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A comparative study of two modes for mapping felsic intrusions using geoinformatics
Accepted Manuscript A comparative study of two modes for mapping felsic intrusions using geoinformatics Yihui Xiong, Renguang Zuo PII:
S0883-2927(16)30057-9
DOI:
10.1016/j.apgeochem.2016.04.004
Reference:
AG 3641
To appear in:
Applied Geochemistry
Received Date: 23 October 2015 Revised Date:
13 April 2016
Accepted Date: 16 April 2016
Please cite this article as: Xiong, Y., Zuo, R., A comparative study of two modes for mapping felsic intrusions using geoinformatics, Applied Geochemistry (2016), doi: 10.1016/j.apgeochem.2016.04.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
A comparative study of two modes for mapping felsic intrusions using
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geoinformatics
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Yihui Xiong, Renguang Zuo*
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State Key Laboratory of Geological Processes and Mineral Resources, China University of
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Geosciences, Wuhan 430074, China
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*E-mail: [email protected] (R.Zuo)
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Abstract
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Identifying felsic intrusions is an essential task in support of mineral exploration because
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the intrusions can be a source of energy and metals for magmatic-hydrothermal mineralization.
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In this paper, two models for mapping felsic intrusions are compared based on regional
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geochemical and geophysical data. Geochemical data as a type of compositional data which
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carry relative information should be preprocessed using log-ratio transformation. The first
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model, a factor ratio (F2/F1) model, was developed based on the chemical characteristics of the
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felsic intrusions, which are rich in K2O and high field strength elements (F2), but poor in Fe2O3
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and compatible elements (F1). The second model, a hybrid model that combines principal
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component analysis and local singularity analysis, was based on the chemical and physical
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properties of the felsic intrusions. The results showed that (1) raw geochemical data should be
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processed using log-ratio transformation prior to multivariate data analysis to avoid spurious
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correlations between variables, and (2) the hybrid model performed better than the ratio of
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factors model for inferring felsic intrusions in the study area. The felsic intrusions mapped in
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this study provide information that can support further mineral exploration in the Dong
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Ujimqin Fe–Cu polymetallic district, Inner Mongolia, northern China.
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Keywords: Compositional data; Factor ratio; Felsic intrusions; Singularity; Geoinformatics
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1. Introduction Geochemical data are typically compositional data which contain relative information
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(Aitchison, 1986; Aitchison et al., 2000; Egozcue et al., 2003; Buccianti and
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Pawlowsky-Glahn, 2005; Filzmoser and Hron, 2008; Filzmoser et al., 2009a, 2009b, 2010).
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Consequently, such property of compositional data may result in spurious correlations
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between geochemical variables and complicate the interpretation of different correlations
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between the same variable among different sub-compositions (Carranza, 2011; Filzmoser and
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Hron, 2008; Filzmoser et al., 2009a; Zuo et al., 2013; Zuo, 2014). Traditional multivariate
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statistical methods, such as principal component analysis (PCA) and factor analysis (FA),
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which are designed in Euclidean space, may not be appropriate for analysis of compositional
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data that lie in simplex space (Aitchison, 1986).
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Felsic intrusions play a significant role in the formation of magmatic-hydrothermal
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mineralization because they could be a source of energy and metals for the mineralization.
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Therefore, mapping of felsic intrusions is critical for mapping prospectivty for
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magmatic-hydrothermal related mineralization, especially in the covered areas (Cheng et al.,
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2011; Wang et al., 2011, 2012, 2014; Zuo et al., 2015b). Granitic intrusions in the western part
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of Yunnan Province (China) are characterized by high values of K2O, Th, U, La, Y, and Zr,
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and low values of Co, Ni, V, Cr, Ti, and Fe2O3 (Xiang et al., 2014). Based on these
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geochemical characteristics of granitic intrusions, Xiang et al. (2014) applied the ratio of
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factors obtained by FA analysis on regional stream sediments geochemical data for mapping
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of granitic intrusions. In addition, a hybrid geoinformatics approach, which combines local
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singularity analysis (LSA) and PCA, has been used to map felsic intrusions based on the
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significant differences of chemical and physical properties among magmatic, metamorphic,
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ACCEPTED MANUSCRIPT and sedimentary rocks. In such a hybrid method, LSA is applied to highlight geochemical and
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geophysical information, and PCA is utilized to integrate this information (Cheng, 2012;
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Cheng et al., 2011; Wang et al., 2011; Zhao et al., 2012; Zuo et al., 2015a; Wang and Zuo,
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2015; Zuo and Wang, 2016).
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The main purposes of this study are (1) to explore the problem of working with
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compositional data in the mapping of felsic intrusions and (2) to compare the two models and
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produce a map using geoinformatics showing the distribution of the inferred felsic intrusions.
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2. Methods
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2.1. Log-ratio transformation
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Standard statistical methods may lead to misleading results if they are directly applied to
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raw geochemical data. Therefore, appropriate data transformation is recommended prior to
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data analysis (Filzmoser et al., 2009a, 2009b, 2010). The additive log-ratio (alr) (Aitchison,
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1986), the centered log-ratio (clr) (Aitchison, 1986), and the isometric log-ratio (ilr) (Egozcue
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et al., 2003) transformations are three main approaches to deal with compositions. The alr
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transformation divides the data values by a reference variable and different selected reference
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variables may lead to different results. Therefore, alr is rather subjective (Aitchison, 1986).
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The clr transformation (Aitchison, 1986) can be written as
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y = (y1 ,..., y D ) T = (log
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x1 D
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where,
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represents the geometric mean of the given compositional dataset (x1, x2,
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x3,…, xD). The original variable names can be used for the interpretation of statistical results
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based on clr transformation (Aitchison and Greencare, 2002). However, the clr transformation Submitted to Applied Geochemistry 4
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multivariate statistical methods (Filzmoser et al., 2009a). This problem can be overcome by
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the ilr transformation which preserves all the advantageous properties of clr transformation
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(Egozcue et al., 2003). For a composition x, the ilr transformation can be expressed as
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follows:
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xj ∏ i j=1 zi = log for i=1,…, D-1, i +1 x i +1 i
(2)
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The ilr is an isometry transformation, and thus it seems to be the best choice for performing
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statistical analysis of compositions (Reimann et al., 2012). However, the ilr transformation
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leads to losting the correspondence between original variables and the ilr-transformed
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variables. Therefore, the resulting ilr-transformed variables are difficult to interpret (Egozcue
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and Pawlowsky-Glahn, 2005). The ilr results (e.g., loadings and scores of PCA) are usually
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transformed back into the clr space (Reimann et al., 2008; Filzmoser et al., 2009a). In this
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study, the clr transformation was used to process the geochemical data.
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2.2. Mapping of felsic intrusions
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Chinese granitic intrusions are characterized by high concentrations of K2O and high
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field-strength elements, such as Ta, Zr, Hf, P and Th, and with low concentrations of Fe2O3
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and compatible elements, such as Cr, Ni, Co and V (Shi et al., 2005; Xiang et al., 2014). There
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are two methods available used for mapping felsic intrusions. The first method refers to the
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ratio of F2/F1, which is produced based on regional stream sediment geochemical data and
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can be written as (Xiang et al., 2014)
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F =
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F1 = 0.95 ⋅ Fe 2O 3 + 0.93 ⋅ V + 0.93 ⋅ Ti + 0.92 ⋅ Co + 0.81 ⋅ Cr + 0.8 ⋅ Ni , (4)
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F2 = 0.87 ⋅ Th + 0.86 ⋅ Y + 0.77 ⋅ U + 0.77 ⋅ Zr + 0.67 ⋅ La + 0.61 ⋅ K 2O + 0.58 ⋅ Al2O3 + 0.53 ⋅ Be , (5)
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Here, F1 represents the compatible element assemblage of Fe2O3, V, Co, Cr and Ni, and F2
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denotes the high field strength element assemblage of Th, Y, U, Zr and La.
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The second method is a hybrid approach that combines LSA and PCA based on regional
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geochemical data consisting of major oxides, such as SiO2, Na2O, K2O, Al2O3, MgO, Fe2O3,
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and CaO, and aeromagnetic and gravity data. A flowchart of the data processing is shown in
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Fig. 1.
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2.3. Local Singularity Analysis (LSA)
The LSA method proposed by Cheng (2007) in the context of multifractal theory is a
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quantitative method of describing the fractal nature of local structures. The core process of
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this method is to estimate a local singularity index for each location on a map. A power-law
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model is generally used to calculate the desired exponent within a local window, i.e.,
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µ(A) = cA 2 , (6)
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where µ(A) denotes the total amount of metal within a window of area A, c is a constant, and a
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represents the local singularity index, which can be estimated using the ratio of the
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logarithmic transformation of the measure µ and the area A as follows:
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α = log(µ1 µ 2 )/log( A1 A 2 ) , (7)
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where A1 and A2 represent areas of two different local windows centered at the same location,
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µ1 and µ2 are the corresponding amount of metal.
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behavior of the amount of metal varies as the size of the window decreases. Specifically, the
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singularity index is used as follows (Cheng, 2007):
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a ≈2 suggests a normal background;
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a < 2 suggests an enriched pattern; and
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a > 2 suggests a depleted pattern.
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Additionally, the local singularity index has been demonstrated as a useful tool for processing
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geoscience data and identifying the weak geo-information (e.g., Cheng, 1999; Cheng, 2007;
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Cheng, 2012; Cheng and Agterberg, 2009; Zuo and Cheng, 2008;
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2015a; Zuo and Wang, 2016).
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3. Study area and data
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Zuo et al., 2009, 2013,
The study area of this research, the Dong Ujimqin Fe–Cu polymetallic district, is located
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in Inner Mongolia, northern China. It has an area of approximately 32,200 km2 and is located
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between the latitudes of 45.3° N and 46.4° N, and between longitudes of 116.0° E and 119.0°
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E. This area has been mapped to consist of 40.2% Quaternary sediments (Q), 33.4% Tertiary
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sediments (N), 17.0% granites, and 9.4% other Formations (Fig. 2). The thickness of the
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Quaternary and Tertiary sediments, which are covered by grassland, ranges from 0.5 m to 3.0
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m and 42.0 m to 77.0 m, respectively, and the thickness of the other formations is greater than
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70.0 m, as indicated by the statistical results of drill holes in this area. The Chaobuleng
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deposit, one of the most famous Fe–Cu polymetallic deposits in this region, is a skarn-type
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deposit located in the northeastern part of this district. It developed in the contact zone
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between the mid-upper Devonian Daerbagete Formation and the Jurassic granites and is
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controlled by regional-scale N–E-oriented faults. The mineral assemblages associated with the
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Fe–Cu polymetallic mineralization have high concentrations of Fe, Cu, Mo, Ag, As, Pb, Zn,
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Bi, and Ti (GSIIM, 2010). The original stream sediment geochemical data used in this study were collected and
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analyzed during the Chinese National Geochemical Mapping (CNGM) Project, as part of the
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Regional Geochemistry National Reconnaissance (RGNR) Project. These data were sampled
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at a low density of 1 sample per 20–50 km2 in areas that were extremely difficult to access
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and at a higher density of 1 sample per 4 km2 in other areas. The data, comprised of 39 major
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and trace geochemical element values, were analyzed by X-ray fluorescence (XRF). Further
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details about the sampling and analysis processes used to acquire the stream sediment
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geochemical data can be found in Xie et al. (1997).
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4. Results and Discussion
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4.1 Compositional data analysis
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4.1.1 Factor ratio model
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Factor analysis was implemented based on raw and clr-transformed geochemical data,
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respectively. Twelve geochemical variables (i.e., Cr, Ni, Co, V, Ti, Fe2O3, Y, La, Zr, U, Th,
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and K2O) were selected based on the factor ratio model (Xiang et al., 2014). The FA results
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obtained based on the raw geochemical data are not sufficient because F1 is composed of
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positive loadings for all of the elements except K2O (Fig. 3a). In contrast, the results obtained
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based on the clr-transformed data exhibit two meaningful associations. The first represents
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compatible elements, which mainly consist of clr(Fe2O3), clr(Cr), clr(Ni), clr(Co), and clr(V).
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clr(Zr), and clr(Th) (Fig. 3b). Comparing Fig. 3a with Fig. 3b, it can be observed that FA
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based on the clr-transformed data can give a meaningful interpretation, indicating that prior to
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performing factor analysis of geochemical data, logratio transformations should be
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considered.
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4.1.2. Hybrid method
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Six major oxides of the geochemical data, including Na2O, K2O, Al2O3, MgO, Fe2O3,
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and CaO, were analyzed using the hybrid model. The PCA results based on the raw
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geochemical data show that PC1 is composed of positive loadings for all elements except K2O
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(Fig. 3c). Meanwhile, the resulting PC1, based on the clr-transformed geochemical data
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exhibit a meaningful association with a positive loading of clr(Al2O3), clr(K2O), and
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clr(Na2O), and a negative loading of clr(Fe2O3), clr(MgO), and clr(CaO), and could reflect
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the geochemical characteristics of felsic intrusions (Fig. 3d).
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4.2 Felsic intrusion mapping
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Based on the loadings of F1 and F2 (Fig. 3b), a new factor ratio for mapping felsic intrusions
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can be expressed as
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F=
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where F1 and F2 can be estimated by the following equations:
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F1 = 0.909 ⋅ clr(Ti) + 0.902 ⋅ clr(Fe2O3 ) + 0.837 ⋅ clr(V) + 0.753 ⋅ clr(Co) + 0.599 ⋅ clr(Ni) + 0.552 ⋅ clr(Cr) , (9)
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F2 = 0.695 ⋅ clr(La) + 0.68 ⋅ clr(Y) + 0.603 ⋅ clr(K 2O) + 0.536 ⋅ clr(Zr) , (10)
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The coefficients of F1 and F2 are rotation factor coefficients. It can be observed that the
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F2 , (8) F1
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factor ratio model could not accurately map the felsic intrusions in the study area (Fig. 4),
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which may be influenced by the covers.
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For the hybrid model, to integrate the geochemical and geophysical data for inferring
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felsic intrusions, the geochemical data were first transformed via clr transformation. The
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geochemical, magnetic, and gravity data were interpolated to generate raster maps at 1 km
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spatial resolution by the inverse distance weighting (IDW) method. Eight raster maps were
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processed by LSA, respectively, and then integrated by PCA using GeoDAS GIS software
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(Cheng, 2000).
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A scree plot (Fig. 5a) shows the relative importance of each component. It can be
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observed that PC2 is dominated by the negative loadings of Fe2O3, Al2O3, and gravity
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anomalies, and the positive loadings of CaO, Na2O, and aeromagnetic anomalies (Fig. 5b),
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which could reflect the felsic intrusions in the study area (Fig. 6). The student’s t involved in
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the weight of evidence (WofE) is a popular index to measure the statistical significance of
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spatial relationship between a point pattern and a polygon pattern (Agterberg et al., 1990;
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Bonham-Carter, 1994). Here, the student’s t was applied to assess the spatial relationship
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between the outcrops and inferring felsic intrusions. The outcrops of felsic intrusions were
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first converted into a set of points, which can be regarded as training points set. Here, a cell
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size of 4 km × 4 km is chosen to convert polygons into 342 points and as the training points
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for calculating the student’s t-values (Fig. 7). The student’s t-value reaches 1.96 at a class of
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10, and reaches a maximum value at a class of 13. These two values divide the results into
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three classes (Fig. 8). The high area occupies 17.6% of the total area and contains 20.6% of
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and contains 44.7% of the mapped units of the felsic intrusions. The results show that the
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spatial distribution of PC2 scores shows a strong spatial correlation with the mapped felsic
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intrusions in the study area and is a noticeable improvement for the recognition of possible
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felsic intrusions, especially in covered areas.
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5. Conclusions
In this study, two models for mapping felsic intrusions based on regional geochemical and
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geophysical data were compared. The clr-transformed geochemical data for constructing the
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factor ratio model were selected based on the geochemical characteristics of the felsic
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intrusions, which are characterized by high K2O and high field strength elements but low Fe2O3
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and compatible elements. The results demonstrated that the derived spatial distribution of the
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factor ratio is inappropriate for mapping felsic intrusions in the covered areas. The hybrid
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model exhibited better performance than the factor ratio model. These results suggest that
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geochemical data should be preprocessed via log-ratio transformation for mapping felsic
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intrusions, which can provide significant information for further mineral exploration.
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Acknowledgements The authors thank guest editor and anonymous reviewers for their valuable comments and Submitted to Applied Geochemistry 11
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suggestions. This research benefited from the joint financial support from the National
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Natural Science Foundation of China (No. 41522206), and the Program for New Century
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Excellent Talents in University (NCET-13-1016).
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Zuo, R., Wang J., Chen G., Yang M., 2015a. Identification of weak anomalies: A multifractal perspective. Journal of Geochemical Exploration 148, 12-24.
Zuo, R., Wang, J., 2016. Fractal/multifractal modeling of geochemical data: A review. Journal of Geochemical Exploration 164, 33-41.
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Zuo, R., Xia, Q., Zhang, D., 2013. A comparison study of the C–A and S–A models with
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singularity analysis to identify geochemical anomalies in covered areas. Applied
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Geochemistry 33, 165–172.
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Zuo, R., Zhang, Z., Zhang, D., Carranza, E.J.M., Wang, H., 2015b. Evaluation of uncertainty
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in mineral prospectivity mapping due to missing evidence: a case study with
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skarn-type Fe deposits in Southwestern Fujian Province, China. Ore Geology Reviews
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Fig. 1. Flowchart showing the hybrid model for granitic intrusion mapping.
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Fig. 2. Simplified geological map of the Dong Ujimqin district, Inner Mongolia (China)
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(compiled from GSIIM, 2010).
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Fig. 3. Biplots of the first and second factors for raw (a) and clr-transformed (b) geochemical
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data; Biplots of the first and second principal components for raw (c) and clr-transformed (d)
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geochemical data
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Fig. 4. Factor ratio map of the opened geochemical data.
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Fig. 5. (a) scree plot of eigenvalues of the principle components; and (b) loadings of the
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geochemical variables of PC2.
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Fig. 6. Map showing the spatial distribution of PC2 scores obtained based on clr-transformed
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geochemical data.
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Fig. 7. Plots of student’s t-values vs. classes of PC2 scores.
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Fig. 8. The spatial relationship between mapped felsic intrusions and outcrop intrusions.
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ACCEPTED MANUSCRIPT 1.The problem of working with relative (compositional) data in geochemistry is addressed. 2.Comparison of methods demonstrates that data need to be log-ratio transformed for the data analysis.
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DOI:
10.1016/j.apgeochem.2016.04.004
Reference:
AG 3641
To appear in:
Applied Geochemistry
Received Date: 23 October 2015 Revised Date:
13 April 2016
Accepted Date: 16 April 2016
Please cite this article as: Xiong, Y., Zuo, R., A comparative study of two modes for mapping felsic intrusions using geoinformatics, Applied Geochemistry (2016), doi: 10.1016/j.apgeochem.2016.04.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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A comparative study of two modes for mapping felsic intrusions using
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geoinformatics
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Yihui Xiong, Renguang Zuo*
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State Key Laboratory of Geological Processes and Mineral Resources, China University of
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Geosciences, Wuhan 430074, China
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*E-mail: [email protected] (R.Zuo)
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Abstract
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Identifying felsic intrusions is an essential task in support of mineral exploration because
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the intrusions can be a source of energy and metals for magmatic-hydrothermal mineralization.
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In this paper, two models for mapping felsic intrusions are compared based on regional
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geochemical and geophysical data. Geochemical data as a type of compositional data which
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carry relative information should be preprocessed using log-ratio transformation. The first
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model, a factor ratio (F2/F1) model, was developed based on the chemical characteristics of the
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felsic intrusions, which are rich in K2O and high field strength elements (F2), but poor in Fe2O3
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and compatible elements (F1). The second model, a hybrid model that combines principal
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component analysis and local singularity analysis, was based on the chemical and physical
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properties of the felsic intrusions. The results showed that (1) raw geochemical data should be
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processed using log-ratio transformation prior to multivariate data analysis to avoid spurious
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correlations between variables, and (2) the hybrid model performed better than the ratio of
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factors model for inferring felsic intrusions in the study area. The felsic intrusions mapped in
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this study provide information that can support further mineral exploration in the Dong
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Ujimqin Fe–Cu polymetallic district, Inner Mongolia, northern China.
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Keywords: Compositional data; Factor ratio; Felsic intrusions; Singularity; Geoinformatics
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1. Introduction Geochemical data are typically compositional data which contain relative information
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(Aitchison, 1986; Aitchison et al., 2000; Egozcue et al., 2003; Buccianti and
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Pawlowsky-Glahn, 2005; Filzmoser and Hron, 2008; Filzmoser et al., 2009a, 2009b, 2010).
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Consequently, such property of compositional data may result in spurious correlations
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between geochemical variables and complicate the interpretation of different correlations
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between the same variable among different sub-compositions (Carranza, 2011; Filzmoser and
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Hron, 2008; Filzmoser et al., 2009a; Zuo et al., 2013; Zuo, 2014). Traditional multivariate
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statistical methods, such as principal component analysis (PCA) and factor analysis (FA),
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which are designed in Euclidean space, may not be appropriate for analysis of compositional
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data that lie in simplex space (Aitchison, 1986).
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Felsic intrusions play a significant role in the formation of magmatic-hydrothermal
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mineralization because they could be a source of energy and metals for the mineralization.
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Therefore, mapping of felsic intrusions is critical for mapping prospectivty for
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magmatic-hydrothermal related mineralization, especially in the covered areas (Cheng et al.,
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2011; Wang et al., 2011, 2012, 2014; Zuo et al., 2015b). Granitic intrusions in the western part
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of Yunnan Province (China) are characterized by high values of K2O, Th, U, La, Y, and Zr,
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and low values of Co, Ni, V, Cr, Ti, and Fe2O3 (Xiang et al., 2014). Based on these
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geochemical characteristics of granitic intrusions, Xiang et al. (2014) applied the ratio of
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factors obtained by FA analysis on regional stream sediments geochemical data for mapping
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of granitic intrusions. In addition, a hybrid geoinformatics approach, which combines local
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singularity analysis (LSA) and PCA, has been used to map felsic intrusions based on the
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significant differences of chemical and physical properties among magmatic, metamorphic,
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ACCEPTED MANUSCRIPT and sedimentary rocks. In such a hybrid method, LSA is applied to highlight geochemical and
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geophysical information, and PCA is utilized to integrate this information (Cheng, 2012;
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Cheng et al., 2011; Wang et al., 2011; Zhao et al., 2012; Zuo et al., 2015a; Wang and Zuo,
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2015; Zuo and Wang, 2016).
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The main purposes of this study are (1) to explore the problem of working with
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compositional data in the mapping of felsic intrusions and (2) to compare the two models and
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produce a map using geoinformatics showing the distribution of the inferred felsic intrusions.
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2. Methods
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2.1. Log-ratio transformation
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Standard statistical methods may lead to misleading results if they are directly applied to
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raw geochemical data. Therefore, appropriate data transformation is recommended prior to
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data analysis (Filzmoser et al., 2009a, 2009b, 2010). The additive log-ratio (alr) (Aitchison,
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1986), the centered log-ratio (clr) (Aitchison, 1986), and the isometric log-ratio (ilr) (Egozcue
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et al., 2003) transformations are three main approaches to deal with compositions. The alr
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transformation divides the data values by a reference variable and different selected reference
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variables may lead to different results. Therefore, alr is rather subjective (Aitchison, 1986).
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The clr transformation (Aitchison, 1986) can be written as
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y = (y1 ,..., y D ) T = (log
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x1 D
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where,
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represents the geometric mean of the given compositional dataset (x1, x2,
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x3,…, xD). The original variable names can be used for the interpretation of statistical results
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based on clr transformation (Aitchison and Greencare, 2002). However, the clr transformation Submitted to Applied Geochemistry 4
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multivariate statistical methods (Filzmoser et al., 2009a). This problem can be overcome by
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the ilr transformation which preserves all the advantageous properties of clr transformation
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(Egozcue et al., 2003). For a composition x, the ilr transformation can be expressed as
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follows:
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The ilr is an isometry transformation, and thus it seems to be the best choice for performing
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statistical analysis of compositions (Reimann et al., 2012). However, the ilr transformation
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leads to losting the correspondence between original variables and the ilr-transformed
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variables. Therefore, the resulting ilr-transformed variables are difficult to interpret (Egozcue
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and Pawlowsky-Glahn, 2005). The ilr results (e.g., loadings and scores of PCA) are usually
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transformed back into the clr space (Reimann et al., 2008; Filzmoser et al., 2009a). In this
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study, the clr transformation was used to process the geochemical data.
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2.2. Mapping of felsic intrusions
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Chinese granitic intrusions are characterized by high concentrations of K2O and high
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field-strength elements, such as Ta, Zr, Hf, P and Th, and with low concentrations of Fe2O3
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and compatible elements, such as Cr, Ni, Co and V (Shi et al., 2005; Xiang et al., 2014). There
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are two methods available used for mapping felsic intrusions. The first method refers to the
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ratio of F2/F1, which is produced based on regional stream sediment geochemical data and
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can be written as (Xiang et al., 2014)
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F =
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F1 = 0.95 ⋅ Fe 2O 3 + 0.93 ⋅ V + 0.93 ⋅ Ti + 0.92 ⋅ Co + 0.81 ⋅ Cr + 0.8 ⋅ Ni , (4)
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F2 = 0.87 ⋅ Th + 0.86 ⋅ Y + 0.77 ⋅ U + 0.77 ⋅ Zr + 0.67 ⋅ La + 0.61 ⋅ K 2O + 0.58 ⋅ Al2O3 + 0.53 ⋅ Be , (5)
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Here, F1 represents the compatible element assemblage of Fe2O3, V, Co, Cr and Ni, and F2
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denotes the high field strength element assemblage of Th, Y, U, Zr and La.
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The second method is a hybrid approach that combines LSA and PCA based on regional
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geochemical data consisting of major oxides, such as SiO2, Na2O, K2O, Al2O3, MgO, Fe2O3,
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and CaO, and aeromagnetic and gravity data. A flowchart of the data processing is shown in
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Fig. 1.
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2.3. Local Singularity Analysis (LSA)
The LSA method proposed by Cheng (2007) in the context of multifractal theory is a
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quantitative method of describing the fractal nature of local structures. The core process of
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this method is to estimate a local singularity index for each location on a map. A power-law
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model is generally used to calculate the desired exponent within a local window, i.e.,
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µ(A) = cA 2 , (6)
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where µ(A) denotes the total amount of metal within a window of area A, c is a constant, and a
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represents the local singularity index, which can be estimated using the ratio of the
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logarithmic transformation of the measure µ and the area A as follows:
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α = log(µ1 µ 2 )/log( A1 A 2 ) , (7)
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where A1 and A2 represent areas of two different local windows centered at the same location,
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µ1 and µ2 are the corresponding amount of metal.
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behavior of the amount of metal varies as the size of the window decreases. Specifically, the
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singularity index is used as follows (Cheng, 2007):
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a ≈2 suggests a normal background;
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a < 2 suggests an enriched pattern; and
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a > 2 suggests a depleted pattern.
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Additionally, the local singularity index has been demonstrated as a useful tool for processing
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geoscience data and identifying the weak geo-information (e.g., Cheng, 1999; Cheng, 2007;
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Cheng, 2012; Cheng and Agterberg, 2009; Zuo and Cheng, 2008;
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2015a; Zuo and Wang, 2016).
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3. Study area and data
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Zuo et al., 2009, 2013,
The study area of this research, the Dong Ujimqin Fe–Cu polymetallic district, is located
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in Inner Mongolia, northern China. It has an area of approximately 32,200 km2 and is located
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between the latitudes of 45.3° N and 46.4° N, and between longitudes of 116.0° E and 119.0°
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E. This area has been mapped to consist of 40.2% Quaternary sediments (Q), 33.4% Tertiary
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sediments (N), 17.0% granites, and 9.4% other Formations (Fig. 2). The thickness of the
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Quaternary and Tertiary sediments, which are covered by grassland, ranges from 0.5 m to 3.0
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m and 42.0 m to 77.0 m, respectively, and the thickness of the other formations is greater than
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70.0 m, as indicated by the statistical results of drill holes in this area. The Chaobuleng
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deposit, one of the most famous Fe–Cu polymetallic deposits in this region, is a skarn-type
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deposit located in the northeastern part of this district. It developed in the contact zone
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between the mid-upper Devonian Daerbagete Formation and the Jurassic granites and is
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controlled by regional-scale N–E-oriented faults. The mineral assemblages associated with the
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Fe–Cu polymetallic mineralization have high concentrations of Fe, Cu, Mo, Ag, As, Pb, Zn,
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Bi, and Ti (GSIIM, 2010). The original stream sediment geochemical data used in this study were collected and
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analyzed during the Chinese National Geochemical Mapping (CNGM) Project, as part of the
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Regional Geochemistry National Reconnaissance (RGNR) Project. These data were sampled
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at a low density of 1 sample per 20–50 km2 in areas that were extremely difficult to access
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and at a higher density of 1 sample per 4 km2 in other areas. The data, comprised of 39 major
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and trace geochemical element values, were analyzed by X-ray fluorescence (XRF). Further
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details about the sampling and analysis processes used to acquire the stream sediment
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geochemical data can be found in Xie et al. (1997).
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4. Results and Discussion
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4.1 Compositional data analysis
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4.1.1 Factor ratio model
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Factor analysis was implemented based on raw and clr-transformed geochemical data,
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respectively. Twelve geochemical variables (i.e., Cr, Ni, Co, V, Ti, Fe2O3, Y, La, Zr, U, Th,
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and K2O) were selected based on the factor ratio model (Xiang et al., 2014). The FA results
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obtained based on the raw geochemical data are not sufficient because F1 is composed of
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positive loadings for all of the elements except K2O (Fig. 3a). In contrast, the results obtained
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based on the clr-transformed data exhibit two meaningful associations. The first represents
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compatible elements, which mainly consist of clr(Fe2O3), clr(Cr), clr(Ni), clr(Co), and clr(V).
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clr(Zr), and clr(Th) (Fig. 3b). Comparing Fig. 3a with Fig. 3b, it can be observed that FA
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based on the clr-transformed data can give a meaningful interpretation, indicating that prior to
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performing factor analysis of geochemical data, logratio transformations should be
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considered.
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4.1.2. Hybrid method
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Six major oxides of the geochemical data, including Na2O, K2O, Al2O3, MgO, Fe2O3,
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and CaO, were analyzed using the hybrid model. The PCA results based on the raw
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geochemical data show that PC1 is composed of positive loadings for all elements except K2O
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(Fig. 3c). Meanwhile, the resulting PC1, based on the clr-transformed geochemical data
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exhibit a meaningful association with a positive loading of clr(Al2O3), clr(K2O), and
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clr(Na2O), and a negative loading of clr(Fe2O3), clr(MgO), and clr(CaO), and could reflect
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the geochemical characteristics of felsic intrusions (Fig. 3d).
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4.2 Felsic intrusion mapping
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Based on the loadings of F1 and F2 (Fig. 3b), a new factor ratio for mapping felsic intrusions
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can be expressed as
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F=
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where F1 and F2 can be estimated by the following equations:
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F1 = 0.909 ⋅ clr(Ti) + 0.902 ⋅ clr(Fe2O3 ) + 0.837 ⋅ clr(V) + 0.753 ⋅ clr(Co) + 0.599 ⋅ clr(Ni) + 0.552 ⋅ clr(Cr) , (9)
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F2 = 0.695 ⋅ clr(La) + 0.68 ⋅ clr(Y) + 0.603 ⋅ clr(K 2O) + 0.536 ⋅ clr(Zr) , (10)
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The coefficients of F1 and F2 are rotation factor coefficients. It can be observed that the
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factor ratio model could not accurately map the felsic intrusions in the study area (Fig. 4),
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which may be influenced by the covers.
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For the hybrid model, to integrate the geochemical and geophysical data for inferring
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felsic intrusions, the geochemical data were first transformed via clr transformation. The
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geochemical, magnetic, and gravity data were interpolated to generate raster maps at 1 km
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spatial resolution by the inverse distance weighting (IDW) method. Eight raster maps were
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processed by LSA, respectively, and then integrated by PCA using GeoDAS GIS software
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(Cheng, 2000).
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A scree plot (Fig. 5a) shows the relative importance of each component. It can be
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observed that PC2 is dominated by the negative loadings of Fe2O3, Al2O3, and gravity
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anomalies, and the positive loadings of CaO, Na2O, and aeromagnetic anomalies (Fig. 5b),
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which could reflect the felsic intrusions in the study area (Fig. 6). The student’s t involved in
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the weight of evidence (WofE) is a popular index to measure the statistical significance of
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spatial relationship between a point pattern and a polygon pattern (Agterberg et al., 1990;
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Bonham-Carter, 1994). Here, the student’s t was applied to assess the spatial relationship
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between the outcrops and inferring felsic intrusions. The outcrops of felsic intrusions were
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first converted into a set of points, which can be regarded as training points set. Here, a cell
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size of 4 km × 4 km is chosen to convert polygons into 342 points and as the training points
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for calculating the student’s t-values (Fig. 7). The student’s t-value reaches 1.96 at a class of
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10, and reaches a maximum value at a class of 13. These two values divide the results into
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three classes (Fig. 8). The high area occupies 17.6% of the total area and contains 20.6% of
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and contains 44.7% of the mapped units of the felsic intrusions. The results show that the
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spatial distribution of PC2 scores shows a strong spatial correlation with the mapped felsic
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intrusions in the study area and is a noticeable improvement for the recognition of possible
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felsic intrusions, especially in covered areas.
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5. Conclusions
In this study, two models for mapping felsic intrusions based on regional geochemical and
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geophysical data were compared. The clr-transformed geochemical data for constructing the
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factor ratio model were selected based on the geochemical characteristics of the felsic
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intrusions, which are characterized by high K2O and high field strength elements but low Fe2O3
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and compatible elements. The results demonstrated that the derived spatial distribution of the
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factor ratio is inappropriate for mapping felsic intrusions in the covered areas. The hybrid
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model exhibited better performance than the factor ratio model. These results suggest that
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geochemical data should be preprocessed via log-ratio transformation for mapping felsic
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intrusions, which can provide significant information for further mineral exploration.
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Acknowledgements The authors thank guest editor and anonymous reviewers for their valuable comments and Submitted to Applied Geochemistry 11
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suggestions. This research benefited from the joint financial support from the National
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Natural Science Foundation of China (No. 41522206), and the Program for New Century
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Excellent Talents in University (NCET-13-1016).
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technique to identify local anomalies using stream sediment geochemical data, a case
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Fig. 1. Flowchart showing the hybrid model for granitic intrusion mapping.
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Fig. 2. Simplified geological map of the Dong Ujimqin district, Inner Mongolia (China)
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(compiled from GSIIM, 2010).
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Fig. 3. Biplots of the first and second factors for raw (a) and clr-transformed (b) geochemical
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data; Biplots of the first and second principal components for raw (c) and clr-transformed (d)
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geochemical data
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Fig. 4. Factor ratio map of the opened geochemical data.
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Fig. 5. (a) scree plot of eigenvalues of the principle components; and (b) loadings of the
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geochemical variables of PC2.
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Fig. 6. Map showing the spatial distribution of PC2 scores obtained based on clr-transformed
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geochemical data.
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Fig. 7. Plots of student’s t-values vs. classes of PC2 scores.
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Fig. 8. The spatial relationship between mapped felsic intrusions and outcrop intrusions.
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Fig.1
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ACCEPTED MANUSCRIPT 1.The problem of working with relative (compositional) data in geochemistry is addressed. 2.Comparison of methods demonstrates that data need to be log-ratio transformed for the data analysis.
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3. A hybrid model performs better than a ratio of factors model for mapping the occurrence of
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