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

Figure 1 shows a very simplistic version of a copper mineralization associated to a zone of fractures 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:
* Is a close system, meaning that the sum of all the values is equal or very close to 100%
* There are no zero values present (I will deal with zero values in a separate example to avoid complicating the initial model).
* There are no statistical outliers (hurricane values) present.
* There is a big difference between the concentRations of the major oxides with respect to the trace elements.
* As shown in Figs. 2-4, there are embedded positive and significant correlation between Cu and As, Ni and Co, and MgO and K$_2$O.
* Finally, I introduced significant negative correlations between K$_2$O and CaO (Fig. 5), SiO$_2$ and Al$_2$O$_3$ (Fig 6), K$_2$O and Cu (Fig. 7), Na$_2$O and K$_2$O (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.