Predictions for Rocks of Unknown Tectonic Affinity

We will now apply the classification tree method to a published dataset of 20 basalts from the Pindos Basin in Greece (Saccani et al., 2003). This exercise will serve as an illustration of the way the tree method works in practice, and of its limitations. The features relevant to the classification tree analysis are shown in Table 9. As a first example, consider sample GR 47b. It travels through the full classification tree of Figure 4 as follows: TiO$_2$$<$2.135% $\rightarrow$ Sr$\geq$156ppm $\rightarrow$ TiO$_2$$\geq$1.285% $\rightarrow$ MgO$<$9.595% $\rightarrow$ MgO$\geq$5.775% $\rightarrow$ Rb $\geq$ 3.675ppm. The same sample travels through the HFS tree of Figure 5 along the following path: TiO$_2$$<$2.135% $\rightarrow$ TiO$_2$$\geq$1.046% $\rightarrow$ Nd$<$12.785ppm. Note that for the last step, the second surrogate variable was used (Table 1), because no isotopic ratios were measured for these samples. No rare earth elements were measured for sample GR 56c. Therefore, its path through the HFS tree stops at node 4, where a ``follow the majority'' decision must be made. Since the distribution of training data in this node is IAB/MORB/OIB = 73/194/43 (Table 2), GR 56c is classified as a MORB, albeit not with the greatest confidence.

Table 9: Summary of geochemical analyses of Triassic basalts of the Pindos Basin, from Saccanti et al. (2003). Most of the analyses point towards a MORB affinity for these rocks. There is agreement between the full classification tree and the one that only uses HFS elements for half of the samples (all agreeing on a MORB affinity). The cases where there is disagreement between the two classifications could be due to the selective loss of Mg and Sr. Sample GR 181b was classified as an IAB with a probability of only $\sim$2/3.

sample	TiO2	MgO	Ni	Rb	Sr	Nb	Nd	Yb	affinity		comment
name	(%)	(%)	(ppm)	(ppm)	(ppm)	(ppm)	(ppm)	(ppm)	full tree	HFS only
GR 47b	1.41	6.60	81	17	163	10.6	12.3	2.87	MORB	MORB
GR 50c	1.60	8.36	61	7	225	9.69	13.1	3.16	MORB	MORB
GR 50d	1.52	5.69	56	18	176	-	-	-	IAB	MORB	Mg loss?
GR 50e	1.56	5.60	66	20	138	9.38	13.1	3.31	MORB	MORB
GR 51a	1.18	7.22	104	4	242	6.87	9.5	2.17	IAB	MORB
GR 51b	1.17	7.05	97	5	180	-	-	-	IAB	MORB
GR 56a	1.68	6.57	85	4	98	5.87	14	3.15	MORB	MORB
GR 56b	1.61	6.77	72	5	200	4.23	11.8	3.40	MORB	MORB
GR 56c	1.68	6.90	65	5	81	-	-	-	MORB	MORB
GR 56d	1.52	6.33	72	7	247	3.94	11.8	3.37	MORB	MORB
GR 71a	2.82	6.87	76	4	114	3.74	19.8	5.96	MORB	OIB	Sr loss?
GR 71b	2.79	6.82	73	3	115	-	-	-	MORB	OIB	Sr loss?
GR 71c	2.36	7.24	80	3	166	3.27	17.7	5.00	MORB	OIB	Sr loss?
GR 71d	2.80	7.12	75	5	125	3.66	19.7	5.92	MORB	OIB	Sr loss?
GR 71e	2.89	6.66	71	3	124	-	-	-	MORB	OIB	Sr loss?
GR 181a	1.38	6.61	83	8	176	-	-	-	MORB	MORB
GR 181b	1.50	7.32	88	4	152	4.18	21.8	6.55	MORB	IAB	43/20/0
GR 181c	1.35	6.64	90	8	366	1.65	10.1	2.91	MORB	MORB
GR 181d	1.30	6.21	85	4	76	-	-	-	MORB	MORB
GR 195a	2.43	6.55	63	4	102	4.35	17.6	5.37	MORB	OIB	Sr loss?

There is agreement between the full tree and the HFS tree for only half of the samples. Samples GR 50d, 51a and 51b were classified as IAB by the full tree, and as MORB by the HFS tree. The distinction between IAB and MORB is the hardest one to make. IABs have a much greater compositional diversity than both MORBs and OIBs. This is also reflected in most discrimination diagrams (see for example Figure 6). Furthermore, it might be possible that Mg was lost during the greenschist metamorphism that affected the Pindos ophiolites (Saccani et al., 2003). This would have caused sample GR 50d to be sent left, rather than right at node 7 of Figure 4. Likewise, it is possible that Sr-loss caused samples GR 71a-e and 195a to be sent left, rather than right at node 3 of the full tree. Finally, sample GR 181b was classified as an IAB by the HFS tree (Figure 5). However, its terminal node (left branch of node 5) is not very pure: IAB/MORB/OIB = 43/20/0, once again illustrating the difficulty of distinction between MORB and IAB affinities, which is caused by the complicated petrogenesis of the latter.