多元统计分析在滨海矿区水源识别中的应用——以三山岛金矿为例

doi:10.11872/j.issn.1005-2518.2019.02.207

黄金科学技术 ›› 2019, Vol. 27 ›› Issue (2): 207-215.doi: 10.11872/j.issn.1005-2518.2019.02.207

多元统计分析在滨海矿区水源识别中的应用——以三山岛金矿为例

刘国伟^1,^2,³(),马凤山^1,²(),郭捷^1,²,杜云龙⁴,侯成录⁴,李威⁴

1. 中国科学院地质与地球物理研究所，中国科学院页岩气与地质工程重点实验室，北京 100029
2. 中国科学院地球科学研究院，北京 100029
3. 中国科学院大学，北京 100049
4. 山东黄金矿业（莱州）有限公司三山岛金矿，山东莱州 261442

收稿日期:2018-07-31 修回日期:2018-11-01 出版日期:2019-04-30 发布日期:2019-04-30
通讯作者: 马凤山 E-mail:l1014893489@163.com;fsma@mail.iggcas.ac.cn
作者简介:刘国伟（1991-），男，山东菏泽人，博士研究生，从事矿山水文地质、工程地质研究工作。l1014893489@163.com|马凤山（1964-），男，河北吴桥人，研究员，博士生导师，从事地质工程与地质灾害研究工作。fsma@mail.iggcas.ac.cn
基金资助:
国家重点研发计划项目“黄渤海不同类型海岸带海水入侵发生机理研究”（编号：2016YFC0402802）和国家自然科学基金重点项目“海底采矿对地质环境的胁迫影响与致灾机理”(编号：41831293)

Application of Multivariate Statistical Analysis to Identify Water Source in Coast Mine Area：As Example of Sanshandao Gold Mine

Guowei LIU^1,^2,³(),Fengshan MA^1,²(),Jie GUO^1,²,Yunlong DU⁴,Chenglu HOU⁴,Wei LI⁴

1. Key Laboratory of Shale Gas and Geoengineering，Institute of Geology and Geophysics，Chinese Academy of Sciences，Beijing 100029，China
2. Institutions of Earth Science，Chinese Academy of Sciences，Beijing 100029，China
3. University of Chinese Academy of Sciences，Beijing 100049，China
4. Sanshandao Gold Mine，Shandong Gold Mining（Laizhou）Co. ，Ltd. ，Laizhou 261442，Shandong，China

Received:2018-07-31 Revised:2018-11-01 Online:2019-04-30 Published:2019-04-30
Contact: Fengshan MA E-mail:l1014893489@163.com;fsma@mail.iggcas.ac.cn

摘要/Abstract

摘要：

海底矿山突水是矿山开采亟待解决的问题，通过对矿山巷道水的研究，能够划分出矿山突水水源类型，进而对突水可能性作出预测。以山东三山岛金矿西山矿区地下水系统为例，对其31个水样的水化学资料进行多元统计分析研究。利用因子分析法对存在相关关系的变量进行空间降维处理，找出能够反映大于90%水样水化学信息的公共正交因子，以其作为系统聚类变量。运用系统聚类并结合实际地下水性质，将研究区地下水划分为典型的2类，然后建立矿区水源的Bayes线性模型，并对其进行验证。通过因子分析法和系统聚类分析法得出，-375 m中段涌水水源划分为2种类型，并得出2种具体的判别函数。结果表明：多元统计方法判别水源具有快速、准确且经济的特点。

关键词: 三山岛金矿, 矿山突水, 因子分析, 系统聚类分析, Bayes线性模型, 水源判别

Abstract:

Xishan gold mine is subordinate to the Sanshandao gold mine and located in the coastal area of Laizhou Bay，Laizhou City，Shandong Province.In terms of geotectonic，it is located in the western part of the second up-warping zone of the Neocathaysian structural system，which is also Sanshandao-Cangshang fracture of the eastern side of Yishu deep facture.Xishan gold mine has been exploited in under the Bohai sea.Submarine mine water inrush has become an urgent problem to be solved in mine mining.The research on subway water can classify the types of mine groundwater and then predict the possibility of water inrush.Taking groundwater system of Sanshandao gold mine for example，hydrochemical data of 31 water samples was chosen to study with multivariate statistical analysis methods.By using factor analysis，it can reduce the spatial dimension of many variables with correlation relationship，and then identify principle factors which represent over ninety percent information of hydrochemical data.Hierarchical clustering analysis（HCA）uses these principle factors as clustering variables.HCA combined with actual groundwater quality divided the studied groundwater into 2 classic groups，then established and validated Fisher identification model.Through FA and HCA，the groundwater of -375 m subway were divided into two types which all have a specific discriminant function could determine which type of water is.The results represent that the water samples were divided into two typical M1 and M2 by factor analysis combined with principle component analysis.Among the 31 water samples，three of them were discriminated wrong，and the correct rate of discriminant reached 90.3%.Stepwise discriminant analysis and factor analysis were combined to process the seven conventional ions data.Bayes linear discriminant function and function values from 1740 exploration line to 2740 exploration line in -375 m sublevel was obtained.Bayes linear function discriminant results are completely consistent with the results of the factor analysis method，and the two selected discriminant water samples also agree.The consistency of the discriminant results shows that the factor analysis method and the stepwise analysis method are mutually verified.A multivariate statistical method was combined to obtain a quantitative Bayes linear discriminant function，which was applied to the recognition of the source type in the mining area.It was only necessary to know the ion concentration of the corresponding variable，and the water sample type could be determined by substituting it.This method has the characters of accurate，fast，and economical.

Key words: Sanshandao gold mine, mine water inrush, factor analysis, systematic cluster analysis, Bayes linear model, discriminate of water sources

中图分类号:

TD745

刘国伟,马凤山,郭捷,杜云龙,侯成录,李威. 多元统计分析在滨海矿区水源识别中的应用——以三山岛金矿为例[J]. 黄金科学技术, 2019, 27(2): 207-215.

Guowei LIU,Fengshan MA,Jie GUO,Yunlong DU,Chenglu HOU,Wei LI. Application of Multivariate Statistical Analysis to Identify Water Source in Coast Mine Area：As Example of Sanshandao Gold Mine[J]. Gold Science and Technology, 2019, 27(2): 207-215.

图/表 11

图1

图2

图3

表1

-375 m中段水样水化学参数"

水样位置	K⁺/（mg·L^-1）	Na⁺/（mg·L^-1）	Ca²⁺/（mg·L^-1）	Mg²⁺ /（mg·L^-1）	Cl^-/（mg·L^-1）	SO₄^2-/（mg·L^-1）	HCO $3 -$ /（mg·L^-1）	pH值（标准值）	EC/（μs·cm^-1）	TDS/（mg·L^-1）
375-1-1	248.4	10 400	761.5	1 287.9	19 852	2 305.4	219.6	7.19	44 900	35 074.8
375-1-2	197	9 750	801.6	1 222.3	18453.5	2 334.3	233.7	7.74	39 600	32 995
375-1-3	205	10 031.2	849.7	1 239.3	18 916.1	2 497.6	244.6	7.07	42 300	33 991.5
375-1-4	190.2	9 800	841.7	1 215	19 224.5	624.4	250.7	7.31	42 100	32 147.5
375-1-5	179.7	9 875	721.4	1 166.4	18 402.1	2 372.7	253.2	7.34	40 000	32 974.6
375-2-1	286	10 650	697.4	1 312.2	19 852	2 286.2	207.4	7.03	45 200	35 292.8
375-3-1	299.2	9 445	537.1	1 132.4	17 583.2	2 017.3	219.6	7.36	40 800	31 233.8
375-3-2	241	8 900	681.4	1 040	16 705.8	2 190.2	233.7	7.56	37 000	29 992.1
375-3-3	275.8	9 200	753.5	1 069.2	17 579.7	2 286.2	273.3	7.45	39 800	31 437.9
375-4-1	316.8	9 825	641.3	1 044.9	17 583.2	2 017.3	201.3	7.49	41 100	31 629.8
375-4-2	258	8 900	921.8	945.3	17 014.2	2 295.8	181.2	7.46	37 200	30 516.3
375-4-3	282.5	9 725	1 122.2	1 001.2	18 607.7	2 516.8	170.8	7.11	41 800	33 433.8
375-4-4	285.5	9 900	1 314.6	831.1	18 710.5	2 401.5	168.4	7.32	40 800	33 614.5
375-4-5	285.1	10 000	1 154.3	916.1	18 874.3	2 401.5	170.8	7.03	40 900	33 821.3
375-5-1	260	12 050	1 146.3	1 020.6	21 979	2 459.1	119.6	7.29	50 400	39 052.7
375-5-2	208	10 886.2	1 523	972	20 818	2 545.6	114.1	7.41	42 500	37 081.6
375-5-3	195	10 900	1 595.2	957.4	19 738.6	2 708.9	108	7.05	45 800	36 216.5
375-5-4	226.5	11 250	1 643.3	823.8	21 280.6	2 603.2	85.4	7.32	44 700	37 916.2
375-5-5	252.5	11 500	11 500	517.6	21 471.7	2 353.5	81.8	7.03	44 700	38 156.3
375-6-1	337.5	11 450	2 084.2	777.6	22 156.3	2 497.6	107.4	7.02	49 700	39 411.6
375-6-2	262	11 819	2 276.5	726.6	22 411.5	2 488	108	7.06	44 400	40 117.1
375-6-3	257.8	9 062.5	505	1 142.1	17 560.5	2 315	236.1	7.64	34 500	31 080.1
375-7-1	305	10 700	1 723.4	923.4	21 270	2 363.1	134.2	7.17	48 100	37 424.9
375-7-2	251	9 562.5	521	1 154.3	17 642.4	2 353.5	225.7	7.16	39 300	31 716.5
375-7-3	265.6	9 187.5	481	1 161.5	17 731.7	2 238.2	230	7.66	34 400	31 296.2
375-8-1	290.4	10 350	1 026	1 078.9	18 965.7	1 729.1	158.6	7.3	44 100	33 598.7
375-8-2	294	10 937.5	2 312.6	626.9	21 794.7	2 257.4	102.5	7.66	43 900	38 344.7
375-8-3	198.1	10 438	721.4	1 287.9	19 597.1	2 401.5	233.7	7.22	43 000	34 884
375-8-4	281.3	9 062.5	521	1 154.3	17 389.3	2 353.5	230	7.54	35 000	30 992.4
375-9-1	205	10 375	681.4	1 268.5	18 919	2 449.5	256.2	7.63	42 500	34 154.6
375-9-2	262.5	9 250	521	1 154.3	17 731.7	2 343.9	222.7	7.57	34 900	31 486.7

表1

表2

表3

表4

表5

表6

图4

表7

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	K⁺	Na⁺	Ca²⁺	Mg²⁺	Cl^-	SO₄^2-	CHO^-	pH	EC	TDS
K⁺	1.000	0.010	0.194	-0.366	0.065	0.037	-0.270	-0.105	0.112	0.065
Na⁺	0.010	1.000	0.763	-0.496	0.956	0.260	-0.766	-0.522	0.878	0.969
Ca²⁺	0.194	0.763	1.000	-0.860	0.842	0.254	-0.880	-0.398	0.640	0.854
Mg²⁺	-0.366	-0.496	-0.860	1.000	-0.555	-0.237	0.829	0.235	-0.334	-0.576
Cl^-	0.065	0.956	0.842	-0.555	1.000	0.209	-0.777	-0.470	0.835	0.987
SO₄^2-	0.037	0.260	0.254	-0.237	0.209	1.000	-0.328	-0.152	0.117	0.345
CHO^-	-0.270	-0.766	-0.880	0.829	-0.777	-0.328	1.000	0.404	-0.621	-0.805
pH	-0.105	-0.522	-0.398	0.235	-0.470	-0.152	0.404	1.000	-0.624	-0.495
EC	0.112	0.878	0.640	-0.334	0.835	0.117	-0.621	-0.624	1.000	0.839
TDS	0.065	0.969	0.854	-0.576	0.987	0.345	-0.805	-0.495	0.839	1.000

主成分	特征值			特征值
主成分	方差	方差/%	累计方差/%	方差	方差/%	累计方差/%
1	6.048	60.476	60.476	6.048	60.476	60.476
2	1.331	13.311	73.787	1.331	60.476	73.787
3	0.972	9.715	83.502	0.972	9.715	83.502
4	0.829	8.290	91.792	0.829	8.290	91.792
5	0.500	5.003	96.794
6	0.137	1.370	98.164
7	0.110	1.099	99.263
8	0.059	0.591	99.854
9	0.015	0.146	100.000
10	0.000002	0.000018	100.000

变量	因子载荷				旋转因子载荷				方差H_I²
变量	F1	F2	F3	F4	F11	F21	F31	F41	方差H_I²
K⁺	0.195	-0.712	-0.451	0.393	0.136	0.055	-0.938	-0.011	0.90
Na⁺	0.933	0.272	0.014	-0.049	0.695	0.652	0.178	0.083	0.95
Ca²⁺	0.918	-0.212	0.030	-0.213	0.915	0.282	-0.100	0.086	0.93
Mg²⁺	-0.722	0.575	-0.032	0.213	-0.869	0.033	0.359	-0.117	0.90
Cl^-	0.945	0.185	-0.024	-0.136	0.770	0.578	0.135	0.022	0.95
SO₄^2-	0.330	-0.166	0.794	0.473	0.170	0.076	0.006	0.977	0.99
CHO^- pH	-0.900	0.273	-0.059	0.096	-0.865	-0.289	0.185	-0.179	0.90
CHO^- pH	-0.575	-0.297	0.264	-0.557	-0.071	-0.861	0.195	-0.120	0.80
EC	0.837	0.353	-0.235	0.130	0.478	0.815	0.044	-0.052	0.90
TDS	0.966	0.161	0.084	-0.053	0.765	0.583	0.127	0.161	0.97

变量	主成分得分系数
变量	F1	F2	F3	F4
K⁺	0.195	-0.712	-0.451	0.393
Na⁺	0.933	0.272	0.014	-0.049
Ca²⁺	0.918	-0.212	0.030	-0.213
Mg²⁺	-0.722	0.575	-0.032	0.213
Cl^-	0.945	0.185	-0.024	-0.136
SO₄^2-	0.330	-0.166	0.794	0.473
CHO^-	-0.900	0.273	-0.059	0.096
pH	-0.575	-0.297	0.264	-0.557
EC	0.837	0.353	-0.235	0.130
TDS	0.966	0.161	0.084	-0.053

水样位置	因子得分
水样位置	F1	F2	F3	F4
375-1-1	0.145	1.681	-0.299	0.707
375-1-2	-4.660	0.781	1.220	-1.139
375-1-3	-1.536	1.969	0.566	0.858
375-1-4	-4.660	2.575	-3.173	-2.340
375-1-5	-3.639	1.595	0.991	-0.270
375-2-1	1.180	1.388	-0.940	1.441
375-3-1	-4.223	-0.812	-1.128	0.426
375-3-2	-6.907	-1.024	0.311	-0.483
375-3-3	-5.205	-0.758	-0.156	0.309
375-4-1	-3.236	-1.471	-1.133	0.118
375-4-2	-4.830	-1.697	0.311	-0.176
375-4-3	0.083	-0.688	-0.063	1.154
375-4-4	0.297	-1.496	-0.008	0.251
375-4-5	0.903	-0.763	-0.363	1.059
375-5-1	8.111	1.430	-0.023	0.119
375-5-2	3.954	0.656	1.285	-0.716
375-5-3	4.935	1.322	1.178	0.440
375-5-4	6.717	0.252	1.057	-0.463
375-5-5	13.600	-1.555	0.094	-1.265
375-6-1	10.150	-0.631	-0.999	1.186
375-6-2	9.644	0.187	0.185	0.061
375-6-3	-6.903	-1.162	0.638	-0.402
375-7-1	6.120	-0.197	-0.785	0.665
375-7-2	-3.798	0.163	-0.005	0.873
375-7-3	-6.697	-1.197	0.421	-0.492
375-8-1	0.153	-0.098	-1.786	-0.198
375-8-2	6.550	-1.847	0.027	-1.430
375-8-3	-0.864	2.346	0.589	0.270
375-8-4	-6.468	-1.429	0.325	0.153
375-9-1	-2.916	1.540	1.098	-0.542
375-9-2	-5.999	-1.060	0.569	-0.175

多元统计分析在滨海矿区水源识别中的应用——以三山岛金矿为例

Application of Multivariate Statistical Analysis to Identify Water Source in Coast Mine Area：As Example of Sanshandao Gold Mine

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点号	Bayes函数值
点号	M1	M2	类型
375-1-1 375-1-3 375-1-4 375-1-5 375-2-1 375-3-1 375-3-2 375-3-3 375-4-1 375-4-2 375-4-3 375-4-5 375-5-1	242.5498 237.3542 230.8616 234.4816 247.6762 207.2148 191.8156 216.3004 215.0894 174.0706 201.0804 211.2554 269.7998	230.4202 219.9806 211.5024 215.1574 238.4558 190.3102 170.2684 190.8676 202.5736 159.6634 192.2126 203.7626 279.5202	M1 M1 M1 M1 M1 M1 M1 M1 M1 M1 M1 M1 M2
375-5-2 375-5-3 375-5-4 375-5-5 375-6-1 375-6-2 375-7-2 375-7-3 375-8-1 375-8-3 375-8-4 375-9-1 375-9-2	224.8802 223.3290 228.6402 236.6734 243.4762 257.3320 213.6241 201.2025 220.0818 248.7216 196.5775 253.9956 201.0476	229.5296 228.8770 239.0118 248.7846 251.8558 267.4750 196.4774 181.5960 215.9982 234.8644 176.3460 236.7634 182.7464	M2 M2 M2 M2 M2 M2 M1 M1 M1 M1 M1 M1 M1
检测水点	Bayes函数值
检测水点	M1	M2	类型
375-1-2	223.2656	205.9684	M1
375-4-4	206.7442	199.0778	M1

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