多重分形局部奇异性分析方法在中国西藏多龙矿集区深层次地球化学异常识别中的应用

唐杰; 王文磊; 袁长江

doi:10.19509/j.cnki.dzkq.tb20230282

多重分形局部奇异性分析方法在中国西藏多龙矿集区深层次地球化学异常识别中的应用

doi: 10.19509/j.cnki.dzkq.tb20230282

唐杰^{1, 2,},
王文磊^1, ,,
袁长江²

1.
中国地质科学院地质力学研究所, 北京 100081
2.
中国地质大学(北京)地球科学与资源学院, 北京 100083

基金项目:

国家自然科学基金项目 41772353

详细信息

作者简介:
唐杰, E-mail: jietangcsu@163.com

通讯作者:
王文磊, E-mail: wenleiw@163.com

中图分类号: P618.41;P618.51;P632
计量
- 文章访问数: 107
- PDF下载量: 46
- 被引次数: 0
出版历程
- 收稿日期: 2023-05-22
- 录用日期: 2023-07-03
- 修回日期: 2023-07-02

Application of multifractal and local singularity analysis method to the identification of deep-level geochemical anomalies in the Duolong mineral district, Tibet, China

TANG Jie^{1, 2
,},
WANG Wenlei^{1
, ,},
YUAN Changjiang²

1.
Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China
2.
School of Earth Sciences and Resources, China University of Geosciences(Beijing), Beijing 100083, China

More Information

Author Bio:
TANG Jie, E-mail: jietangcsu@163.com

Corresponding author: WANG Wenlei, E-mail: wenleiw@163.com

摘要

摘要:
勘查地球化学数据作为成矿地质体预测最重要的信息载体之一，在识别提取成矿异常以及挖掘深层次成矿信息中具有重要作用。基于地球化学元素空间分布的尺度不变性和广义自相似性，以多龙矿集区1∶5万勘查地球化学数据中的Cu、Au元素为例，运用分形/多重分形和奇异性理论开展分析研究，进行成矿元素空间分布模式的识别和异常提取。针对研究区全区、断裂缓冲区和地层分区分别运用矩方法计算多重分形谱，用于描述局部地区元素的相对富集及亏损程度，并对区内Cu、Au成矿元素进行局部奇异性分析，以识别提取成矿元素的弱、缓异常信息，圈定成矿潜力区。研究表明，多龙矿集区内Cu、Au元素均表现为成矿有利模式。其中，Cu元素存在区域的弱富集，Au元素存在局部范围的超富集，近EW向与NE向断裂的交汇区域以及侏罗系为区内最有利成矿位置。通过绘制局部奇异性指数空间分布图，表征了Cu、Au元素地球化学异常空间分布特征，进而圈定了矿集区的中部和北部为成矿潜力区。
- 勘查地球化学数据 /
- 多龙矿集区 /
- 分形/多重分形 /
- 局部奇异性 /
- 异常提取
Abstract: Objective
As one of the most crucial information carriers for predicting mineralized geological bodies, exploration geochemical data play a significant role in the identifying and extracting mineralization-associated anomalies as well as in analyzing deep-level mineralization information.
Methods
Based on the scale invariance and generalized self-similarity characteristics of the spatial distribution of geochemical elements, this paper uses Cu and Au in the 1:50 000 exploratory geochemical data of the Duolong mineral district as an example and conducts a study using fractal/multifractal and singularity theories to identify the spatial distribution patterns of ore-forming elements and extract anomalies. The multifractal spectrum which is derived by the exploratory moment method for the whole study area, the fault buffer zone and the stratigraphic zone, is used to describe the relative enrichment and depletion of elements in the local area and to analyze the local singularity of Cu and Au mineralized elements, so as to identify and extract weak and low anomalies of mineralized elements and delineate potential mineralization zones.
Results
Both Cu and Au exhibit mineralization-favoured patterns in the Duolong mineral district, with the Cu showing weak enrichment in the region and Au being over-enriched on a local scale. The intersections of the east-west and northeast-trending faults, as well as the Jurassic strata, are identified as the most promising locations for mineralization in this region.
Conclusion
The spatial distribution of the local singularity index is mapped to characterize the distribution features of Cu and Au geochemical anomalies, therefore, the central and northern regions of the ore district are subsequently identified as potential areas for mineralization.
- exploratory geochemical data /
- Duolong mineral district /
- fractal/multifractal /
- local singularity /
- anomaly extraction
注释:

所有作者声明不存在利益冲突。

HTML全文

图 1 多龙矿集区区域位置图(a)及地质简图(b)^[37]

Figure 1. Regional geological map(a) and simplified geological map(b) of the Duolong mineral district

下载: 全尺寸图片幻灯片

图 2 自相似图形模式图^[47]

a.格子尺度为1；b.格子尺度为2；c.格子尺度为4；d.格子尺度为8

Figure 2. Self-similar pattern diagram

下载: 全尺寸图片幻灯片

图 3 局部奇异性计算方法示意图^{[30, 50]}

a.不同大小的方形窗口估计奇异性指数α; b.对数-对数图估计奇异性指数α

Figure 3. Diagram of the local singularity calculation method

下载: 全尺寸图片幻灯片

图 4 Cu元素(a)和Au元素(b)对数变换直方图

Figure 4. Cu(a) and Au(b) logarithm conversion histograms

下载: 全尺寸图片幻灯片

图 5 Cu元素(a)和Au元素(b)对数变换分布Q-Q图

Figure 5. Q-Q diagrams of logarithmic transformation distribution of Cu(a) and Au(b)

下载: 全尺寸图片幻灯片

图 6 Cu元素(a)和Au元素(b)多重分形谱分析图

Figure 6. Cu(a) and Au(b) multifractal spectrum ciagram

下载: 全尺寸图片幻灯片

图 7 多龙矿集区断裂分布缓冲区图

Figure 7. Fault distribution buffer map of the Duolong mineral district

下载: 全尺寸图片幻灯片

图 8 多龙矿集区地层分区图(地层代号含义同图 1)

Figure 8. Stratigraphic zoning map of the Duolong mineral district

下载: 全尺寸图片幻灯片

图 9 不同分区Cu、Au元素多重分形R值对比图

Figure 9. R-value diagram of the multifractal spectrum of Cu and Au in different partitions

下载: 全尺寸图片幻灯片

图 10 Cu元素IDW插值图(a)和局部奇异性指数空间分布图(b)

Figure 10. IDW interpolation diagram of Cu concentration(a) and spatial distribution diagram of local singularity index(b)

下载: 全尺寸图片幻灯片

图 11 Au元素IDW插值图(a)和局部奇异性指数空间分布图(b)

Figure 11. IDW interpolation diagram of Au concentration(a) and spatial distribution diagram of local singularity index(b)

下载: 全尺寸图片幻灯片

图 12 Cu(a)和Au(b)局部奇异性指数频率分布直方图

Figure 12. Local singularity index frequency distribution histogram of Cu(a) and Au(b)

下载: 全尺寸图片幻灯片

图 13 Cu元素(a)和Au元素(b)局部奇异性富集规律图

Figure 13. Local singularity enrichment of Cu(a) and Au(b)

下载: 全尺寸图片幻灯片

表 1 多龙矿集区勘查地球化学数据分析精确度、精密度及检测方法^[25]

Table 1. Analytical accuracy, precision and detection methods for exploration geochemical data in the Duolong mineral district

元素	检测下限/w_B	平均精度	检测方法
Ag	0.03×10^-6	0.004	ES
As	1×10^-6	0.004	AFS
Au	0.3×10^-9	0.002	GFAAS
Bi	0.1×10^-6	0.007	AFS
Cr	10×10^-6	0.002	XRF
Cu	2×10^-6	0.010	XRF
Hg	0.01×10^-6	0.013	AFS
Mn	30×10^-6	0.001	XRF
Mo	0.5×10^-6	0.004	CP
Ni	5×10^-6	0.004	XRF
Pb	5×10^-6	0.012	XRF
Sb	0.3×10^-6	0.002	AFS
Sn	1×10^-6	0.000	ES
W	0.5×10^-6	0.010	CP
Zn	20×10^-6	0.001	XRF
注：XRF为X射线荧光光谱法；CP为催化极谱法；AFS为原子荧光光谱法；ES为发射光谱法；GFAAS为石墨炉原子吸收光谱法

下载: 导出CSV

表 2 盒子大小及对应数目

Table 2. Box size and corresponding number

盒子尺寸ε	1	2	4	8
盒子数目N(ε)	340	155	52	20

下载: 导出CSV

表 3 多龙矿集区勘查地球化学元素统计参数

Table 3. Statistical parameters of geochemical elements for exploration in the Duolong mineral district

元素	统计量	最小值	最大值	均值	标准差	变异系数	中值	偏度
w(Cu)/10^-6	3 358	6.2	854.0	38.5	52.0	1.4	26.8	8.7
w(Au)/10^-9	3 358	0.4	1 058.5	4.8	25.0	5.3	2.2	29.6

下载: 导出CSV

表 4 多龙矿集区Cu、Au元素多重分形谱参数(-10≤q≤10)

Table 4. Multifractal spectrum parameters of Cu and Au in Duolongite mineral district (-10≤q≤10)

元素	α_min	α(0)	α_max	Δα	f(α_min)	f(α_max)	Δf	R
Cu	1.385	2.017	2.184	0.799	0.243	0.868	-0.625	3.752
Au	0.962	2.015	2.682	1.720	0.072	-1.221	1.293	1.580

下载: 导出CSV

表 5 多龙矿集区断裂缓冲区内Cu元素多重分形谱参数(-10≤q≤10)

Table 5. Multifractal spectrum parameter table of Cu in fault buffer zone of the Duolong mineral district(-10≤q≤10)

方向	α_min	α(0)	α_max	Δα	f(α_min)	f(α_max)	Δf	R
全区断裂	1.396	2.017	2.112	0.716	0.389	0.811	-0.422	6.508
NW向断裂	1.498	2.000	2.152	0.654	0.736	1.192	-0.456	3.303
NE向断裂	1.405	2.000	2.146	0.741	0.473	1.432	-0.959	4.075
EW向断裂	1.442	2.000	2.052	0.610	0.631	1.900	-1.269	10.731
注：表中各物理量的含义见正文，下同

下载: 导出CSV

表 6 多龙矿集区断裂缓冲区内Au元素多重分形谱参数(-10≤q≤10)

Table 6. Multifractal spectrum parameter table of Au in fault buffer zone of the Duolong mineral district(-10≤q≤10)

方向	α_min	α(0)	α_max	Δα	f(α_min)	f(α_max)	Δf	R
全区断裂	0.962	2.015	2.671	1.709	0.075	-0.768	0.843	1.606
NW向断裂	0.792	1.972	2.096	1.304	0.033	1.637	-1.604	9.467
NE向断裂	0.895	1.972	2.699	1.804	0.029	-0.446	0.475	1.479
EW向断裂	0.962	2.014	2.087	1.125	0.075	1.596	-1.522	14.385

下载: 导出CSV

表 7 多龙矿集区主要地层Cu元素多重分形谱参数(-10≤q≤10)

Table 7. Multifractal spectrum parameter table of Cu in the main strata in the Duolong mineral district(-10≤q≤10)

地层代号	α_min	α(0)	α_max	Δα	f(α_min)	f(α_max)	Δf	R
T₃r	1.606	2.036	2.164	0.558	0.716	0.942	-0.226	3.369
JM	1.403	2.009	2.062	0.659	0.440	1.862	-1.422	11.364
J₁q	1.514	1.994	2.034	0.520	0.908	2.010	-1.102	12.098
J₂s	1.408	2.007	2.054	0.646	-0.111	1.968	-2.079	12.658
K₁m	1.445	1.999	2.084	0.639	0.666	1.847	-1.181	6.580
K₂a	1.472	1.978	2.079	0.607	0.736	1.639	-0.903	4.980
注：表中地层代号同图 1, 下同

下载: 导出CSV

表 8 多龙矿集区主要地层Au元素多重分形谱参数(-10≤q≤10)

Table 8. Multifractal spectrum parameter table of Au in the main strata in the Duolongmineral district(-10≤q≤10)

地层代号	α_min	α(0)	α_max	Δα	f(α_min)	f(α_max)	Δf	R
T₃r	1.784	2.091	2.186	0.402	0.924	1.629	-0.705	3.223
JM	1.072	2.010	2.215	1.143	0.004	0.440	-0.436	4.583
J₁q	0.995	1.963	2.663	1.668	0.028	0.440	-0.412	1.383
J₂s	0.962	2.038	2.225	1.263	0.075	0.601	-0.526	5.771
K₁m	1.210	2.034	2.449	1.239	-0.065	-0.369	0.304	1.988
K₂a	0.967	1.913	2.417	1.450	0.017	-0.467	0.484	1.877

下载: 导出CSV

参考文献(63)

[1]	CHENG Q M. Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas[J]. Journal of Geochemical Exploration, 2012, 122: 55-70. doi: 10.1016/j.gexplo.2012.07.007
[2]	廖勋, 刘申态, 周菲, 等. 矿体二次圈定在西藏玉龙铜矿的应用[J]. 矿产与地质, 2021, 35(2): 211-215. LIAO X, LIU S T, ZHOU F, et al. Application of secondary delineation of ore body in Yulong copper mine, Tibet[J]. Mineral Resources and Geology, 2021, 35(2): 211-215. (in Chinese with English abstract)
[3]	MAO J W, PIRAJNO F, LEHMANN B, et al. Distribution of porphyry deposits in the Eurasian continent and their corresponding tectonic settings[J]. Journal of Asian Earth Sciences, 2014, 79: 576-584. doi: 10.1016/j.jseaes.2013.09.002
[4]	唐菊兴, 王登红, 汪雄武, 等. 西藏甲玛铜多金属矿矿床地质特征及其矿床模型[J]. 地球学报, 2010, 31(4): 495-506. TANG J X, WANG D H, WANG X W, et al. Geological features and metallogenic model of the Jiama copper-polymetallic deposit in Tibet[J]. Acta Geoscientica Sinica, 2010, 31(4): 495-506. (in Chinese with English abstract)
[5]	蒋少涌, 王微. 战略性关键金属是如何发生超常富集成矿的?[J]. 地球科学, 2022, 47(10): 3869-3871. JIANG S Y, WANG W. What are the super-enrichment mechanisms for strategic critical metal deposits?[J]. Earth Science, 2022, 47(10): 3869-3871. (in Chinese with English abstract)
[6]	孙涵, 王箫鳕, 孟正豪. 战略性新兴产业关键金属供给安全吗?[J]. 地球科学, 2022, 47(10): 3889-3890. SUN H, WANG X X, MENG Z H. Is the supply of key metals in strategic emerging industries secure?[J]. Earth Science, 2022, 47(10): 3889-3890. (in Chinese with English abstract)
[7]	方向, 唐菊兴, 宋杨, 等. 西藏铁格隆南超大型浅成低温热液铜(金、银)矿床的形成时代及其地质意义[J]. 地球学报, 2015, 36(2): 168-176. FANG X, TANG J X, SONG Y, et al. Formation epoch of the south tiegelong supelarge epithermal Cu(Au-Ag) deposit in Tibet and its geological implications[J]. Acta Geoscientica Sinica, 2015, 36(2): 168-176. (in Chinese with English abstract)
[8]	李玉彬, 钟婉婷, 郭建慈, 等. 西藏班公湖-怒江成矿带西段拿厅斑岩Cu(Au)矿床的火成岩岩石成因与成矿物质来源[J]. 岩石学报, 2019, 35(6): 1717-1737. LI Y B, ZHONG W T, GUO J C, et al. Petrogenesis of igneous rocks and ore-forming material source of the Nating porphyry Cu(Au) deposit in the western section of the Bangong Co-Nujiang metallogenic belt, Tibet[J]. Acta Petrologica Sinica, 2019, 35(6): 1717-1737. (in Chinese with English abstract)
[9]	林彬, 方向, 王艺云, 等. 西藏铁格隆南超大型铜(金、银)矿含矿斑岩岩石成因及其对多龙地区早白垩世成矿动力学机制的启示[J]. 岩石学报, 2019, 35(3): 642-664. LIN B, FANG X, WANG Y Y, et al. Petrologic genesis of ore-bearing porphyries in Tiegelongnan giant Cu(Au, Ag) deposit, Tibet and its implications for the dynamic of Cretaceous mineralization, Duolong[J]. Acta Petrologica Sinica, 2019, 35(3): 642-664. (in Chinese with English abstract)
[10]	韦少港, 唐菊兴, 宋扬, 等. 西藏班公湖-怒江缝合带美日切错组中酸性火山岩锆石U-Pb年龄、Sr-Nd-Hf同位素、岩石成因及其构造意义[J]. 地质学报, 2017, 91(1): 132-150. WEI S G, TANG J X, SONG Y, et al. Petrogenesis, zircon U-Pb geochronology and Sr-Nd-Hf isotopes of the intermediate-felsic volcanic rocks from the Duolong deposit in the Bangonghu-Nujiang suture zone, Tibet, and its tectonic significance[J]. Acta Geologica Sinica, 2017, 91(1): 132-150. (in Chinese with English abstract)
[11]	杨超, 唐菊兴, 王艺云, 等. 西藏铁格隆南浅成低温热液型斑岩型Cu-Au矿床流体及地质特征研究[J]. 矿床地质, 2014, 33(6): 1287-1305. YANG C, TANG J X, WANG Y Y, et al. Fluid and geological characteristics researches of southern Tiegelong epithemal porphyry Cu-Au deposit in Tibet[J]. Mineral Deposits, 2014, 33(6): 1287-1305. (in Chinese with English abstract)
[12]	陈华勇, 程佳敏, 张俊岭. 多维度矿床学研究: 现状与未来展望[J]. 地质科技通报, 2022, 41(5): 1-4. doi: 10.19509/j.cnki.dzkq.2022.0243 CHEN H Y, CHENG J M, ZHANG J L. Multidimensional study of ore deposits: Current status and future prospects[J]. Bulletin of Geological Science and Technology, 2022, 41(5): 1-4. (in Chinese with English abstract) doi: 10.19509/j.cnki.dzkq.2022.0243
[13]	CHENG Q M. IUGS' initiative on data-driven geoscience discovery[J]. Journal of Earth Science, 2021, 32(2): 468-470. doi: 10.1007/s12583-021-1455-6
[14]	CHENG Q M, CHEN Y Q, ZUO R G. Preface to the special issue on digital geosciences and quantitative exploration of mineral resources[J]. Journal of Earth Science, 2021, 32(2): 267-268. doi: 10.1007/s12583-021-1460-9
[15]	王川, 石文杰, 朱建东, 等. 基于磁异常信息的鄂东北四方山地区沉积变质型锰矿找矿预测[J]. 地质科技通报, 2022, 41(4): 184-196. doi: 10.19509/j.cnki.dzkq.2022.0109 WANG C, SHI W J, ZHU J D, et al. Prospecting of sedimentary-metamorphic type manganese deposits in the Sifangshan area, northeastern Hubei Province: Insight from magnetic anomaly information[J]. Bulletin of Geological Science and Technology, 2022, 41(4): 184-196. (in Chinese with English abstract) doi: 10.19509/j.cnki.dzkq.2022.0109
[16]	黄啸坤, 魏俊浩, 石文杰, 等. 基于汇水盆地的化探异常识别与评价: 以东昆仑乌拉斯太地区1∶5万水系沉积物地球化学测量为例[J]. 地质科技通报, 2023, 42(1): 324-338. doi: 10.19509/j.cnki.dzkq.2021.0093 HUANG X K, WEI J H, SHI W J, et al. Identification of the geochemical anomalies using the catchment basin analysis: A case study of 1∶50 000 geochemical survey of stream sediments in Wulasitai region, East Kunlun Orogenic Belt[J]. Bulletin of Geological Science and Technology, 2023, 42(1): 324-338. (in Chinese with English abstract) doi: 10.19509/j.cnki.dzkq.2021.0093
[17]	朱平平, 刘岳, 成秋明. 定量确定胶东毕郭地区勘查地球化学异常的分布方向及地质意义[J]. 地学前缘, 2023, 30(2): 440-446. ZHU P P, LIU Y, CHENG Q M. Quantitative determinations of the dispersion pattern and geological significance of geochemical anomalies in Biguo area, Jiaodong Terrane[J]. Earth Science Frontiers, 2023, 30(2): 440-446. (in Chinese with English abstract)
[18]	GUO L F, CHEN Y Q, ZHAO B B. Application of singular value decomposition(SVD) to the extraction of gravity anomalies associated with Ag-Pb-Zn-W polymetallic mineralization in the Bozhushan ore field, southwestern China[J]. Journal of Earth Science, 2021, 32(2): 310-317.
[19]	ZHAO J N, CHEN S Y. Identification of the ore-forming anomaly component by MSVD combined with PCA from element concentrations in fracture zones of the Laochang ore field, Gejiu, SW China[J]. Journal of Earth Science, 2021, 32(2): 427-438.
[20]	ZHAO P D, CHEN Y Q. Digital geosciences and quantitative mineral exploration[J]. Journal of Earth Science, 2021, 32(2): 269-275.
[21]	MANDELBROT B. How long is the coast of Britain? statistical self-similarity and fractional dimension[J]. Science, 1967, 156: 636-638.
[22]	CHENG Q M. Multifractal modelling and spatial analysis with GIS: Gold potential estimation in the Mitchell-Sulphurets area, northwestern British Columbia[D]. Ottawa, Canada: University of Ottawa, 1994.
[23]	CHENG Q M, XU Y G, GRUNSKY E. Multifractal power spectrum-area method for geochemical anomaly separation[J]. Natural Resources Research, 2000, 9: 43-51.
[24]	RAD E H, HASSANI H, SHIRI Y, 等. 叠后地震数据的自相似分段和多重分形[J]. 石油勘探与开发, 2020, 47(4): 730-738. RAD E H, HASSANI H, SHIRI Y, et al. Self-similar segmentation and multifractality of post-stack seismic data[J]. Petroleum Exploration and Development, 2020, 47(4): 730-738. (in Chinese with English abstract)
[25]	WANG W L, CHENG Q M, TANG J X, et al. Fractal/multifractal analysis in support of mineral exploration in the Duolong mineral district, Tibet, China[J]. Geochemistry(Exploration, Environment, Analysis), 2017, 17(3): 261-276.
[26]	肖凡, 陈建国, 侯卫生, 等. 钦-杭结合带南段庞西垌地区Ag-Au致矿地球化学异常信息识别与提取[J]. 岩石学报, 2017, 33(3): 779-790. XIAO F, CHEN J G, HOU W S, et al. Identification and extraction of Ag-Au mineralization associated geochemical anomaly in Pangxitong district, southern part of the Qinzhou-Hangzhou Metallogenic Belt, China[J]. Acta Petrologica Sinica, 2017, 33(3): 779-790. (in Chinese with English abstract)
[27]	张焱, 周永章. 基于多重分形的信息融合技术在琼东南盆地深水区油气勘探中的应用[J]. 地质学刊, 2019, 43(3): 359-366. ZHANG Y, ZHOU Y Z. Application of multi-fractal information fusion in oil and gas exploration in the deep water area of Qiongdongnan Basin[J]. Journal of Geology, 2019, 43(3): 359-366. (in Chinese with English abstract)
[28]	ZHAO P Q, WANG Z L, SUN Z C, et al. Investigation on the pore structure and multifractal characteristics of tight oil reservoirs using NMR measurements: Permian Lucaogou Formation in Jimusaer Sag, Junggar Basin[J]. Marine and Petroleum Geology, 2017, 86: 1067-1081.
[29]	ZUO R G. Mineral exploration using subtle or negative geochemical anomalies[J]. Journal of Earth Science, 2021, 32(2): 439-454.
[30]	CHENG Q M, AGTERBERG F P. Multifractal modeling and spatial statistics[J]. Mathematical Geology, 1996, 28(1): 1-16.
[31]	秦涛, 陈建平, 赵洁. 基于地球化学数据的滇东南地区断裂构造信息提取[J]. 地质学刊, 2020, 44(4): 386-393. QIN T, CHEN J P, ZHAO J. Extraction of fault information based on geochemical data in southeastern Yunnan[J]. Journal of Geology, 2020, 44(4): 386-393. (in Chinese with English abstract)
[32]	CHENG Q M. Fractal calculus and analysis for characterizing geoanomalies caused by singular geological processes[J]. Journal of Earth Science, 2021, 32(2): 276-278.
[33]	LI J X, QIN K Z, LI G M, et al. Geochronology, geochemistry, and zircon Hf isotopic compositions of Mesozoic intermediate-felsic intrusions in central Tibet: Petrogenetic and tectonic implications[J]. Lithos, 2014, 198: 77-91.
[34]	王勤, 唐菊兴, 陈毓川, 等. 西藏多龙超大型铜(金)矿集区成矿模式与找矿方向[J]. 岩石学报, 2019, 35(3): 879-896. WANG Q, TANG J X, CHEN Y C, et al. The metallogenic model and prospecting direction for the Duolong super large copper(gold) district, Tibet[J]. Acta Petrologica Sinica, 2019, 35(3): 879-896. (in Chinese with English abstract)
[35]	冀全伟, 王文磊, 刘治博, 等. 一种基于机器学习算法的岩性填图方法[J]. 地质力学学报, 2021, 27(3): 339-349. JI Q W, WANG W L, LIU Z B, et al. A machine learning-based lithologic mapping method[J]. Journal of Geomechanics, 2021, 27(3): 339-349. (in Chinese with English abstract)
[36]	刘治博, 王文磊, 宋扬, 等. 多龙矿集区控矿构造信息提取、识别与融合[J]. 地球学报, 2017, 38(5): 803-812. LIU Z B, WANG W L, SONG Y, et al. Geo-information extraction and integration of ore-controlling structure in the duolong ore concentration area of Tibet[J]. Acta Geoscientica Sinica, 2017, 38(5): 803-812. (in Chinese with English abstract)
[37]	王明, 解超明, 范建军. 西藏改则多不扎1∶5万4幅区调[R]. 长春: 吉林大学地质调查研究院, 2016. WANG M, XIE C M, FAN J J. 1∶50 000 regional surveys in Duobuza, Gaize County, Tibet[R]. Changchun: Geological Survey and Research Institute of Jilin University, 2016. (in Chinese)
[38]	唐菊兴, 宋扬, 王勤, 等. 西藏铁格隆南铜(金银)矿床地质特征及勘查模型: 西藏首例千万吨级斑岩-浅成低温热液型矿床[J]. 地球学报, 2016, 37(6): 663-690. TANG J X, SONG Y, WANG Q, et al. Geological characteristics and exploration model of the Tiegelongnan Cu(Au-Ag) deposit: The first ten million tons metal resources of a porphyry-epithermal deposit in Tibet[J]. Acta Geoscientica Sinica, 2016, 37(6): 663-690. (in Chinese with English abstract)
[39]	SO G B, SO H R, JIN G G. Enhancement of the box-counting algorithm for fractal dimension estimation[J]. Pattern Recognition Letters, 2017, 98: 53-58.
[40]	PENTLAND A P. Fractal-based description of natural scenes[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, 6(6): 661-674.
[41]	MANDELBROT B B. Self-affine fractals and fractal dimension[J]. Physica Scripta, 1985, 32(4): 257-260.
[42]	LI J, DU Q, SUN C X. An improved box-counting method for image fractal dimension estimation[J]. Pattern Recognition, 2009, 42(11): 2460-2469.
[43]	LIN M, CHEN L J, MA Y. Research on stream flow series fractal dimension analysis and its relationship with soil erosion[C]//Anon. 2013 IEEE International Geoscience and Remote Sensing Symposium - IGARSS. Melbourne, VIC, Australia: IEEE, 2013: 1821-1823.
[44]	SHYU K K, WU Y T, CHEN T R, et al. Measuring complexity of fetal cortical surface from MR images using 3-D modified box-counting method[J]. IEEE Transactions on Instrumentation and Measurement, 2011, 60(2): 522-531.
[45]	YU L, ZHANG D, WANG K Q, et al. Coarse iris classification using box-counting to estimate fractal dimensions[J]. Pattern Recognition, 2005, 38(11): 1791-1798.
[46]	GAGNEPAIN J J, ROQUES-CARMES C. Fractal approach to two-dimensional and three-dimensional surface roughness[J]. Wear, 1986, 109(1/2/3/4): 119-126.
[47]	陈志军. 多重分形局部奇异性分析方法及其在矿产资源信息提取中的应用[D]. 武汉: 中国地质大学(武汉), 2007. CHEN Z J. Multifractal theory based local singularity analysis method and its application in spatial information extraction for mineral exploration[D]. Wuhan: China University of Geosciences(Wuhan), 2007. (in Chinese with English abstract)
[48]	成秋明. 成矿过程奇异性与矿产预测定量化的新理论与新方法[J]. 地学前缘, 2007, 14(5): 42-53. CHENG Q M. Singular mineralization processes and mineral resources quantitative prediction: New theories and methods[J]. Earth Science Frontiers, 2007, 14(5): 42-53. (in Chinese with English abstract)
[49]	EVERTSZ C J, MANDELBROT B B. Multifractal measures: Chaos and fractals[M]. New York: Springer Verlag, 1992: 922-953.
[50]	HALSEY T C, JENSEN M H, KADANOFF L P, et al. Fractal measures and their singularities: The characterization of strange sets[J]. Physical Review A(General Physics), 1986, 33(2): 1141-1151.
[51]	AI T, ZHANG R, ZHOU H W, et al. Box-counting methods to directly estimate the fractal dimension of a rock surface[J]. Applied Surface Science, 2014, 314: 610-621.
[52]	BASHAN A, BARTSCH R, KANTELHARDT J W, et al. Comparison of detrending methods for fluctuation analysis[J]. Physica A(Statistical Mechanics and Its Applications), 2008, 387(21): 5080-5090.
[53]	IHLEN E A F. Introduction to multifractal detrended fluctuation analysis in Matlab[J]. Frontiers in Physiology, 2012, 3: 141.
[54]	XIE H P, WANG J N, KWAŜNIEWSKI M A. Multifractal characterization of rock fracture surfaces[J]. International Journal of Rock Mechanics and Mining Sciences, 1999, 36(1): 19-27.
[55]	KONG X G, WANG E Y, HE X Q, et al. Time-varying multifractal of acoustic emission about coal samples subjected to uniaxial compression[J]. Chaos, Solitons & Fractals, 2017, 103: 571-577.
[56]	TAN J Q, HU C E, LÜ Q, et al. Multi-fractal analysis for the AE energy dissipation of CO₂ and CO₂+ brine/water treated low-clay shales under uniaxial compressive tests[J]. Fuel, 2019, 246: 330-339.
[57]	高原. 闽西南铜多金属矿找矿信息挖掘与成矿预测[D]. 武汉: 中国地质大学(武汉), 2019. GAO Y. Mineral prospecting information mining and mapping mineral prospectivity for copper polymetallic mineralization in southwest Fujian Province, China[D]. Wuhan: China University of Geosciences(Wuhan), 2019. (in Chinese with English abstract)
[58]	ZHAO J N, ZUO R G, CHEN S Y, et al. Application of the tectono-geochemistry method to mineral prospectivity mapping: A case study of the Gaosong tin-polymetallic deposit, Gejiu district, SW China[J]. Ore Geology Reviews, 2015, 71: 719-734.
[59]	AHRENS L H. Lognormal-type distributions: Ⅲ[J]. Geochimica et Cosmochimica Acta, 1957, 11(4): 205-212.
[60]	CHENG Q M, AGTERBERG F P, BALLANTYNE S B. The separation of geochemical anomalies from background by fractal methods[J]. Journal of Geochemical Exploration, 1994, 51(2): 109-130.
[61]	ZUO R G, WANG J. Fractal/multifractal modeling of geochemical data: A review[J]. Journal of Geochemical Exploration, 2016, 164: 33-41.
[62]	XIE S Y, BAO Z Y. Fractal and multifractal properties of geochemical fields[J]. Mathematical Geology, 2004, 36(7): 847-864.
[63]	CHENG Q M. Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China[J]. Ore Geology Reviews, 2007, 32(1/2): 314-324.