One-dimensional to three-dimensional density distribution functions and their applications in visualized big data analysis: Exemplified by picritic basalt and some other rocks
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摘要:
提出不同维度的密度分布函数的计算方法和可视化方案，以解决不同数量级和不同测量误差的岩石样本数据分析对比困难的问题。通过SiO2、全碱和MgO指标的三维密度分布函数和t-分布随机邻域嵌入可视化方法对GEOROC和PETDB数据库进行发掘，发现大洋岩（oceanite）和富辉橄玄岩（ankaramite）与苦橄质玄武岩（basalt，picritic）成分相近，而铁质苦橄岩（picrite，ferro）与侵入的橄榄辉长岩和苦橄岩（picrite）成分相似。利用二维密度分布函数和可视化技术，对比分析了不同岩石在TAS图解和硅镁图上的数据分布状态和数据集中核心区域。发现总体分布上，更富镁的苦橄岩的SiO2含量高于苦橄质玄武岩，超基性的苦橄岩（picrate）核心区域主要分布在TAS图解的B区，这与以SiO2=45%划分基性岩和超基性岩界线的观点矛盾。
Abstract:In this paper, the calculation methods and visualization schemes of density distribution functions of different dimensions are proposed to solve the problem of difficulties in analysis and comparison of rock sample data with different orders of magnitude and different measurement errors. Data mining based on the GEOROC and PETDB databases by using the three-dimensional density distribution function of SiO2, total alkali and MgO index as well as the t-distribution random neighborhood embedding visualization method revealed that picritic basalt is similar to oceanite and ankaramite, while picrate is similar to intrusive olivine gabbro and ferropicrate. Comparisons between two-dimensional density distribution function and cumulative density contour visualization were used to analyze the data distribution of different rocks on TAS and Si-Mg maps and the core area of data concentration. It is found that the SiO2 content of magnesium-rich picrite is higher than that of picrite basalt in general distribution. The core area of picrite is mainly located in the B area of TAS diagram, which is contrary to the traditional view that SiO2=45% is used as the boundary between basic and ultramafic rocks.
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Keywords:
- density distribution function /
- visualization /
- big data /
- picrite /
- picritic basalt
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图 1 一维到三维密度分布分析及其可视化流程图
Figure 1. 1-D to 3-D density distribution analysis and visualization flow chart
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图 2 SiO2-全碱-MgO三维密度分布函数的t-sne可视化
（圆圈的半径代表数据量的大小，圆圈的距离与密度分布函数的相似程度有关，三维密度函数接近的岩石在二维图中距离越接近）
Figure 2. T-sne visualization of three-dimensional density distribution function of SiO2-Na2O+K2O-MgO
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图 3 8类岩石数据的SiO2-全碱投图和二维累积密度分布函数可视化（a~h分别为8类岩石数据的SiO2-全碱投图和二维密度分布函数等高线，紫色-淡红色等不同颜色代表累积密度从10%递增到100%；样本数据点同样按照累积密度等高线的数值进行了涂色；i是8类岩石50%核心区域的等高线，其中红色曲线代表苦橄质玄武岩、大洋岩、富辉橄玄岩；绿色曲线代表苦橄岩、铁质苦橄岩、橄榄辉长岩；蓝色曲线代表玄武岩和拉斑玄武岩）
Pc—苦橄玄武岩；B—玄武岩；O1—玄武安山岩；O2—安山岩；O3—英安岩；R—流纹岩；S1—粗面玄武岩；S2—玄武质粗面安山岩；S3—粗面安山岩；T—粗面岩、粗面英安岩；F—似长石岩；U1—碱玄岩、碧玄岩；U2—响岩质碱玄岩；U3—碱玄质响岩；Ph—响岩
Figure 3. SiO2- (Na2O+K2O)maps and visualization of two-dimensional cumulative density distribution function for 8 rock data
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图 4 8类岩石数据的SiO2-MgO投图和二维累积密度分布函数可视化
（a~h分别是8类岩石数据的SiO2-MgO投图和二维密度分布函数等高线，其中图例同图 3）
Figure 4. SiO2-MgO maps and visualization of two-dimensional cumulative density distribution function for 8 rock data
表 1 各类岩石样本数量和t-sne投影的坐标统计
Table 1 Statistics of the number of rock samples and the coordinates of t-sne projection
岩石名称 样本数量 x y BASALT 64352 15.58721 -10.9474 ANDESITE 17916 21.4111 -10.6686 RHYOLITE 14007 27.85793 -6.25479 THOLEIITE 10955 16.06146 -11.0261 ANDESITE, BASALTIC 10280 18.69086 -10.4295 DACITE 9632 23.64114 -8.29206 BASALT, ALKALINE 6740 14.7485 -7.35955 BASANITE 4503 14.01691 -4.57348 TRACHYTE 4281 26.31998 -5.30974 DOLERITE 4150 15.61033 -11.0084 GABBRO 3911 15.36645 -12.8639 BASALT, THOLEIITIC 3086 16.08896 -10.9825 KOMATIITE 2775 20.62374 -1.04221 TRACHYBASALT 2616 16.46776 -6.83638 DIABASE 2577 16.00959 -11.5096 PHONOLITE 2360 27.12145 -4.78326 HAWAIITE 2284 16.52253 -6.8893 KIMBERLITE 2183 22.28322 -2.60571 TRACHYANDESITE 2159 20.31939 -6.99264 PICRITE 2041 12.17082 -10.4823 GRANITE 1950 26.97359 -6.63372 PERIDOTITE 1692 21.06825 -3.27859 BASALT, OLIVINE 1628 14.923 -10.3652 RHYODACITE 1420 24.47356 -7.45667 TRACHYANDESITE, BASALTIC 1371 18.51673 -7.00667 THOLEIITE, OLIVINE 1062 14.85753 -10.7395 GRANODIORITE 1052 23.58413 -8.47572 BASALT, ALKALINE, OLIVINE 1043 14.93627 -7.37283 BASALT, TRANSITIONAL 1028 15.26546 -9.62936 AMPHIBOLITE 994 15.54768 -12.2647 SHOSHONITE 964 18.75574 -7.2569 MUGEARITE 929 18.29329 -6.94383 LAMPROPHYRE 860 13.60072 -6.21256 ADAKITE 851 23.28493 -9.10343 NEPHELINITE 828 13.22807 -2.34986 TEPHRA 793 19.43718 -9.34711 TEPHRITE 782 14.38127 -5.19469 GRANULITE 779 15.48294 -13.2801 DIORITE 771 21.66719 -11.5719 LHERZOLITE, SPINEL, XENOLITH 770 19.70123 -3.84926 LATITE 676 20.40854 -6.92619 BONINITE 651 17.89986 -13.172 SERPENTINITE 308 20.96866 -2.27882 SYENITE, NEPHELINE 304 26.82648 -4.19666 NEPHELINITE, OLIVINE 300 13.65233 -2.65991 ANDESITE, THOLEIITIC 291 18.6852 -10.1085 DIORITE, QUARTZ 282 21.47555 -10.9256 DUNITE 278 25.30984 -4.2026 SANDSTONE 275 28.60756 -7.08053 ANDESITE, HORNBLENDE 274 21.53134 -10.2483 TRACHYTE, ALKALINE 274 26.14345 -5.14133 FOIDITE 260 12.75653 -2.12454 BASALT, PICRITIC 258 12.25989 -8.42502 KOMATIITE, PERIDOTITIC 253 20.65545 -1.33371 BRECCIA 250 17.77428 -12.6955 HARZBURGITE, SPINEL, XENOLITH 233 20.42683 -4.38752 ANDESITE, HYPERSTHENE-AUGITE 224 20.10768 -10.4155 GRANOPHYRE 212 26.01027 -7.47253 GRANITE, BIOTITE 211 27.42636 -6.28287 LHERZOLITE, GARNET, XENOLITH 208 20.37776 -3.82075 GABBRO, OLIVINE 203 12.6403 -11.0718 MINETTE 189 18.14181 -5.84798 DUNITE, XENOLITH 187 22.27814 -4.36065 ANDESITE, 2-PYROXENE 186 20.50536 -10.2287 LEUCITITE 179 16.38811 -4.22292 BASALT, SHOSHONITIC 171 17.19932 -7.11009 SCHIST 170 16.81794 -14.5571 RHYOLITE, PERALKALINE 168 29.3796 -5.73169 ANDESITE, CALC-ALKALINE 167 21.03326 -10.2375 GREYWACKE 163 23.37688 -10.1065 GABBRO, HORNBLENDE 161 15.04572 -12.0369 PICRITE, FERRO 154 12.55557 -11.0981 KAMAFUGITE 149 13.79827 -2.67388 META-BASALT 141 13.97634 -10.6699 BASALT, OLIVINE-AUGITE 140 16.18754 -9.64572 LATITE, QUARTZ 140 23.46039 -7.10849 CARBONATITE, NATRO 139 29.91534 -5.4673 GRANODIORITE, HORNBLENDE- BIOTITE 138 23.33243 -8.18094 IJOLITE 137 18.40342 -3.13221 BASALT, PLAGIOCLASE 134 15.63237 -9.35873 GRANODIORITE, BIOTITE 133 24.2588 -7.49518 SYENITE, QUARTZ 133 27.05632 -5.49837 WEHRLITE 132 20.79014 -1.90888 OCEANITE 130 12.24017 -7.43482 CARBONATITE 630 24.04427 -5.02497 BASALT, KOMATIITIC 625 12.99641 -12.8862 PYROXENITE 576 10.73488 -10.634 PERIDOTITE, XENOLITH 567 22.3647 -4.38247 LHERZOLITE, XENOLITH 561 19.89378 -3.86592 SYENITE 529 26.50009 -5.27382 LHERZOLITE 512 20.09564 -3.43263 GNEISS 502 25.04601 -9.08702 ANDESITE, AUGITE- HYPERSTHENE 492 20.32324 -10.5224 BENMOREITE 475 20.48017 -6.71672 PHONOTEPHRITE 473 16.8542 -4.36147 PHONOLITE, TEPHRI 469 17.4231 -4.07109 HARZBURGITE, XENOLITH 454 20.6322 -4.34245 BASALT, CALC-ALKALINE 447 17.44508 -11.11 TONALITE 430 23.25654 -9.35807 THOLEIITE, QUARTZ 427 16.85698 -10.7168 LAMPROITE 425 18.13194 -5.69225 BASALTIC ANDESITE 414 18.62987 -10.4017 BASALT, SUBALKALINE 406 15.58202 -10.2094 ANKARAMITE 404 12.39872 -8.09435 PANTELLERITE 401 28.84587 -6.0132 ALKALI BASALT 376 14.92808 -7.45134 GREENSTONE 375 14.26073 -7.98944 ANDESITE, PYROXENE 364 20.74207 -10.4955 TRACHYDACITE 358 23.74495 -6.6863 COMENDITE 335 28.86098 -6.02774 BASALT, ANDESITIC 324 18.24308 -10.1489 HARZBURGITE 317 21.28159 -4.13447 PERIDOTITE, SPINEL, XENOLITH 314 20.04048 -3.85302 ANDESITE, OLIVINE 129 19.14709 -11.091 GABBRONORITE 129 14.12052 -11.8272 CARBONATITE, CALCITE 125 24.21048 -5.31015 PYROXENITE, XENOLITH 125 18.24421 -0.99496 MONZONITE 124 19.71715 -7.20648 CLINOPYROXENITE 123 18.19991 -1.06767 NEPHELINITE, MELILITE 123 14.32507 -1.5421 ANDESITE, BASALTIC, CALC-ALKALINE 122 18.2815 -9.66621 ECLOGITE 122 14.00808 -9.68333 ASH 121 28.73349 -5.64124 BASALT, AUGITE-OLIVINE 121 16.23734 -10.202 BASANITE, LEUCITE 121 15.00156 -4.76666 MELILITITE, OLIVINE 119 15.84212 -1.30137 TEPHRITE, LEUCITE 119 16.90621 -4.32697 KOMATIITE, BASALTIC 115 12.97848 -12.8844 LAMPROPHYRE, SHOSHONITIC 114 20.37735 -13.1823 ABSAROKITE 113 15.99625 -7.46797 MELILITITE 111 14.73207 -1.42496 ANDESITE, OLIVINE- AUGITE- HYPERSTHENE 109 19.51345 -10.4657 TRACHYPHONOLITE 109 25.84436 -5.11671 TRONDHJEMITE 109 25.15069 -7.20645 CAMPTONITE 107 13.91801 -5.10844 BASANITE, NEPHELINE 103 13.86844 -4.0752 RHYOLITE, ALKALINE 103 28.50523 -6.15424 TURBIDITE 102 20.15457 -11.9278 PELITE 101 22.64466 -11.4284 LIMBURGITE 100 13.73771 -3.64633 MONZONITE, QUARTZ 100 23.11145 -7.15484 TRACHYTE, COMENDITIC 100 27.70746 -5.52258 
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