Multivariate Analysis, Mass Balance Techniques, and Statistical Tests as Tools in Igneous Petrology: Application to the Sierra de las Cruces Volcanic Range (Mexican Volcanic Belt)

Table 4

Tectonic discrimination analysis of intermediate magmas from the Sierra de las Cruces using multidimensional diagrams [21].

Figure name^a	Figure type^a	Total number of samples	Number of discriminated samples
			Arc			Within-plate	Collision
			IA + CA [𝑥±𝑠]; (𝑝IA+CA)^b	IA [𝑥±𝑠]; (𝑝IA)^b	CA [𝑥±𝑠]; (𝑝CA)^b	CR + OI [𝑥±𝑠]; (𝑝CR+OI)^b	Col [𝑥±𝑠]; (𝑝Col)^b
Major elements	1+2-3+4-5	10	0	—	—	3  [0.27±0.31]; (0.009–0.767)	7  [0.52±0.30]; (0.152–0.848)
	1-2-3+4	10	—	0	8  [0.60±0.29]; (0.108–0.944)	2  [0.25±0.32]; (0.015–0.858)	—
	1-2-5	10	—	0	5  [0.44±0.24]; (0.068–0.946)	—	5  [0.45±0.23]; (0.030–0.861)
	1-3+4-5	10	—	0	—	3  [0.28±0.32]; (0.011–0.802)	7  [0.62±0.32]; (0.147–0.959)
	2-3+4-5	10	—	—	4  [0.39±0.17]; (0.159–0.778)	1  [0.19±0.21]; (0.010–0.650)	5  [0.42±0.26]; (0.032–0.756)
All major element based diagrams	{∑𝑛}   {∑prob}; [% prob]	{50}	{0}  {0.0}; [---]	{0}  {0.0}; [0%]	{17}  {16.552}; [37.9%]	{9}  {7.112}; [16.3%]	{24}  {20.061}; [ 45.8% ]
Major and trace elements	1+2-3+4-5	9	3  [0.34±0.33]; (0.005–0.846)	—	—	6  [0.49±0.35]; (0.016–0.886)	0
	1-2-3+4	9	—	1  [0.19±0.20]; (0.004–0.584)	2  [0.27±0.20]; (0.012–0.545)	6  [0.55±0.38]; (0.012–0.984)	—
	1-2-5	9	—	1  [0.27±0.17]; (0.016–0.518)	6  [0.42±0.16]; (0.042–0.567)	—	2  [0.31±0.30]; (0.045–0.942)
	1-3+4-5	9	—	3  [0.31±0.32]; (0.005–0.816)	—	6  [0.50±0.33]; (0.019–0.855)	0
	2-3+4-5	9	—	—	5  [0.51±0.38]; (0.002–0.921)	4  [0.37±0.31]; (0.012–0.855)	0
All major and trace element based diagrams	{∑𝑛}  {∑prob}; [% prob]	{45}	{3}  {3.037}; [---]	{5}  {8.023}; [17.8%]	{13}  {12.649}; [28.1%]	{22}  {17.163}; [ 38.1%]	{2}  {7.193}; [16.0%]
Trace elements	1+2-3+4-5	10	6  [0.47±0.33]; (0.019–0.822)	—	—	2  [0.20±0.32]; (0.001–0.961)	2  [0.33±0.27]; (0.016–0.933)
	1-2-3+4	10	—	0	7  [0.50±0.25]; (0.026–0.938)	3  [0.27±0.36]; (0.001–0.958)	—
	1-2-5	10	—	1  [0.21±0.16]; (0.009–0.467)	7  [0.49±0.18]; (0.050–0.676)	—	2  [0.30±0.26]; (0.090–0.942)
	1-3+4-5	10	—	5  [0.41±0.32]; (0.012–0.785)	—	3  [0.21±0.32]; (0.002–0.940)	2  [0.39±0.29]; (0.026–0.941)
	2-3+4-5	10	—	—	7  [0.62±0.35]; (0.026–0.925)	2  [0.17±0.31]; (0.001–0.958)	1  [0.20±0.24]; (0.016–0.838)
All trace element based diagrams	{∑𝑛}  {∑prob}; [% prob]	{50}	{6}  {4.715}; [---]	{6}  {9.459}; [18.9%]	{21}  {19.856}; [ 39.7% ]	{10}  {8.503}; [17.0%]	{7}  {12.178}; [24.4%]

a“Figure name” corresponds to one of the three sets of diagrams based on major elements, immobile major and trace elements, and immobile trace elements, respectively, whereas “Figure type” gives the tectonic fields being discriminated where the tectonic group numbers are as follows: 1—IA (island arc), 2—CA (continental arc), 3—CR (continental rift) and 4—OI (ocean island) together as within-plate, and 5—Col (collision); 𝑥±𝑠—mean ± one standard deviation of the probability estimates for all samples discriminated in a given tectonic setting; these are reported in [].
^bProbability estimates for different tectonic groups are summarized after the number of discriminated samples as follows: [𝑝_IA+CA]—range of probability values estimated for IA + CA combined setting, [𝑝_IA]—for IA, [𝑝_CA]—for CA, [𝑝_CR+OI]—for CR + OI, and [𝑝_Col]—for Col. Boldface font shows the expected or more probable tectonic setting; the final row gives a synthesis of results as {∑𝑛}  {∑prob}  [%prob] where one has the following: {∑𝑛}—number of samples plotting in all five diagrams which are reported in the column of total number of samples whereas the sum of samples plotting in a given tectonic field is reported in the respective tectonic field column, {∑prob}—sum of probability values for all samples plotting in a given tectonic field which are reported in the respective tectonic field column, and [%prob]—total probability of a given tectonic setting expressed in percent after assigning the probability of IA + CA to IA and CA using weighing factors. For details of principles, equations, and application rules of the multidimensional diagrams see [21].