Discriminant Model of River-Lake Facies in the Upper Reach of Hanjiang Section of Jianghan Basin Based on Fisher Principle
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摘要: 为了探究Fisher模型在盆地第四纪河湖相演变上的实用性，以江汉盆地汉江上游段某单一钻孔的粒度资料和沉积相划分作为模型的训练样本，利用Fisher基本原理计算得到河湖相判别模型，最终利用模型实现对研究区沉积环境演化分析.依据单因素方差以及显著性分析结果可知，Fisher模型对河流相、河湖过渡相、湖相具有很好的区分效果.留一交叉验证结果达到80.6%，超过了判别模型应用要求的75%标准.同时，将多孔沉积相判别结果与定性划分结果进行了对比，其综合吻合率达到85.06%，进一步验证了Fisher模型在河湖相判别上的实用性.依据判别分析结果可知，自早更新世开始，研究区存在4期较大的沉积旋回，可划分为8个沉积阶段，不同沉积阶段水动力来源复杂且变化迅速，区域沉积环境演化与新构造运动相吻合.本研究说明依据粒度资料建立Fisher模型用于沉积相以及沉积环境的分析是可行的，同时丰富了江汉盆地汉江段沉积环境资料，为盆地水资源调查及保护提供重要参考.Abstract: In order to explore the practicality of the Fisher model in the Quaternary river-lake evolution of the basin, in this paper it takes the particle size data and sedimentary facies of a single borehole in the upper reach of the Hanjiang River in the Jianghan basin as the training samples of the model, which is calculated by Fisher's basic principle. Then the river-lake phase discrimination model is used to analyze the sedimentary environment evolution of the study area by using the model discrimination results. According to the one-way variance and the significance analysis results, the Fisher model has a good distinguishing effect on the river phase, the river-lake transition phase, and the lake phase. The leave-one-out-cross-validation result reaches 80.6%, exceeding the 75% standard required for the discriminant model application. At the same time, the results of the quantitative evaluation of porous sedimentary facies are compared with the qualitative classification results, and the comprehensive coincidence rate reaches 85.06%, which further verifies the practicality of the Fisher model in the identification of rivers and lakes. According to the results of discriminant analysis, since the Early Pleistocene, there are four large sedimentary cycles in the study area, which can be divided into eight sedimentary stages. The hydrodynamic sources are complex and changing rapidly in different sedimentary stages, and the regional sedimentary environment evolution and Neotectonic movement are consistent. This study demonstrates that it is feasible to establish Fisher model based on particle size data for analyzing sedimentary facies and sedimentary environment, and enrich the sedimentary environment data of Hanjiang Section of Jianghan basin. It provides an important reference for basin water resources investigation and protection.
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图 1 江汉盆地汉江上游段钻孔分布
Fig. 1. Distribution of boreholes in the upper reach of Hanjiang River in Jianghan basin
图 2 粒度频率曲线与典型沉积相
Fig. 2. Particle size frequency curves and typical sedimentary facies
图 3 沉积相判别二维分组图
Fig. 3. Two-dimensional grouping of discriminant phases of sedimentary facies
图 4 HJ015孔沉积相判别结果及其对比验证
Fig. 4. Discriminant results of HJ015 pore sedimentary facies and its comparative verification
图 5 HJ013孔粒度参数分布及沉积旋回划分
Fig. 5. Distribution of particle size parameters of boreholes and division of sedimentary cycles
图 6 多孔沉积相及沉积旋回划分图
Fig. 6. Sedimentary facies in the study area and division of sedimentary cycles
表 1 Fisher判别分析训练样本
Table 1. Training samples for Fisher discriminant analysis
样品编号 平均粒径 标准差 偏态 峰态 沉积相划分 01 51.131 101 62 3.554 969 -0.201 610 1.016 3 2 02 70.812 676 07 2.615 387 -0.233 360 1.191 4 2 03 62.780 400 69 3.925 418 -0.313 550 0.942 2 2 04 38.656 427 08 2.594 851 -0.326 720 1.314 7 1 05 112.966 903 1 3.234 160 -0.466 250 1.061 7 3 06 120.018 659 5 2.955 526 -0.436 710 1.109 6 3 07 17.032 798 07 3.786 894 -0.083 670 0.960 5 1 08 8.363 780 912 3.038 145 -0.023 800 1.012 1 1 09 8.844 834 076 2.807 966 -0.092 110 1.061 6 1 10 8.557 623 511 2.957 768 -0.061 010 0.988 4 1 11 10.098 961 50 3.099 973 -0.090 380 0.958 2 1 12 28.301 271 52 3.345 976 -0.232 760 1.062 3 1 13 56.514 773 28 4.097 760 -0.107 850 0.865 6 2 14 37.683 375 41 4.033 479 -0.171 590 0.970 0 2 15 59.472 706 67 6.581 987 -0.066 430 0.907 1 2 16 73.242 320 36 5.336 122 -0.272 020 0.755 0 2 17 80.871 407 31 4.891 506 -0.622 300 0.762 5 3 18 71.413 548 90 5.157 396 -0.458 660 0.743 0 3 19 39.514 562 71 5.187 817 -0.026 920 0.953 9 2 20 42.698 104 32 7.655 457 -0.033 190 0.918 6 2 21 11.290 370 79 3.124 726 -0.010 670 1.025 6 1 22 45.811 045 80 4.170 028 -0.330 520 0.770 7 1 23 12.601 434 68 6.230 988 0.367 407 1.299 4 2 24 122.301 223 2 3.715 868 -0.502 020 1.010 1 3 25 55.542 567 62 7.035 185 0.006 348 0.672 0 2 26 28.075 645 62 7.222 934 0.243 520 1.064 6 2 27 27.349 379 91 3.875 744 -0.140 160 0.950 7 2 28 62.439 108 34 6.212 808 -0.208 610 0.691 3 3 29 109.532 956 8 5.783 568 -0.467 120 0.708 5 3 30 38.261 742 89 3.544 544 -0.394 670 0.903 3 3 31 6.145 801 807 3.576 619 0.053 488 1.032 3 1 32 3.945 493 723 2.883 212 0.076 891 1.227 6 1 33 36.102 239 38 4.280 104 -0.008 410 0.776 0 2 34 67.319 464 44 3.844 993 -0.355 020 0.809 1 2 35 96.186 135 17 6.209 262 -0.507 750 0.678 2 3 36 103.590 710 3 6.170 378 -0.618 870 0.742 6 3 37 117.055 969 8 5.251 232 -0.619 390 0.814 5 3 
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表 2 不同沉积相质心函数
Table 2. The function of the centroid of each sedimentary facies
沉积相划分 判别函数1 判别函数2 湖相 2.424 -0.292 河湖过渡相 -0.772 1.356 河流相 -1.371 -1.558
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表 3 部分钻孔沉积物的沉积相判别结果
Table 3. Discriminant results of sedimentary facies in some borehole sediments
样品编号 最高概率组 次高概率组 沉积相划分结果 马氏距离 分组概率 预测分组 马氏距离 分组概率 预测分组 38 3.463 0.658 1 4.782 0.340 2 1 39 1.055 1.000 1 20.888 0.000 2 1 40 0.727 1.000 1 18.896 0.000 2 1 41 1.372 0.848 2 5.906 0.088 3 2 42 0.441 1.000 1 18.135 0.000 2 1 43 0.225 0.996 1 11.298 0.004 2 1 44 0.552 0.992 1 11.309 0.005 3 1 45 1.344 0.999 1 15.260 0.001 3 1 46 2.092 0.544 2 2.449 0.455 3 2 47 3.368 0.825 1 6.472 0.175 2 1
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表 4 组均值的均等性检验
Table 4. Equivalence test of mean within groups
Wilks的Lambda F df1 df2 Sig. 平均粒径 0.327 34.989 2 34 0.000 标准差 0.657 8.891 2 34 0.001 偏态 0.429 22.646 2 34 0.000 峰态 0.790 4.520 2 34 0.018
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表 5 箱式检验结果
Table 5. The results of the test box
箱的M 72.839 F 近似 2.989 df1 20 df2 3 507.550 Sig. 0.000
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表 6 判别函数方差附加特征值
Table 6. Additional eigenvalues of the variance of the discriminant function
判别函数 特征值 方差贡献率（%） 累计方差贡献率（%） 正则相关性 1 2.772 63.1 63.1 0.857 2 1.624 36.9 100.0 0.787
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表 7 留一交叉验证结果
Table 7. The results of LOOCV
湖相 河湖过渡相 河流相 总计 湖相 90.9% 9.1% 0% 100% 河湖交替相 13.3% 73.3% 13.3% 100% 河流相 10.0% 10.0% 80.0% 100%
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表 8 判别结果与定性分析结果对比
Table 8. Comparison of the results of discriminant analysis with the results of qualitative analysis
钻孔编号 样品数 识别正确个数及正确率(%) 识别错误个数及误判率(%) HJ012 19 15（78.95%） 4（21.05%） HJ014 23 21（91.30%） 2（8.70%） HJ015 45 38（84.44%） 7（15.56%） 总计 87 74（85.06%） 13（14.94%）
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