Why, and How, Should Geologists Use Compositional Data Analysis/The Model

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Why, and How, Should Geologists Use Compositional Data Analysis

Summary — The Model — Normal Processing of the Data — Factor Analysis — Dealing With Zero Values — Conclusions and Recommendations — References — Licensing — Discuss

Figure 1 shows a very simplistic version of a copper mineralization associated to a zone of fractures within a granodiorite intrusive.

Figure 1. Ore deposit model of a copper mineralization associated to a tectonic zone within a granodiorite intrusive.

Table 1 shows the results of a random sampling using existing access to the top of the intrusive.

Table 1. Chemical composition of the sampling of the granodiorite intrusive.


Sample Easting Northing SiO2 TiO2 Al203 Fe2O3 MgO CaO K2O Na2O P2O5
259021 845962.7 833189 56.00 2.20 6.00 3.62 5.11 2.08 5.03 7.08 3.00
259022 831978.5 859092 57.00 1.25 4.00 2.54 5.40 2.19 5.08 7.19 3.74
259023 857644.3 846310 55.00 2.05 7.00 3.86 5.55 2.29 5.19 7.29 3.46
259024 840369.6 833920 62.00 2.19 0.00 2.47 5.63 2.29 5.29 7.29 3.80
259025 833367.4 857854 56.04 1.14 6.00 3.66 5.69 2.43 5.29 7.43 3.14
259026 841526.8 837288 58.36 1.48 2.00 2.75 5.89 2.45 5.43 7.45 3.70
259027 850152.3 854634 61.00 1.60 1.00 2.26 5.95 2.49 5.45 7.49 3.17
259028 836406.1 847121 57.34 1.58 4.02 2.94 6.25 2.54 5.49 7.54 3.26
259029 893494.7 891521 62.00 1.25 0.66 2.21 6.28 2.55 5.54 7.55 3.08
259030 898079.8 900849 61.00 1.60 1.85 3.19 6.44 2.60 5.55 7.60 3.96
259031 917124.2 893796 61.00 2.05 1.49 2.55 6.46 2.63 5.60 7.63 3.66
259032 904564.7 893086 59.02 1.15 1.04 2.70 6.47 2.65 5.63 7.65 3.85
259033 900474.9 898141 59.00 1.36 2.47 3.53 6.49 2.68 5.65 7.68 3.44
259034 894560.4 895311 59.00 1.61 2.34 3.56 6.82 2.71 5.68 7.71 3.36
259035 913232.2 903356 57.80 2.15 3.09 2.63 6.98 2.86 5.71 7.86 3.45
259036 893128.5 902967 56.44 1.15 6.00 3.48 6.98 2.91 5.86 7.91 3.40
259037 892202.8 894592 59.00 1.41 2.30 2.59 7.18 2.99 5.91 7.99 3.13
259038 913071.1 897870 57.30 1.06 4.00 3.62 7.22 3.02 5.99 8.02 3.82
259039 906249.3 907340 58.09 1.71 3.50 2.51 7.74 3.10 6.02 8.10 3.66
259040 916724.1 891607 57.00 1.16 4.00 3.27 7.83 3.15 6.10 8.15 3.83
259041 909848.3 915457 60.00 1.47 1.44 2.47 7.89 3.38 6.15 8.38 3.27
259042 915608.1 915306 57.47 1.83 3.00 3.57 7.95 3.56 6.38 8.56 3.28
259043 871460 863020 55.66 1.03 7.00 2.23 7.96 3.58 6.56 8.58 3.08
259044 877894.5 886973 59.00 1.13 2.00 3.33 8.07 3.68 6.58 8.68 3.99
259045 886538.3 888754 59.00 1.80 2.80 2.36 8.10 3.71 6.68 8.71 3.60
259046 860434.9 872223 53.00 1.36 5.00 3.16 8.28 3.82 6.71 8.82 3.90
259047 885897.4 864158 57.00 1.43 4.00 2.09 8.30 3.88 6.82 8.88 3.91
259048 867351 861364 54.30 2.16 4.00 3.98 8.57 3.90 6.88 8.90 3.83
259049 860971.4 864924 54.20 1.77 3.36 3.72 8.59 3.91 6.90 8.91 3.82
259050 866588.3 860513 58.50 1.00 2.00 3.10 8.83 1.00 6.91 2.00 3.65
Sample Easting Northing Cu As Pb Co Ni Sc L.O.I. Other
259021 845962.7 833189 0.00191 0.00199 0.00002 0.00002 0.00002 0.01936 6.19 9.88
259022 831978.5 859092 0.00190 0.00198 0.00003 0.00004 0.00005 0.01763 8.16 11.61
259023 857644.3 846310 0.00188 0.00196 0.00003 0.00010 0.00012 0.02056 5.09 8.31
259024 840369.6 833920 0.00182 0.00190 0.00006 0.00014 0.00017 0.00013 5.97 9.03
259025 833367.4 857854 0.00171 0.00179 0.00006 0.00015 0.00018 0.01834 6.60 9.18
259026 841526.8 837288 0.00168 0.00176 0.00004 0.00022 0.00026 0.01058 8.01 10.48
259027 850152.3 854634 0.00158 0.00166 0.00005 0.00023 0.00027 0.00341 7.40 9.59
259028 836406.1 847121 0.00156 0.00164 0.00003 0.00025 0.00030 0.01372 6.97 9.03
259029 893494.7 891521 0.00138 0.00146 0.00005 0.00027 0.00032 0.00035 7.00 8.88
259030 898079.8 900849 0.00115 0.00123 0.00002 0.00027 0.00033 0.00085 4.00 6.22
259031 917124.2 893796 0.00110 0.00117 0.00005 0.00030 0.00036 0.00119 4.00 6.92
259032 904564.7 893086 0.00102 0.00110 0.00002 0.00032 0.00038 0.00799 8.00 9.84
259033 900474.9 898141 0.00099 0.00107 0.00002 0.00032 0.00039 0.00725 5.00 7.69
259034 894560.4 895311 0.00091 0.00099 0.00004 0.00034 0.00041 0.00623 4.00 7.20
259035 913232.2 903356 0.00086 0.00094 0.00003 0.00036 0.00043 0.01060 5.00 7.47
259036 893128.5 902967 0.00071 0.00079 0.00001 0.00043 0.00052 0.01361 3.00 5.88
259037 892202.8 894592 0.00068 0.00076 0.00001 0.00045 0.00054 0.00629 5.00 7.51
259038 913071.1 897870 0.00065 0.00073 0.00005 0.00049 0.00059 0.01008 2.00 5.94
259039 906249.3 907340 0.00063 0.00071 0.00005 0.00051 0.00061 0.00812 1.50 5.57
259040 916724.1 891607 0.00060 0.00068 0.00004 0.00055 0.00066 0.01036 1.56 5.50
259041 909848.3 915457 0.00055 0.00062 0.00004 0.00058 0.00069 0.00220 2.00 5.55
259042 915608.1 915306 0.00054 0.00062 0.00004 0.00069 0.00083 0.00707 1.23 4.39
259043 871460 863020 0.00049 0.00057 0.00001 0.00078 0.00094 0.01274 1.12 4.32
259044 877894.5 886973 0.00045 0.00053 0.00004 0.00079 0.00095 0.00172 0.35 3.53
259045 886538.3 888754 0.00043 0.00051 0.00004 0.00084 0.00101 0.00157 0.08 3.24
259046 860434.9 872223 0.00029 0.00037 0.00003 0.00085 0.00103 0.00855 1.25 5.96
259047 885897.4 864158 0.00029 0.00037 0.00004 0.00091 0.00109 0.00642 0.08 3.68
259048 867351 861364 0.00019 0.00027 0.00001 0.00094 0.00113 0.00461 0.05 3.46
259049 860971.4 864924 0.00008 0.00016 0.00003 0.00095 0.00114 0.00149 0.89 4.81
259050 866588.3 860513 0.00003 0.00011 0.00005 0.00096 0.00115 0.00099 6.94 13.01

The initial data respond to the following pre-established conditions:

  1. Is a close system, meaning that the sum of all the values is equal or very close to 100%
  2. There are no zero values present (I will deal with zero values in a separate example to avoid complicating the initial model).
  3. There are no statistical outliers (hurricane values) present.
  4. There is a big difference between the concentRations of the major oxides with respect to the trace elements.
  5. As shown in Figs. 2-4, there are embedded positive and significant correlation between Cu and As, Ni and Co, and MgO and K2O.
  6. Finally, I introduced significant negative correlations between K2O and CaO (Fig. 5), SiO2 and Al2O3 (Fig 6), K2O and Cu (Fig. 7), Na2O and K2O (Fig. 8), and Co with Cu (Fig 9).


According to these embedded conditions, any correlation analysis must give us two coefficients (Range Correlation Coefficient or RCC):

Equation 1
Range Correlation Coefficient type A for the initial data, according to the embedded correlations.
Equation 2
Range Correlation Coefficient type B for the initial data, according to the embedded correlations.
Why, and How, Should Geologists Use Compositional Data Analysis
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