1. Introduction

2. Geological Setting and Geochemical Data

2.1. Regional Geological Background

The western part of the Gangdese belt is located in the south-central part of the Tibet Autonomous Region. The tectonic structure belongs to the Gangdese-Nyainqentanglha landmass in the Gangdese-Himalayan tectonic area, which is between the Yarlung Zangbo River and the Bangong Lake-Nujiang Belt [22]. The basement is composed of the Nyainqentanglha group of presinian. On the crystalline basement of presinian, the Cambrian and low-middle Triassic strata are generally absent, since the Ordovician stratigra development more complete. The Ordovician-Permian strata are mainly distributed in the northern part of the study area, and the Upper Triassic-Jurassic strata are distributed in the northern part of the study area, while the Cretaceous-Neogene strata are distributed in the whole area. The magmatic rocks with large times, large exposing areas, wide distribution range, complicated causes and diverse types in the area are very developed. The intrusive rocks since the Triassic and the volcanic rocks since the Triassic have been extensively developed and mainly formed in Cretaceous-Paleogene, the latest volcanic magma activities to the Miocene. Pan, et al., [23] divided the tectonic unit of the Gangdese orogenic belt. By comparing the tectonic units, the study area is divided into four magmatic belts consisting of inetrmediate-acidic magmatic rocks including South Gangdese, Longgeer-Nyainqentanglha, Ze long and Ban-Bengcuo. The four magmatic belts is closely related to the distribution of the porphyry copper-molybdenum-gold deposits. The porphyry copper polymetallic deposits in the study area are mainly distributed in the volcanomagmatic arc of the South Gangdes including Zhunuo, Jiru, Xiongcun, Dongga etc, the uplift of Longgeer-Nanmulin arc-back belt containing Ria in Coqen and the Island arc belt of Coqen-Xainza consisting of Balazha, Gaerqiong ect. The detailed chronology and tectonic setting of the typical porphyry deposits mentioned above have been studied by many authors. It shows that the formation environment and metallogenic characteristics of the porphyry deposits in this area are formed in 3 tectonic settings-Island arcs, syn collisional and post collisional extensional environments and 4 metallogenic periods-Early Middle Jurassic, Late Cretaceous, Eocene and Miocen. The porphyry deposits in island arc such as Dongga and Xiongcun only distributed in the south of the southern margin of the Gangdese volcano magmatic arc zone. The porphyry deposits in syncollisional postcollisional extensional environment such as Zhunuo and Jiru are mainly distributed in the southern Gangdese volcanomagmatic arc. Secondly there are a few porphyry deposits such as Balazha and Gaerqiong distributed in the northern part of Cuoqin-Xainza Island arc, Bangor magmatic arc belt. All these insights greatly extend the prospecting of porphyry copper polymetallic ore in the western Gangdese.

Figure 1. regional geological map [24,25,26]

Figure 1. regional geological map [24,25,26]

3. Methods

4. Results and Discussion

4.1. The Question of ilr-RPCA-Back clr

The extraction of geochemical combined elements has attracted much attention in geochemical prospecting, and there are many related methods. At present, the methods of combination element identification are mainly PCA, RPCA, FA, RFA and so on. These methods require the use of logarithmic transformations or logarithmic ratio transformations (alr, clr, ilr, and so on) to eliminate or attenuate the effect of component data closure as much as possible, here on the widely used ilr-RPCA-back clr method is discussed.

Question 1: The influence of elemental interchange on the composition of geochemical elements?

The ilr transform method itself belongs to the asymmetric transformation, and the correspondence between the variables before and after the transformation is disrupted. In essence, because the order changes, the elements corresponding to the x_i+1 in the ilr formula change, so for the data of stream sediment, when the element positions are transformed, different element combinations can be obtained by the same method. Based on the experiments of the six elements related to the original data of porphyry copper deposit, the influence of the order change of different elements on ilr transformation is discussed. As shown in the figure, the Ag, Mo and W elements in Figure 2a represent the first principal component and are closely related and have good correlation, and the Ag, Mo and W elements in Figure 2b are poor representation and bad correlation, and the Ag-Mo-W and Au-Cu elements in Figure 2c represent respectively the first principal component negative load and position load, and the Ag, Mo and W elements in Figure 2d represent the first principal component and Ag, Mo have good correlation. It can be concluded that the application of this method to the determination of geochemical elements should be further studied.

Question 2: Score and load transform to clr space, whether the element correspondence has changed?

$$clr\left(Y\right)=\mathit{log}\frac{x_i}{\sqrt[D]{{\prod }_{i=1}^D{x}_i}}(i=\mathrm{1,2},3,\cdots ,D-1,D)$$

(5)

$$u_i=\sqrt{\frac{i}{i+1}}\left[\underset{\begin{array}{cc}i& elements\end{array}}{\underbrace{\frac{1}{i},\cdots ,\frac{1}{i}}},-\mathrm{1,0},\cdots ,0\right](i=\mathrm{1,2},3,\cdots ,D-1)$$

(6)

$$U={\left[u_1,u_2,\cdots ,u_{D-2},u_{D-1}\right]}^T(i=\mathrm{1,2},3,\cdots ,D-1)$$

(7)

$$ilr\left(X\right)=\sqrt{\frac{i}{i+1}}\mathit{ln}\left[\frac{\sqrt[i]{\prod _{j=1}^i{x}_j}}{x_{i+1}}\right](i=\mathrm{1,2},3,\cdots ,D-1)$$

(8)

$$clr\left(Y\right)=ilr\left(X\right)U$$

(9)

Figure 2. biplots of different elements in sequence.

Figure 2. biplots of different elements in sequence.

Based on the above problems, this paper analyzes the reason from the basic formula. Although the score and load can be projected into the clr space after the transformation between clr and ilr, the following problem can be seen according to the calculation steps of ilr-RPCA-back clr:

Step1: The original data matrix A(R × D), after the ILR transformation, finds that the last element has not been given the value of the ILR transform, so that the matrix B (R × (D-1)) of an element is reduced.

Step2: The RPCA transformation of data matrix B (R × (D-1)) after ilr can only obtain D-1 principal components, at this time the elements represented are only the first D-1 elements, the score is matrix C (R × (D-1)), and the load is matrix D ((D-1) × (D-1)).

Step3: U transformation of matrix C and D transform to CLR space, ·U score matrix (R×(D-1))·((D-1)×D)to get a new score matrix E (R·D), namely U^T·matrix(D×(D-1))·((D-1)×(D-1)) get the new matrix F(D×(D-1)), and set up a corresponding contact element.

We can see that the last element does not participate in the principal component analysis, and finally the result of transforming the load with the transformation formula does not actually have the information of the corresponding element. And the corresponding elements of the load after the transformation is not the original relationship between the elements, but a comprehensive relationship. Moreover, the relationship between clr and ilr is ·U instead of U^T·, so the correspondence between the elements in the new load matrix needs to be treated rationally. Since ilr is not a matrix, clr= ilr·U can not be converted to “clr = U^T·ilr”. So the final clr space inverse transformation, the only problem is the corresponding elements of the relationship.

This paper argues that the CLR, ILR and RPCA does not have any problems, but the combination of the three should be considered carefully for the identification of geochemical combined elements and types of deposits. For this issue, this paper does not propose a good solution, but would like to take this opportunity to throw out the question and hope that the mathematical geologists will study deeply and solve this problem.

4.2. Selection of Element Association Associated with Porphyry Copper Mineralization

Since stream sediment data belong to compositional data, it is not suitable to do relevant combinatorial analysis in the data without elimination of the closure effect.

Based on the original geochemical data, this paper is under the guidance of the study of geological laws, the establishment of geochemical markers and the exploration of geochemical models (supergene). According to the porphyry deposits in Gangdese metallogenic belt in part has been found for the geochemical elements combined statistical, that elements of porphyry copper deposit in combination with Cu, Mo, Au, Ag, W, Bi, which is convenient to distinguish with other types of ore deposits.

Table 2. Composite element statistics table.

Table 2. Composite element statistics table.

Deposits and Metallogenic Belts	Geochemical Anomaly Element Combination	Sampling Mode	References
Xiong Cun	`	regional geochemical anomalies	[36]
Xiong Cun	Cu, Au, Ag, Pb, Zn	soil anomaly	[37]
Ji Ru	Cu, Mo, W, Bi	regional geochemical anomalies	[36]
Zhu Nuo	Au, Cu, Mo, W	regional geochemical anomalies	[36]
Zhu Nuo	Cu, Mo, W, Au, Pb, Zn, Ag	stream sediment	[38]
Chong Jiang	Cu, Mo, Au, Ag, Pb, Zn, Hg, Sb	stream sediment	[38]
Chong Jiang	Cu, Mo, W, Bi, Pb, Ag	regional geochemical anomalies	[38]
Qu Long	Cu, Mo, W, Bi, Pb, Ag	stream sediment	[39]
Qu Long	Cu, Mo, W, Bi, Sn	regional geochemical anomalies	[5]
Jia Ma	Cu, Bi, Au, Ag, Pb, Zn	stream sediment	[40]
Jia Ma	Cu, Mo, Au, Ag, Bi, Sn	soil geochemistry	[40]
Gangdese polymetallic metallogenic belt	Cu, Mo, W, Au, Ag , Bi	geochemical anomaly	[41]
Gangdese polymetallic metallogenic belt	Cu-Mo, Au-Ag, Cu-Mo-Au, Cu-Au-Ag	combination geochemical anomaly	[41]
Gangdese porphyry copper deposit	Cu, Mo, Pb, Zn, Ag		[42]
Gangdese copper polymetallic metallogenic belt	Cu, Au, Ag, W, Mo, Bi	geochemical anomaly	[43]
Gangdese copper polymetallic metallogenic belt	Cu-Mo, Cu, Cu-Mo-Au, Cu-Au	geochemical anomaly	[43]
statistical results	Cu(21), Mo(16), Au(14), Ag(12), W(8), Bi(8), Pb(7), Zn(5), Hg(1), Sb(1), Sn(1)	final choice	Cu(21), Mo(16), Au(14), Ag(12), W(8), Bi(8)

4.3. Spatial Overlay Analysis of Geochemical Singularity Index α-Value of Porphyry Copper Deposit

Recent advances in the identification of weak geochemical anomalies refer to the singularity mapping technique proposed by Cheng [14], and it has been demonstrated as a powerful multifractal tool to identify the weak geochemical anomalies in complex geological settings or in overburden covered areas [18,20,21,44]. The window-based method was used to calculate the local singularity index based on GeoDAS. Considering that the formation of porphyry copper deposits in the western Gangdese metallogenic belt is closely related to the specific geochemical composition elements, only the local singularity analysis of single elements can not be used to meet the objective of recognizing the weak anomalies of porphyry copper deposits. Therefore, according to the geochemical composition elements of porphyry copper deposits, singularity analysis of each element has been carried out, and the local singular maps of porphyry copper deposits have been obtained by spatial overlay analysis. The spatial distribution map of α-A (Figure 3b) highlights the weak anomalies relative to α-Cu raster contour maps (Figure 3a). It is also shown that the spatial overlay singular values (α-A) are apparently enriched in the acid intrusive rocks and volcanic rocksand spread in the NW-trending according to the regional faults. The anomaly threshold values of α-A, α-Cu were obtained by method of C-A model. Furthermore, the log–log plots of the concentration (α) versus the number of samples with concentration values greater than or equal to α are constructed to examine whether or not the distribution of A and Cu follows a fractal. It can be observed that two straight lines can be fitted (Figure 4), suggesting they may satisfy a multifractal distribution.

Figure 3. (a) anomaly map of singular values of copper elements; (b) singular value anomaly map of porphyry copper deposit geochemical composition element.

Figure 3. (a) anomaly map of singular values of copper elements; (b) singular value anomaly map of porphyry copper deposit geochemical composition element.

Figure 4. (a) log-log plot of C-A fractal model of Copper element; (b) log-log plot of C-A fractal model of porphyry copper mineral combination elements.

Figure 4. (a) log-log plot of C-A fractal model of Copper element; (b) log-log plot of C-A fractal model of porphyry copper mineral combination elements.

In order to facilitate the analysis of the advantages and disadvantages of the two methods, this paper based on the known deposit and abnormal range of the degree of fit, a typical deposit analysis map (Figure 5) is made. It can be shown from the analysis diagram that the recognition degree of porphyry copper is obviously improved compared with single element method(Figure 5a1-5a3 and Figure 5 b1-5b3). In the case of skarn-type copper deposits, there is a large area anomaly in the Ri a deposit. The reason is that the copper ore bodies in the Ri a deposit are produced in the porphyry bodies. Therefore, this method is difficult to identify or distinguish such deposits and porphyry copper mine. However, skarn-type deposits unrelated to porphyry, the method has a certain degree of distinction, especially the Shesuo deposit(Figure 5 b5). This method distinguishes porphyry molybdenum ore from single element method, but both of them have abnormalities, which indicates that these two methods have very limited ability to distinguish porphyry copper and porphyry molybdenum. This method is worse than the single element method in distinguishing the porphyry type molybdenum ore, but both of them have abnormalities, which indicates that these two methods have extremely limited ability to distinguish porphyry copper from porphyry molybdenum. In the case of porphyry gold, this method has the advantage of reducing the abnormal level compared with the single element method. Such as Sa ka(Figure 5 a5-b5) and Ri na(Figure 5 a6-b6) deposits, the use of single element method is divided into three abnormal zones, but the use of this method only two levels of zoning. This advantage can be reduced in the early stage of abnormal evaluation of porphyry copper, reducing the input of such abnormal identification.

Figure 5. This is a figure. profile chart. a1-a8 Singular anomalies of copper elements of Zhu nuo, Jianglaang-zong, Balazha,Ri a, She suo, Tuan jie, Sa ka, Ri na;b1-b8 Singular anomalies of associa-tion elements of Zhu nuo, Jianglaangzong ,Balazha ,Ri a ,She suo, Tuan jie,Sa ka,Ri na; porphyry Cu deposit: Zhu nuo, Jianglaangzong,Balazha;skarn Cu deposit: Ri a,She suo;porphyry Mo deposit: Tuan jie;porphyry Au deposit: Sa ka,Ri na.

Figure 5. This is a figure. profile chart. a1-a8 Singular anomalies of copper elements of Zhu nuo, Jianglaang-zong, Balazha,Ri a, She suo, Tuan jie, Sa ka, Ri na;b1-b8 Singular anomalies of associa-tion elements of Zhu nuo, Jianglaangzong ,Balazha ,Ri a ,She suo, Tuan jie,Sa ka,Ri na; porphyry Cu deposit: Zhu nuo, Jianglaangzong,Balazha;skarn Cu deposit: Ri a,She suo;porphyry Mo deposit: Tuan jie;porphyry Au deposit: Sa ka,Ri na.

5. Conclusions

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