Statistical analysis of the spatial distribution and genesis of lithium in geothermal water in the Yangbajing-Gulu rift, Xizang
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摘要:
位于西藏羊八井−谷露裂谷中的地热水锂含量高于西藏温泉平均水平，但其水化学成因仍有争议，主要原因之一为该区域地热水中锂的空间分布规律不明。常见的空间规律分析方法为普通克里金法(Ordinary Kriging)和协同克里金法(CO-Kriging)，但前者精度不高，后者难以获得合适的辅助变量。为此，提出2种确定辅助变量的方法：一是采用与锂相关性最强的物理化学指标Cl−浓度作为辅助变量；二是采用主成分分析综合指标F作为辅助变量。将2种辅助变量分别耦合进CO-Kriging中，形成Cl−-CO-Kriging和F-CO-Kriging方法，用以分析西藏羊八井−谷露裂谷中的地热水锂分布规律。结果表明，相比于Ordinary Kriging，F-CO-Kriging和Cl−-CO-Kriging预测精度有明显提高；其中F-CO-Kriging的EMA和ERMS平均提高30.3%，Cl−-CO-Kriging的EMA和ERMS平均提高28.5%，而且显示地热水中的锂与断裂在空间分布上具有一致性，在谷露地热区锂有明显的富集现象。进一步采用系统聚类和因子分析方法，探究影响地热水中锂空间分布的水化学成因发现，高温、高TDS、低Ca2+浓度、低Mg2+浓度、高硼浓度的碱性环境中锂浓度更高。研究成果为探讨青藏高原地热水中的高锂乃至其他稀有金属的成因和资源评价奠定基础。
Abstract:In the Yangbajing-Gulu rift, located in Xizang, the lithium concentration in geothermal water exceeds the average level of thermal springs in Xizang. However, the hydrochemical genesis of lithium in geothermal water in this rift remains controversial, and one primary reason for this is the unclear spatial distribution pattern of lithium. Common methods for analyzing spatial distribution patterns include Ordinary Kriging and CO-Kriging. Nevertheless, the former suffers low precision. For the latter, it is difficult to obtain suitable auxiliary variables. Given this, this study determined two auxiliary variables: (1) the Cl− concentration, a physicochemical parameter exhibiting the strongest correlation with lithium, and (2) comprehensive index F, as determined using principal component analysis. Integrating these two auxiliary variables separately into the CO-Kriging method formed the Cl−-CO-Kriging and F-CO-Kriging methods, which were employed to analyze the spatial distribution patterns of lithium in geothermal water in the Yangbajing-Gulu rift. The results indicate that, compared to Ordinary Kriging, both F-CO-Kriging and Cl−-CO-Kriging demonstrated significantly elevated prediction accuracy, with the former increasing EMA and ERMS by 30.3% and the latter by 28.5% on average. Furthermore, both methods revealed that lithium in geothermal water exhibits a spatial distribution consistent with faults and notable enrichment in the Yangbajing-Gulu geothermal area. This study further explored the hydrochemical genesis of the spatial distribution of lithium in geothermal water using hierarchical clustering and factor analysis. The results show that an alkaline environment characterized by high temperatures, high total dissolved solids (TDS), low Ca2+ and Mg2+ concentrations, and elevated born concentrations presents high lithium concentrations. The findings of this study will lay the groundwork for exploring the origin of high-concentration lithium and other rare metals in geothermal water on the Qinghai-Xizang Plateau and conducting relevant resource evaluation.
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图 3 羊八井−谷露裂谷Li空间分布趋势
Fig. 3 Spatial distribution trend of lithium in geothermal water in the Yangbajing-Gulu rift
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图 4 各个指标与Li+的皮尔逊相关系数
Fig. 4 Pearson correlation coefficients between various indices and Li+ concentration
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图 6 3种方法模拟的地热水Li空间分布
Fig. 6 Spatial distribution of lithium concentration in geothermal water simulation by three methods
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图 7 羊八井−谷露裂谷地热水系统聚类谱系图
Fig. 7 Cluster pedigree chart of geothermal water in the Yangbajing-Gulu rift
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图 8 羊八井−谷露裂谷地热水聚类组分分布
Fig. 8 Cluster distributions of geothermal water in the Yangbajing-Gulu rift
表 1 羊八井−谷露裂谷地热水水化学数据
Table 1 Hydrochemical data of geothermal water in the Yangbajing-Gulu rift
种类 温度t/℃ pH TDS/(g·L−1) 离子质量浓度/(mg·L−1) 电荷平衡/% 参考文献 Na+ K+ Ca2+ Mg2+ Li+ ${\mathrm{CO}}_3^{2-} $ ${\mathrm{HCO}}_3^- $ Cl− ${\mathrm{SO}}_4^{2-} $ F− SiO2 HBO2 As 曲才沸泉 87 8.80 2.044 532.0 131.0 0.60 2.65 10.20 60.90 496.00 512.00 192.00 7.04 203.0 132.0 1.672 −1.32 佟伟等[36] 古令曲热泉 54 8.30 0.639 195.0 10.0 4.00 0.30 0.50 0 444.00 19.00 13.50 15.40 155.0 3.5 0 0.70 古令曲沸泉 85 8.50 0.64 185.0 10.0 5.00 0.40 0.50 9.80 380.00 20.10 38.40 24.30 145.0 10.3 0 −3.06 桑巴沙曲灿温泉 39 6.75 1.54 400.0 54.0 72.00 10.40 6.50 0 819.00 311.00 41.10 2.65 56.3 175.0 0.006 2.09 羊八井1区热水湖 48 7.50 1.751 450.0 57.0 15.85 2.72 11.50 0 476.24 543.07 73.53 16.30 134.0 202.5 2.670 −3.67 羊八井2区藏布曲心滩沸泉 84 8.50 1.619 405.0 47.5 6.89 4.18 13.15 31.99 296.20 468.88 90.87 14.20 163.4 219.0 1.500 −0.86 羊八井3、4区沸泉塘 91 7.90 1.600 400.0 45.5 13.80 4.18 9.75 0 439.00 468.00 51.20 14.20 170.0 203.0 2.150 −2.79 羊八井5区热泉 87 9.20 1.877 480.0 49.0 1.38 2.30 28.60 209.07 4.64 597.13 45.44 14.70 155.0 273.4 2.650 1.70 羊八井6区热泉 80 9.00 1.656 426.0 60.5 0.20 0.15 9.10 48.80 149.00 518.00 8.42 14.90 214.0 265.0 2.534 4.33 羊八井7区热泉 83 8.80 1.686 425.0 34.0 1.72 2.72 13.15 142.23 127.89 530.55 47.93 13.60 135.0 261.2 2.670 −4.34 羊八井8区热泉 50 7.20 0.907 240.0 14.0 24.13 4.18 2.90 0 339.80 187.12 45.44 6.50 86.0 121.5 0.216 2.54 羊八井9区热泉 87 8.90 1.823 467.5 58.5 1.72 5.23 13.15 74.59 185.84 542.86 66.09 14.90 171.5 303.7 2.500 2.63 羊八井12区热泉 67 6.60 1.329 310.0 34.0 25.85 2.30 7.00 0 376.37 350.31 46.25 9.70 194.3 157.1 0.920 −1.97 羊八井13、14区热泉 58 7.20 1.399 365.0 39.0 9.60 1.05 10.00 0 369.36 410.05 55.91 11.50 158.3 148.0 1.620 −1.33 羊八井15区热泉 85 7.70 1.891 467.5 58.5 10.30 2.08 11.25 0 438.47 525.70 41.12 6.20 247.6 298.0 2.250 1.99 羊八井地热井水Z1(钻孔Y) 84 8.60 1.790 445.0 53.5 5.15 1.03 12.75 62.83 178.91 623.65 53.46 6.50 124.8 303.0 4.000 −2.49 羊易地热田 87 9.70 1.708 450.0 30.0 1.00 0.10 13.00 200.00 357.00 183.00 217.00 23.50 258.0 150.0 1.820 −2.59 门曲库低温温泉 29 8.00 0.670 150.0 8.2 48.00 28.10 0.10 0 482.00 14.30 132.00 2.06 31.1 11.0 0 1.44 脱玛热泉 51 6.80 2.220 570.0 72.5 117.00 18.70 0.60 0 1020.00 38.20 798.00 6.65 78.9 15.0 0 −0.92 谷露热泉 86 9.14 3.87495 1138.2 130.36 0 0 24.52 261.65 969.56 893.42 235.22 15.20 146.70 59.23 1.25 0.76 张萌等[35] 谷露热泉 94 8.85 4.06234 1098.0 138.28 0 0 24.77 133.73 1235.59 896.96 219.35 15.27 131.74 168.12 1.37 −0.48 谷露热泉 83 8.54 4.40290 1253.6 134.72 0 0 24.92 81.40 1318.36 892.07 389.70 14.50 135.72 156.79 1.47 2.66 谷露热泉 61 7.30 4.35387 1165.5 115.06 12.83 3.89 20.45 0 1433.05 829.66 370.25 11.80 240.17 149.83 1.40 2.05 谷露热泉 84 8.15 3.93883 998.0 121.22 4.81 1.95 21.03 0 1513.46 779.97 192.22 12.40 131.61 161.15 1.29 −1.51 谷露热泉 68 7.64 3.77993 953.4 137.20 3.21 0.97 21.55 0 1377.48 790.60 179.53 12.60 156.98 145.47 1.23 −0.99 谷露热泉 44 7.01 3.54220 831.3 105.80 48.12 13.62 16.71 0 1460.25 627.52 125.31 7.20 179.37 125.44 0.58 0.20 续迈中低温温泉 78 8.22 0.68951 149.59 9.76 8.02 0.97 1.77 10.49 96.98 89.34 144.16 8.85 120.26 47.91 0.19 −2.83 刘昭等[38] 续迈沸泉 86 8.20 0.70492 152.95 9.84 8.02 0.97 1.58 9.30 96.96 85.09 153.59 9.40 129.87 46.17 0.28 −2.44 吉达果中低温温泉 64 7.29 1.18173 228.68 14.93 40.10 4.86 2.84 0 472.95 97.85 138.01 6.20 116.64 58.36 0.29 −2.12 刘昭等[38] 嘎日桥沸泉 80 8.17 1.26264 273.59 21.88 16.04 1.95 2.37 0 679.87 67.36 38.81 9.30 105.67 45.30 0.27 −2.07 宁中沸泉 88 8.27 2.61245 637.25 116.28 30.48 7.78 10.88 58.14 621.94 479.32 362.44 7.45 128.47 148.08 1.95 1.23 宁中地热井水 80 7.70 2.65201 620.15 109.66 32.08 10.70 11.26 0 747.27 486.42 350.23 7.00 128.48 144.60 2.14 0.39 月腊中低温温泉 69 7.03 1.47051 239.59 36.54 70.58 14.59 1.63 0 856.05 44.67 59.59 2.36 116.49 27.00 0 −0.99 董翁沸泉 86 7.31 1.46048 279.56 60.00 69.95 7.81 8.65 0 454.04 419.59 13.46 3.20 67.59 74.91 0.79 −1.64 脱玛中低温温泉 55 7.48 2.49132 549.45 68.56 60.95 11.67 1.62 0 1531.46 187.19 5.25 6.20 62.08 24.39 0 −1.51 罗玛中低温温泉 49 7.17 2.56408 541.48 68.40 117.09 10.21 0.61 0 997.93 36.16 678.33 5.30 86.86 20.91 0 0.47 羊八井地热井水Z2 8.86 417 48.4 1.89 0.10 10.3 479 32.8 13.2 205 赵平等[37] 羊八井地热井水Z3 8.82 328 38.5 3.99 0.10 7.5 415 35.6 13.7 206 羊八井地热井水Z4 8.88 338 44.2 3.64 <0.01 7.6 472 40.8 14.7 224 羊八井地热井水Z5 8.89 337 39.6 4.40 0.10 8.1 481 39.7 14.9 214 羊八井地热井水Z6 8.21 316 35.7 3.57 <0.05 7.6 412 33.8 13.2 216 羊八井地热井水Z7 8.17 332 41.7 3.89 <0.05 8.1 451 34.6 13.2 217 羊八井地热井水Z8 8.80 377 44.8 3.70 <0.05 9.1 491 38.1 14.2 238 羊八井地热井水Z9 8.93 387 45.8 3.19 0.10 9.4 513 38.4 14.3 248 羊八井地热井水Z10 8.49 408 47.3 3.56 <0.05 9.2 489 37.7 14.6 241 羊八井地热井水Z11 8.90 421 55.6 2.82 <0.05 10.3 531 39.6 14.0 260 羊八井地热井水Z12 8.94 383 48.4 3.97 <0.05 9.1 519 39.9 15.1 247 羊八井地热井水Z13 8.92 370 47.5 2.84 <0.01 8.7 514 43.2 14.4 256 注：电荷平衡[39]=$[(\displaystyle\sum {阳离子} - \left| {\displaystyle\sum {阴离子} } \right|) \div (\displaystyle\sum {阳离子} + \left| {\displaystyle\sum {阴离子} } \right|)] \times 100$%。 
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表 2 各物理化学指标之间皮尔逊相关系数
Table 2 Pearson correlation coefficients between various physicochemical indices
指标 t pH TDS Na+ K+ Ca2+ Mg2+ Li+ ${\mathrm{CO}}_3^{2-} $ ${\mathrm{HCO}}_3^{-} $ Cl− ${\mathrm{SO}}_4^{2-} $ F− SiO2 HBO2 As t 1 0.667 0.139 0.170 0.219 −0.574 −0.617 0.418 0.483 −0.263 0.382 −0.125 0.434 0.431 0.390 0.507 pH 1 0.057 0.028 −0.004 −0.711 −0.516 0.328 0.752 −0.332 0.313 −0.263 0.673 0.521 0.330 0.487 TDS 1 0.985 0.918 −0.064 −0.093 0.754 0.265 0.798 0.788 0.454 0.109 0.201 0.170 0.208 Na+ 1 0.909 −0.077 −0.125 0.790 0.342 0.743 0.760 0.473 0.114 0.028 0.197 0.239 K+ 1 −0.002 −0.038 0.703 0.235 0.688 0.735 0.465 −0.046 0.008 0.198 0.273 Ca2+ 1 0.757 −0.438 −0.408 0.302 −0.491 0.539 −0.677 −0.620 −0.483 −0.539 Mg2+ 1 −0.367 −0.340 0.236 −0.391 0.331 −0.651 −0.593 −0.377 −0.407 Li+ 1 0.598 0.301 0.900 0.072 0.328 0.247 0.568 0.580 ${\mathrm{CO}}_3^{2-} $ 1 −0.155 0.410 0.020 0.482 0.271 0.302 0.423 ${\mathrm{HCO}}_3^{-} $ 1 0.354 0.421 −0.144 −0.128 −0.291 −0.311 Cl− 1 −0.029 0.285 0.383 0.616 0.628 ${\mathrm{SO}}_4^{2-} $ 1 −0.204 −0.285 −0.284 −0.162 F− 1 0.592 0.229 0.319 SiO2 1 0.490 0.492 HBO2 1 0.876 As 1
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表 3 主成分特征值和累计贡献率
Table 3 Eigenvalues and cumulative contribution rates of principal components
成分 初始特征值 提取载荷平方和 总计 方差百分比/% 累积/% 总计 方差百分比/% 累积/% F1 5.526 42.508 42.508 5.526 42.508 42.508 F2 3.704 28.494 71.003 3.704 28.494 71.003 F3 1.337 10.285 81.287 1.337 10.285 81.287 F4 0.868 6.674 87.962 F5 0.566 4.352 92.313 F6 0.307 2.363 94.677 F7 0.294 2.261 96.937 F8 0.130 0.998 97.935 F9 0.112 0.864 98.799 F10 0.080 0.614 99.413 F11 0.042 0.327 99.740 F12 0.029 0.222 99.961 F13 0.005 0.039 100.000
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表 4 Cl−-CO-Kriging、F-CO-Kriging与Ordinary Kriging精度对比
Table 4 Accuracy comparison between the Cl−-CO-Kriging, F-CO-Kriging, and Ordinary Kriging methods
插值方法 EMA ERMS 数值 精度提升/% 数值 精度提升/% Ordinary Kriging 1.79 0 2.72 0 Cl−-CO-Kriging 1.25 30.2 1.99 26.8 F-CO-Kriging 1.32 26.3 1.79 34.2
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表 5 聚类分析组分水化学数据统计结果
Table 5 Statistics of hydrochemical data of clusters
分类 参数 t/℃ pH TDS Na+ K+ Ca2+ Mg2+ Li+ ${\mathrm{CO}}_3^{2-} $ ${\mathrm{HCO}}_3^{-} $ Cl− ${\mathrm{SO}}_4^{2-} $ F− SiO2 HBO2 As A A1 最大值 67 7.50 1.75 450.00 57.00 25.85 2.72 11.50 476.24 543.07 73.53 16.30 194.30 202.50 2.67 最小值 48 6.60 1.33 310.00 34.00 9.60 1.05 7.00 0 369.36 350.31 46.25 9.70 134.00 148.00 0.92 平均值 57 7.10 1.49 375.00 43.33 17.10 2.02 9.50 407.32 434.48 58.56 12.50 162.20 169.20 1.74 A2 最大值 90.5 9.00 1.89 467.50 60.50 13.80 5.23 13.15 142.23 439.00 623.65 90.87 14.90 247.60 303.70 4.00 最小值 80 7.70 1.60 400.00 34.00 0.20 0.15 9.10 0 127.89 468.00 8.42 6.20 124.80 203.00 1.50 平均值 84 8.49 1.72 433.71 51.14 5.68 2.80 11.76 51.49 259.33 525.38 51.30 12.07 175.19 264.70 2.51 最大值 91 9.70 2.65 637.25 131.00 72.00 14.59 28.60 209.07 1531.46 623.65 362.44 24.30 258.00 303.70 4.00 最小值 39 6.60 0.64 149.59 9.76 0.20 0.10 0.50 0 4.64 19.00 5.25 2.36 56.30 3.50 0 平均值 74 8.03 1.55 375.92 47.44 20.59 4.13 8.29 35.31 439.82 337.20 92.05 10.62 144.11 147.80 1.35 B 最大值 94 9.14 4.40 1253.60 138.28 48.12 13.62 24.92 261.65 1513.46 896.96 389.7 15.27 240.17 168.12 1.47 最小值 44 7.01 3.54 831.30 105.80 0 0 16.71 0 969.56 627.52 125.31 7.20 131.61 59.23 0.58 平均值 74 8.09 3.99 1062.57 126.09 9.85 2.92 21.99 68.11 1329.68 815.74 244.51 12.71 160.33 138.00 1.23 C 最大值 51 8.00 2.56 570.00 72.50 117.09 28.10 0.61 1020.00 38.20 798.00 6.65 86.86 20.91 最小值 29 6.80 0.67 150.00 8.20 48.00 10.21 0.10 0 482.00 14.30 132.00 2.06 31.10 11.00 0 平均值 43 7.32 1.82 420.49 49.70 94.03 19.00 0.44 833.31 29.55 536.11 4.67 65.62 15.64
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表 6 因子分析中各物理化学指标因子载荷
Table 6 Factor loadings of various physicochemical indices derived from factor analysis
指标 1 2 3 旋转前F1 旋转后F'1 旋转前F2 旋转后F'2 旋转前F3 旋转后F'3 t 0.691 0.055 −0.344 0.711 −0.107 0.313 pH 0.691 −0.023 −0.456 0.868 −0.308 0.163 TDS 0.583 0.986 0.801 0.077 −0.065 0.083 Na+ 0.650 0.970 0.738 0.178 −0.112 0.088 K+ 0.585 0.932 0.748 0.053 0.032 0.176 Ca2+ −0.731 0.009 0.439 −0.781 0.100 −0.356 Mg2+ −0.658 −0.016 0.379 −0.750 0.195 −0.228 ${\mathrm{CO}}_3^{2-} $ 0.669 0.199 −0.183 0.702 −0.265 0.138 ${\mathrm{HCO}}_3^{-} $ 0.056 0.857 0.934 −0.276 −0.234 −0.344 Cl− 0.846 0.742 0.403 0.291 0.246 0.551 F− 0.607 0.041 −0.352 0.842 −0.468 −0.035 HBO2 0.648 0.069 −0.215 0.217 0.673 0.931 As 0.738 0.101 −0.242 0.356 0.555 0.880
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