 2007; Guillén et al., 2011). These
multifractal techniques are used not only in environmental science but also
in a number of differing fields, including geophysics (Schertzer et
al., 2011), medicine (Jennane et al., 2001), computer science (Wendt et
al., 2009), geology (Cheng, 1995; Deng et al., 2011; Yuan et al., 2012,
2015), and ecology (Pascual et al., 1995), among others.
Hefei is the capital of Anhui Province, China, and has an urban area that
includes the towns of Daxing and Yicheng, which focus on industrial and
agricultural activities, respectively. Here, we use multifractal spectra
techniques and three parameters (Δα, Δf(α), and τ′′(1)) to analyse and compare the degree and characteristics of the
multifractality of heavy metal contamination in soils associated with
anthropogenic activities in this region. The results will further enable and
inform future planning for any necessary remediation of the soils in the
Daxing and Yicheng areas.
Study area and geochemical dataStudy area
The city of Hefei is situated in central-eastern China (Fig. 1a), has
approximately 7.7 million inhabitants, and covers an area of around
11 408 km2. This paper focuses on the towns of Daxing and Yicheng
(Fig. 1b), with the former representing one of the traditional industrial
areas of Hefei and containing numerous factories that are involved in the
steel industry, chemical industry, paper making, and the production of
furniture and construction materials, among others. In contrast, the town of
Yicheng focuses its economic activities on agricultural production, byproduct
processing, livestock and poultry breeding, ornamentals, and other
enterprises related to agricultural activity.
Location of Hefei in central-eastern China (a); location of
the study areas within Hefei (b); the 1km×1km grids used for soil sampling in the towns of
Daxing (c) and Yicheng (d).
Sampling and analysis
The study areas are covered by Quaternary sedimentary soils and are free of
both natural mineralization and mining-related contamination. A total of
169 surface (< 20 cm depth) soil samples were taken from the towns of
Daxing and Yicheng on 1km×1km grids, yielding 78
samples from Daxing and 91 samples from Yicheng (Fig. 1c, d). Sampling errors
were minimized by splitting each sample into three to five sub-samples, each
of which weighed more than 500 g. Each of these sub-samples was
air-dried before being broken up using a wooden roller and then sieved to
pass through a 0.85 mm mesh. The concentrations of six heavy metal elements
(Cu, Pb, Zn, Cd, As, and Hg) were determined during this study, with Cd, Cu,
Pb, and Zn concentrations determined by inductively coupled plasma–mass
spectrometry (ICP–MS), whereas Hg and As concentrations were determined by
hydride generation–atomic fluorescence spectrometry (AFS; Armstrong et
al., 1999; Gómez-Ariza et al., 2000). These techniques have detection
limits of 1 ppm for Cu, 2 ppm for Pb and Zn, 30 ppb
for Cd, 0.5 ppm for As, and 5 ppb for Hg. The accuracy of
these data was monitored by repeat and replicate determinations using
instrumental neutron activation analysis (INAA), with analytical precision
monitored using variance of the results obtained from duplicate analyses.
Multifractal spectrum analysis
Multifractal formalisms can decompose self-similar measures into intertwined
fractal sets that are characterized by singularity strength and fractal
dimensions (Cheng, 1999). Using multifractal techniques allows non-linear
characteristics within data sets to be identified, enabling the extraction of
information that can be used to understand the factors controlling the
distribution of key elements within the data. Fractal spectra (f(α))
are formalisms that can be used to describe the multifractal characteristics
of a data set and can be estimated using box-counting, gliding-box, histogram, and
wavelet methods, among others (Cheng, 1999; Lopes and Betrouni, 2009). The
most widely used of these methods are the box-counting and gliding-box
methods, both of which are based on the moment method.
The calculation of the mass exponent function τ(q) for the gliding-box
method is different from the box-counting method, with the gliding-box method
providing a useful approach that can increase the number of samples that are
available for statistical estimation within a data set (Buczkowski et
al., 1998; Tarquis et al., 2006; Xie et al., 2010). This means that the
gliding-box approach often provides better results with lower uncertainties
than the box-counting method (Cheng, 1999). As such, we have used the
gliding-box approach during this study. The calculation of the mass exponent function
τ(q) for the gliding-box method uses a partition function as follows
(Cheng, 1999):
〈τ(q)〉+D=limε→0logμq(ε)log(ε)=limε→0log1N∗(ε)∑i=1N∗(ε)μiq(ε)log(ε),
where μi(ε) denotes a measure with the ith cell of a
gliding box of size ε, q is the order moment of this measure
(this paper used a range of q values from -10 to 10 with an interval of
1), <> indicates the statistical moment, and N∗(ε)
indicates the total number of gliding boxes of size ε with
μi(ε) values different from 0.
The values of τ(q) derived using this equation can be then used to
determine singularity α and fractal spectra f(α) values using a
Legendre transformation, as expressed below:
α(q)=dτ(q)dq,f(α)=qα(q)-τ(q)=qdτ(q)dq-τ(q).Δα and Δf are essential parameters required to analyse
the multifractal characteristics of a given data set. The widths of the left
(ΔαL) and right (ΔαR) branches
within the multifractal spectra are then defined using the following
equations:
ΔαL=α0-αmin,ΔαR=αmax-α0,Δα=αmax-αmin.
The height difference Δf(α) between the two ends of the
multifractal spectrum is then extracted using
Δf(α)=fαmax-fαmin.
Higher Δα and Δf(α) values are generally indicative
of data sets with more heterogeneous patterns (ordered, complex, clustered)
and higher levels of multifractality (Cheng, 1999; Kravchenko et al., 1999).
In addition, local multifractality τ′′(1), which may determined by
ordinary spatial analysis functions (autocorrelations and semivariograms),
can also be used as a measure to quantitatively characterize the
multifractality of a data set using Eq. (8) (Cheng, 2006):
τ′′(1)=τ(2)-2τ(1)+τ(0),Δf(α)=fαmax-fαmin.
If μ is a multifractal and -D<τ′′(1)<0, where D is the
gliding-box dimension, then more negative values of τ′′(1) are
indicative of higher degrees of multifractality, whereas otherwise τ′′(1)=0 for monofractal.
Geochemical analysis results
A statistical summary of the soil geochemical data for the study area is
given in Table 1. Samples from the Daxing area have higher Cu, Pb, Zn, Cd, and
As maximum, mean, standard deviation, skewness, and kurtosis values than soil
samples from the Yicheng area, whereas the Yicheng area has a higher maximum
Hg concentration value than the Daxing area. In addition, the soil samples
from Daxing have much higher coefficient of variation (CV) values for Cu, Pb,
Zn, Cd, and As than the samples from the Yicheng area, indicating that soils
in the Daxing area contain higher and more variable concentrations of these
elements. This also suggests that samples from the Daxing area containing
elevated concentrations of heavy metals were probably contaminated by
anthropogenic activity.
All of the elements (barring Pb and Cu in the Yicheng area) in both the
Yicheng and Daxing areas yielded concentration histograms that are
positively skewed and contain some outliers (Fig. 2), indicating that these
data have non-normal and potentially fractal- or multifractal-type
distributions. This means that multifractal techniques are highly suited for
the characterization of the geochemistry of the soils.
Summary statistics of soil heavy metal concentrations within samples
from the Daxing and Yicheng areas.
Histograms showing the distribution of Cu (a),
Pb (b), Zn (c), Cd (d), As (e), and
Hg (f) concentrations within soils from the towns of Daxing and
Yicheng.
Calculation processes of multifractal spectrum and discussion
The multifractal spectra (in the form of an α–f(α) diagram) for
the geochemical data are shown in Fig. 3.
These multifractal spectra have inverse bell shapes (Fig. 3) and are
asymmetric (i.e. ΔαL values significantly differ from
ΔαR, Eqs. 5–6), with the exception of the Cu data for
soils from the Yicheng area, indicating that the samples containing low and
high concentrations of these elements are not evenly distributed within the
study area (as is expected for areas containing point source pollutants like
factories or animal breeding facilities).
Multifractal spectra (f(α) vs. α) of the soil
geochemical data from the Daxing and Yicheng areas.
The multifractal results given in Table 2 indicate that all of the elements
(barring Cu and Pb in the Yicheng area) are characterized by a wide range of
α values, with τ′′(1) values less than -0.01 and Δf(α) values larger than 0.5, all of which indicate that these elements
have a high multifractality within the soils in these two areas. All of the
elements analysed during this study (barring Hg) have higher Δf(α) and α values (except Zn) and lower τ′′(1) values in
soils from the Daxing area, with Hg having higher Δf(α) and
Δα and lower τ′′(1) values in soils from the Yicheng area
(Table 2). This suggests that the industrial activities in the Daxing area
generate multi-element heavy metal soil contamination, whereas the most
significant heavy metal pollution associated with the agricultural activity
in the Yicheng area is Hg contamination. The Δf(α) and
Δα values of Hg in the Yicheng area are larger than the values
for all other elements in this area as well as some of the elements in the
Daxing area, indicating both the prevalence and significant degree of
agricultural Hg contamination in the Yicheng area, even considering the lower
overall concentrations of Hg within the Yicheng area compared to the Daxing
area. This contamination should be considered a priority in terms of
remediation, because the interaction between the agricultural activity in the
Yicheng area and this Hg pollution could seriously impact human health, as Hg
is preferentially concentrated upward in the food chain (e.g. Jiang et
al., 2006). This means that, although contamination in both areas needs to be
evaluated further and should be remediated to avoid any deleterious effects,
the fact that the Hg contamination in the Yicheng area may be more
bioavailable and may have a larger effect on the population of this region
(as a result of the agricultural activity in this area) means it should be
considered a priority.
In order to compare variations in multifractality, the elements within the
samples from the Daxing and Yicheng areas were sorted by Δα, Δf(α), and τ′′(1) parameters, in addition to sorting
by coefficient of variation values (Table 3). The data shown in Table 3
indicate that the Pb data within the Daxing area have close to the lowest
coefficient of variation, but the largest Δf(α) and τ′′(1)
values for these Pb data are indicative of strongest multifractality compared
to the other heavy metals in the soils within the Daxing area. In comparison,
the As data for soils in the Daxing area yielded the largest coefficient of
variation but moderate Δf(α) and τ′′(1) values,
indicating these As data only have moderate multifractality. These
differences indicate that the multifractal parameters reveal new information
about the non-linear variability and the characteristics of these geochemical
data compared to the basic statistics for these samples. In addition, the
data given in Table 3 indicate that these elements have different orders
depending on whether they are sorted by Δα, Δf(α), or
τ′′(1) values, all of which reflects differing aspects of the
multifractality of these data. Here we consider that Δα, Δf(α), and τ′′(1) have equal weightings that reflect the overall
multifractality of the data from the study area. As such, the ordering of
these elements by Δα, Δf(α), or τ′′(1)
involved the summation of these values, with the summed ordering then sorted
again to compare the overall multifractality of these data.
Multifractal parameters of the elements analysed during this study.
a CV: coefficient of variation.
b Overall: the overall order of Δα, Δf(α), and τ′′(1).
The overall amount of multifractality within the soil geochemical data for
the Daxing area decreases as follows:
Pb > Cd > As > Zn > Hg > Cu, whereas the overall amount
of multifractality within the soil geochemical data for the Yicheng area
decreases as follows: Hg > As > Zn > Cd > Pb > Cu. The
overall orders indicate that the Pb and Hg soil data have the highest degree
of multifractality in the Daxing and Yicheng areas, respectively, whereas Cu
has the weakest multifractality irrespective of the area.
Filled contour map generated by inverse distance-weighted
interpolation showing the spatial distribution of soil Pb concentrations in
the Daxing area (generated using the Inverse Distance Weighting spatial
analyst tool of the ArcGIS
software package).
We further analysed the spatial distribution of contamination within soils
from the Daxing and Yicheng areas and evaluated whether there is any
significant correlation between multifractality and anthropogenic activity.
Filled contour maps showing the distribution of Pb in the Daxing area and Hg
and Cu in the Yicheng area were calculated using inverse distance-weighted
interpolation (Figs. 4, 5, 6). These figures show that areas with elevated
levels of Pb contamination within the Daxing area are correlated with the
location of industrial factories, although interestingly the areas in the
upper and lower left-hand side of Fig. 4 contain factories but not elevated
concentrations of Pb. This indicates that the Pb concentrations in these
soils may be dependent on both the presence and type of industry in this
area, with some industries polluting more than others, either as a direct
result of the differing industries present in this area or as a result of
differing approaches to lessening environmental impacts. In comparison, the
Hg contamination in the Yicheng area is definitely spatially correlated with
the location of agricultural breeding facilities. Although the mean
concentrations of Hg in soils are greater in the Daxing area, all of the
multifractal parameters determined during this study (Δα, Δf(α), and τ′′(1)) indicate that the Hg data in the Daxing area
have a lower multifractality than the Hg data in the Yicheng area. The
Yicheng area is heavily agricultural, meaning that the agricultural
activities in this area may be both concentrating Hg and contaminating soils.
In addition, although the mean concentrations of Hg in the Yicheng area are
lower than in the soils in the Daxing area, the former has a higher maximum
concentration than the latter, and both areas have significant Hg
contamination. Indeed, the contamination in the Yicheng area may be of more
concern than the contamination in the Daxing area, as the agricultural
activity in the Yicheng area may lead to greater human intake of Hg than from
the soils in the mainly industrial Daxing area, a factor that could lead to
serious health issues (e.g. Minamata disease) caused by the potential
concentration of Hg up the food chain. This indicates that soils in both
areas may well require control and remediation.
Filled contour map generated by inverse distance-weighted interpolation
showing the spatial distribution of soil Hg concentrations in
the Yicheng area (generated using the Inverse Distance Weighting
spatial analyst tool of the ArcGIS software package).
Filled contour map generated by inverse distance-weighted interpolation
showing the spatial distribution of soil Cu concentrations and
the location of breeding facilities in the Yicheng area (generated using
the Inverse Distance Weighting spatial analyst tool
of the ArcGIS software package).
Density map of breeding facilities in the Yicheng area (generated using
the Kernel Density spatial analyst tool of the ArcGIS software
package).
This distribution of soils with elevated concentrations of Hg also contrasts
with the symmetrical distribution and weakest multifractality for Cu within
the Yicheng area (Figs. 3, 5, 6). Here, we generated a correlation matrix
that compares the relationship between the spatial density of breeding locations in the Yicheng area
(Fig. 7) and filled contour maps showing the distribution of Hg (Fig. 5) and
Cu (Fig. 6) in this region to identify whether there are any spatial
correlations between the location of agricultural facilities and areas
containing soils with elevated heavy metal concentrations (Table 4). The
correlation matrix shows a significant correlation between agricultural
facilities and high concentrations of Hg (coefficient of
correlation = 0.434), whereas the location of these agricultural breeding
facilities and areas of high Cu concentrations either have no relationship or
are negatively correlated (coefficient of correlation =-0.064). This
indicates that very little Cu has been anthropogenically added to (or removed
from) the soils in the Yicheng area, suggesting that these soils may contain
only natural background concentrations of Cu and that the breeding facilities
in this area do not produce significant Cu contamination. The negative
correlation coefficient, symmetrical distribution, and weakest
multifractality of Cu give one clue as to the spatial relationship between Cu
contamination and the river in the right-hand side of Fig. 6. This may
suggest a non-anthropogenic source (e.g. flooding causing the deposition of
Cu or some other relationship between water and Cu contamination) for some of
the slightly elevated Cu concentrations in this region. In addition, the fact
that some breeding facilities are not associated with significant Hg
contamination (Fig. 5) suggests again that, although there is a relationship
between the presence of these facilities and contamination, it may be that
the Hg contamination in this area reflects differing types of breeding
facilities or differing approaches to lessening environmental impacts.
Correlation matrix comparing the breeding facility density map and
the filled contour maps for Hg and Cu data for the Yicheng area (calculated
using the Band Collection Statistics spatial analyst tool of the
ArcGIS software package).
Layer 1: density map of breeding factories of Yicheng area (Fig. 7).Layer 2: filled contour map of Hg concentrations of Yicheng area (Fig. 5).Layer 3: filled contour map of Cu concentrations of Yicheng area (Fig. 6).
These results indicate that multifractal modelling and the associated
generation of multifractal parameters are a useful approach in the
evaluation of heavy metal pollution in soils and the identification of major
element of heavy metal contamination. In addition, the differing orders of
the multifractality of the geochemical data for soils within the Daxing area
and Yicheng area are indicative of a significant difference in the
geochemical characteristics (and heavy metal pollution) in the soils within
these two areas. This indicates that differing treatment strategy and
clean-up approaches to remediating these two polluted areas are needed,
rather than a single cover-all strategy and approach to the remediation of
heavy metal pollution. A significant number of different remediation
approaches can be used to resolve the issues of heavy metal soil
contamination (e.g. Bech et al., 2014; Koptsik, 2014). Although somewhat
beyond the scope of this study, the multi-element nature of the
contamination in the Daxing area means that physical and chemical approaches
to remediation (i.e. soil removal, soil vitrification, soil consolidation,
electroremediation, or soil washing) are probably well suited for the
remediation of heavy-metal-contaminated soil in this region (especially Pb).
In comparison, the differing (i.e. Hg-dominated) type of soil contamination
in the Yicheng area could be more efficiently treated using microremediation
and phytoremediation, primarily as the agriculture in this area requires a
rapid reduction in the mobility and biological availability of heavy metals
in the soils (Mulligan et al., 2001; Wang and Greger, 2006). In addition,
the source of the Hg contamination (e.g. fertilizer, fodder, pesticides,
water) remains unclear. Identifying this source is also beyond the scope of
this paper although it is also clearly an area for future research, as the
identification of the source or sources of this contamination may prevent
the future heavy metal pollution of soils in this region.
Conclusions
Multifractal modelling and the resulting multifractal parameters
in this paper indicate that the soils from the Daxing area have stronger
multifractality for Cu, Pb, Zn, Cd, and As than soils from the Yicheng area,
although the latter have relatively strong multifractality for Hg. The
ordering of values for the multifractal parameters Δα, Δf(α), and τ′′(1) indicates that the degree of multifractality for the
geochemical data for soils within the Daxing area descends as follows:
Pb > Cd > As > Zn > Hg > Cu; within the Yicheng
area it descends as follows: Hg > As > Zn > Cd > Pb > Cu. In
addition, Cu concentrations in soils in the Yicheng area may still have their
original (i.e. natural) distribution and may not have been influenced by
human activities. These data indicate that the industrial activity
concentrated in the Daxing area generates multi-element heavy metal soil
contamination, whereas the agricultural activity concentrated in the Yicheng
area generates Hg-dominated heavy metal soil contamination. The latter is
important, as Hg contamination can cause serious health issues (e.g. Minamata
disease), and the soils in this area may require remediation, especially as Hg
can be concentrated up the food chain and the Yicheng area is heavily
agricultural, indicating that this activity may both be concentrating Hg and
contaminating soils in this area.
The results presented here indicate that multifractal modelling can be a
useful approach in the evaluation of heavy metal pollution in soils and the
identification of problematic heavy metals that need remediation in the
research area.
Data availability
The raw data used in this paper are not publicly accessible.
Acknowledgements
This research was financially supported by funds from the Chinese Academy of
Science “Light of West China” Program, the Fundamental Research Funds for
the Central Universities, and the Program for New Century Excellent
Talents in University (grant no. NCET-10-0324).
Edited by: J. M. Miras Avalos
Reviewed by: J. Miranda and two anonymous referees
References
Albanese, S., De Vivo, B., Lima, A., and Cicchella, D.: Geochemical
background and baseline values of toxic elements in stream sediments of
Campania region (Italy), J. Geochem. Explor., 93, 21–34, 2007.
Armstrong, H. E. L., Corns, W. T., Stockwell, P. B., O'Connor, G., Ebdon, L.,
and Evans, E. H.: Comparison of afs and icp-ms detection coupled with gas
chromatography for the determination of methylmercury in marine samples,
Anal. Chim. Acta, 390, 245–253, 1999.
Bech, J., Korobova, E., Abreu, M., Bini, C., Chon, H. T., and
Pérez-Sirvent, C.: Soil pollution and reclamation, J. Geochem. Explor.,
147, 77–79, 2014.
Buczkowski, S., Hildgen, P., and Cartilier, L.: Measurements of fractal
dimension by box-counting: a critical analysis of data scatter, Physica A,
252, 23–34, 1998.
Caniego, F. J., Espejo, R., Martın, M. A., and José, F. S.:
Multifractal scaling of soil spatial variability, Ecol. Model., 182,
291–303, 2005.
Cheng, Q.: The perimeter-area fractal model and its application to geology,
Math. Geol., 27, 69–82, 1995.
Cheng, Q.: The gliding box method for multifractal modeling, Comput. Geosci.,
25, 1073–1079, 1999.
Cheng, Q.: Selection of Multifractal Scaling Breaks and Separation of
Geochemical and Geophysical Anomaly, Journal of China University of
Geosciences, 1, 54–59, 2001.
Cheng, Q.: Multifractal modelling and spectrum analysis: Methods and
applications to gamma ray spectrometer data from southwestern Nova Scotia,
Canada, Sci. China. Ser. D, 49, 283–294, 2006.
Dathe, A., Tarquis, A. M., and Perrier, E.: Multifractal analysis of the
pore- and solid-phases in binary two-dimensional images of natural porous
structures, Geoderma, 134, 318–326, 2006.
Deng, J., Wang, Q., Wan, L., Liu, H., Yang, L., and Zhang, J.: A
multifractal analysis of mineralization characteristics of the Dayingezhuang
disseminated-veinlet gold deposit in the Jiaodong gold province of China,
Ore Geol. Rev., 40, 54–64, 2011.
Gómez-Ariza, J. L, Sánchez-Rodas, D., Giráldez, I., and Morales,
E.: A comparison between ICP-MS and AFS detection for arsenic speciation in
environmental samples, Talanta, 51, 257-268, 2000.
Gonçalves, M. A.: Characterization of Geochemical Distributions Using
Multifractal Models, Math. Geol., 33, 41-61, 2000.
Guillén, M. T., Delgado, J., Albanese, S., Nieto, J. M., Lima, A., and
De Vivo, B.: Environmental geochemical mapping of Huelva municipality soils
(SW Spain) as a tool to determine background and baseline values, J.
Geochem. Explor., 109, 59-69, 2011.
Jennane, R., Ohley, W. J., Majumdar, S., and Lemineur, G.: Fractal analysis
of bone X-ray tomographic microscopy projections, IEEE T. Med. Imaging, 20,
443–449, 2001.
Jiang, G. B., Shi, J. B., and Feng, X. B.: Mercury Pollution in China,
Environ. Sci. Technol., 40, 3672–3678, 2006.Koptsik, G. N.: Modern approaches to remediation of heavy metal polluted
soils: A review, Eurasian Soil. Sci.+, 47, 707–722, 2014.
Kravchenko, A., Boast, C., and Bullock, D.: Multifractal analysis of soil
spatial variability, Agron. J., 91, 1033–1041, 1999.
Leyval, C., Turnau, K., and Haselwandter, K.: Effect of heavy metal pollution
on mycorrhizal colonization and function: physiological, ecological and
applied aspects, Mycorrhiza, 7, 139–153, 1997.
Lima, A., De Vivo, B., Cicchella, D., Cortini, M., and Albanese, S.:
Multifractal IDW interpolation and fractal filtering method in environmental
studies: an application on regional stream sediments of (Italy), Campania
region, Appl. Geochem., 18, 1853–1865, 2003.
Lopes, R. and Betrouni, N.: Fractal and multifractal analysis: A review, Med.
Image Anal., 13, 634–649, 2009.
Luo, C., Liu, C., Yan, W., Xiang, L., Li, F., Gan, Z., and Li, X.: Heavy
metal contamination in soils and vegetables near an e-waste processing site,
South China, J. Hazard. Mater., 186, 481–490, 2011.
McGrath, D., Zhang, C., and Carton, O. T.: Geostatistical analyses and hazard
assessment on soil lead in Silvermines area, Ireland, Environ. Pollut., 127,
239–248, 2004.
Mulligan, C., Yong, R., and Gibbs, B. F.: Remediation technologies for
metal-contaminated soils and groundwater: an evaluation, Eng. Geol., 60,
193–207, 2001.
Pascual, M., Ascioti, F., and Caswell, H.: Intermittency in the plankton: a
multifractal analysis of zooplankton biomass variability, J. Plankton Res.,
17, 167–168, 1995.
Salvadori, G., Ratti, S. P., and Belli, G.: Fractal and multifractal approach
to environmental pollution, Environ. Sci. Pollut. R., 4, 91–98, 1997.
Schertzer, D., Lovejoy, S., Schmitt, F., Chigirinskaya, Y., and Marsan, D.:
Multifractal Cascade Dynamics and Turbulent Intermittency, Fractals, 5,
427–471, 2011.
Tarquis, A. M., Mcinnes, K. J., Key, J. R., Saa, A., García, M. R., and
Díaz, M. C.: Multiscaling analysis in a structured clay soil using 2D
images, J. Hydrol., 322, 236–246, 2006.
Thomas, K. and Stefan, S.: Estimate of heavy metal contamination in soils
after a mining accident using reflectance spectroscopy, Environ. Sci.
Technol., 36, 2742–2747, 2002.Wang, Y. and Greger, M.: Use of iodide to enhance the phytoextraction of
mercury-contaminated soil, Sci. Total. Environ., 368, 30–39, 2006.
Wang, Y. P., Shi, J. Y., Wang, H., Lin, Q., Chen, X. C., and Chen, Y. X.: The
influence of soil heavy metals pollution on soil microbial biomass, enzyme
activity, and community composition near a copper smelter, Ecotox. Environ.
Safe., 67, 75–81, 2007.
Wendt, H., Roux, S. G., Jaffard, S., and Abry, P.: Wavelet leaders and
bootstrap for multifractal analysis of images, Signal Process., 89,
1100–1114, 2009.
Xie, S., Cheng, Q., Xing, X., Bao, Z., and Chen, Z.: Geochemical multifractal
distribution patterns in sediments from ordered streams, Geoderma, 160,
36–46, 2010.
Yuan, F., Li, X., Jowitt, S. M., Zhang, M., Jia, C., Bai, X., and Zhou, T.:
Anomaly identification in soil geochemistry using multifractal interpolation:
A case study using the distribution of Cu and Au in soils from the Tongling
mining district, Yangtze metallogenic belt, Anhui province, China,
J. Geochem. Explor., 116–117, 28–39, 2012.
Yuan, F., Li, X., Zhou, T., Deng, Y., Zhang, D., Xu, C., Zhang, R., Jia, C.,
and Jowitt, S. M.: Multifractal modelling-based mapping and identification of
geochemical anomalies associated with Cu and Au mineralisation in the NW
Junggar area of northern Xinjiang Province, China, J. Geochem. Explor., 154,
252–264, 2015.
Zuo, R., Carranza, E. J. M., and Cheng, Q.: Fractal/multifractal modelling of
geochemical exploration data, J. Geochem. Explor., 122, 1–3, 2012.