JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, B06206, doi: /2005jb003799, 2006

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2005jb003799, 2006 A reevaluation of tectonic discrimination diagrams and a new probabilistic approach using large geochemical databases: Moving beyond binary and ternary plots Cameron A. Snow 1 Received 26 April 2005; revised 15 February 2006; accepted 14 March 2006; published 20 June [1] Statistically rigorous confidence intervals calculated from analyses of basaltic volcanic samples obtained from two large geochemical databases (PetDB and GEOROC) demonstrate that published binary and ternary discrimination diagrams seldom correctly classify samples from mid-ocean ridges, island arcs, and ocean islands with better than 60% accuracy. The confidence intervals provide a measure of certainty that was previously absent from these diagrams, allowing for a more robust analysis of results. A new probabilistic method for geochemical discrimination is developed using the geochemical databases. The new method is N-dimensional and uses a priori data to construct probability distribution functions from which a posteriori probabilities are generated. Tests of the new method demonstrate single analysis classification success rates for volcanic rocks from island arcs to be 83%, from ocean islands to be 75%, and from mid-ocean ridges to be 76%. Citation: Snow, C. A. (2006), A reevaluation of tectonic discrimination diagrams and a new probabilistic approach using large geochemical databases: Moving beyond binary and ternary plots, J. Geophys. Res., 111,, doi: /2005jb Introduction [2] Determining the original plate tectonic setting of basaltic lavas now removed from their setting of origin is a formidable task central to unraveling the geologic history of complex areas. In order to differentiate between volcanic rocks erupted at mid-ocean ridges, ocean islands, and island arcs, several authors developed discrimination diagrams, which allow for distinctions in plate tectonic setting to be made based on the geochemistry of the sample [e.g., Pearce and Cann, 1973; Pearce, 1974; Pearce and Norry, 1979; Wood, 1980; Pearce, 1982; Shervais, 1982; Mullen, 1983]. These diagrams are widely cited in the literature, and many studies concerned with determining the original tectonic settings of volcanic rocks have utilized them. [3] There are several inherent difficulties in constructing discrimination diagrams. The most vexing problem is that geochemical theory, though well understood in a qualitative sense, is not constrained well enough to accurately predict absolute elemental abundances for chemically complex systems. Volcanic rocks from island arcs (VAB), for example, have a broad range of trace element abundances that cannot be readily modeled without defining several parameters (e.g., fluid flux from slab, proportions of mantle wedge vs. slab vs. subducted sediment sources, etc.) that are difficult, if not impossible, to constrain. An additional difficulty is that the compositional ranges for VAB greatly overlap those of volcanic rocks from mid-ocean ridges 1 Department of Geological and Environmental Sciences, Stanford University, Stanford, California, USA. Copyright 2006 by the American Geophysical Union /06/2005JB003799$09.00 (MORB) and ocean islands (OIB). This overlap is largely due to source similarities among VAB, MORB and OIB. For example, an island arc system dominated by a mantle wedge signature is difficult to chemically distinguish from MORB when viewed in binary and ternary systems. Therefore it is necessary to use multiple elements and rigorous statistics when using geochemistry to determine the tectonic setting of volcanic terranes of unknown origin. This paper will focus on treating the data in a statistically rigorous manner, and will not attempt to discern the underlying physical processes that are influencing the chemistry. Thorough reviews of the geochemical theories behind discrimination diagrams are given by Rollinson [1993] and Pearce [1996]. [4] Though the basis for discrimination diagrams is geochemical theory, the discrimination fields are statistical. Pearce [1996] documented that the discrimination fields were determined by eye and neither based on statistical theory nor rigorously tested after their initial conception. Pearce [1996] also hypothesized that to thoroughly discriminate amongst lavas from different tectonic settings several elements are needed. However, none of the most commonly used discrimination diagrams allow for simultaneous evaluation of more than three elements because they are visually based. Furthermore, because these diagrams have fields that are not statistically based it is impossible to evaluate the certainty of interpretations made from them. [5] Since the development of these diagrams, large geochemical databases such as GEOROC ( and PetDB ( have been constructed. These databases contain thousands of whole rock analyses of volcanic rocks from different locales of known geologic setting. This study utilizes those 1of13

2 Figure 1. World map with names and locations of mid-ocean ridge (squares), island arc (diamonds), and ocean island (circles) samples used in this study. databases to rigorously evaluate previous discrimination methods by presenting statistically rigorous confidence intervals for many of the most widely used discrimination diagrams and discusses their statistical attributes. This study also proposes a new probabilistic discrimination method that utilizes seven elements and multiplicative rule statistics to classify lavas from mid-ocean ridges, ocean islands, and island arcs. 2. Data Sources and Usage [6] The geochemical data utilized in this paper were compiled from two large geochemical databases: GEOROC and PetDB. The data utilized for this study are from seven mid-ocean ridge segments, 22 island arcs, and 34 ocean islands, which are shown in Figure 1. All of the analyses used in this study are from samples with less than 53 wt % SiO 2, are from published papers, are from samples described as fresh or unaltered (by the papers authors), and performed by X-ray fluorescence (XRF), inductively coupled plasma mass spectrometry (ICP-MS), or instrumental neutron activation analysis (INAA) analytical techniques. For testing previously published discrimination diagrams only samples that met the criteria outlined by Pearce and Cann [1973] and Pearce [1996] were used. These criteria are as follows: (1) the sample has to come from a location of known geologic setting, (2) the sample has to be fresh, (3) the methods of analyses have to meet resolution requirements for discrimination, and (4) CaO + MgO must be between 12 and 20 wt %. For developing the new probabilistic model all samples with up to 53 wt % SiO 2 were utilized. 3. Previous Discrimination Systems [7] The confidence intervals (CI) plotted on the subsequent diagrams were constructed utilizing the methods of Weltje [2002]. Confidence intervals for binary discrimination systems were constructed using an additive logistic normal model, whereas CI for ternary discrimination diagrams were constructed using an additive bivariate logistic normal model. For all lava types the 0.50, 0.60, 0.70, 0.80, and 0.90 CI are shown on each of the discrimination diagrams (Figures 2 8). A 0.50 CI indicates that 50% of the data fall within the CI whereas a 0.90 CI indicates that 2of13

3 Figure 2. Confidence intervals for Ti-Zr diagram with discrimination fields of Pearce and Cann [1973]: (a) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for MORB; (b) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for VAB; and (c) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for OIB. Figure 3. Confidence intervals for Zr/Y-Zr diagram with discrimination fields of Pearce and Norry [1979]: (a) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for MORB; (b) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for VAB; and (c) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for OIB. 3of13

4 Figure 4. Confidence intervals for Ti-V diagram with discrimination fields of Shervais [1982]: (a) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for MORB; (b) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for VAB; and (c) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for OIB. Figure 5. Confidence intervals for Cr-Y diagram with discrimination fields of Pearce [1982]: (a) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for MORB; (b) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for VAB; and (c) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for OIB. 4of13

5 Figure 6. Confidence intervals for Ti-Zr-Y diagram with discrimination fields of Pearce and Cann [1973]: (a) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for MORB; (b) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for VAB; and (c) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for OIB. Figure 7. Confidence intervals for Zr-Nb-Y diagram with discrimination fields of Meschede [1986]: (a) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for MORB; (b) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for VAB; and (c) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for OIB. 5of13

6 Figure 8. Confidence intervals for Ta-Hf-Th diagram with discrimination fields of Wood [1980]: (a) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for MORB; (b) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for VAB; and (c) 0.50, 0.60, 0.70, 0.80, and 0.90 confidence intervals for OIB. 90% of the data fall inside of the CI. It should be noted that since the confidence regions were constructed in lognormal space, zero values for compositions could not be used. [8] In this paper, MORB, VAB, and OIB refer to volcanic rocks formed at mid-ocean ridges, island arcs, and ocean islands, respectively. Hence the terms MORB, VAB, and OIB imply formation at a specific plate tectonic setting, and are not a chemical definition (e.g., basalts with certain characteristics). Furthermore, no distinction is made between varying chemical styles for volcanic rocks erupted at the same setting (e.g., enriched MORB (EMORB) and normal MORB (NMORB) are both considered to be MORB and calc-alkaline basalts (CAB) and island arc tholeiites (IAT) are both considered VAB) Binary Systems Ti-Zr [9] The Ti-Zr discrimination diagram of Pearce and Cann [1973] is used to discriminate between oceanic island arc tholeiites and calc-alkaline basalts (both VAB) and MORB. Confidence intervals for MORB are centered over the original MORB discrimination field, and the 0.50 CI lies entirely within that field (Figure 2a). MORB and VAB overlap at the 0.50 CI, whereas MORB and OIB are distinguishable (where distinguishable reads no overlap of the specified confidence intervals) until the 0.60 CI (Figures 2a 2c). Although VAB have lower average abundances of both Ti and Zr than MORB, the compositional ranges for VAB are much wider (Figures 2a and 2b). OIB have much higher abundances of Ti and Zr than either MORB or VAB, and are well distinguished on this discrimination diagram, even though there is no predefined OIB discrimination field Zr/Y-Zr [10] The Zr/Y-Zr diagram of Pearce and Norry [1979] discriminates among MORB, OIB, and VAB. The 0.50 CI for MORB is centered on the original MORB discrimination field, and minimally overlaps the OIB and VAB discrimination fields (Figure 3a). MORB and OIB are distinguishable until the 0.60 CI (Figures 3a and 3c), whereas, the 0.50 CI for MORB and VAB overlap one another (Figures 3a and 3b). VAB are not well distinguished on this discrimination diagram, and the 0.90 CI for VAB completely encompasses the 0.90 CI for MORB and strongly overlaps the 0.50 CI for OIB. Although the 0.80 CI for OIB does not overlap with the originally defined MORB or VAB fields, discrimination can only be made at the 0.60 CI for both MORB and VAB Ti-V [11] The Ti-V plot [Shervais, 1982] utilizes the variable valence state of vanadium and ranges in titanium abundances to delineate MORB, OIB, and VAB. Figures 4a 4c shows the results of contouring MORB, VAB, and OIB, respectively. The 0.80 CI for MORB nearly lies completely within the original MORB field, and MORB are distinguishable from VAB and OIB at the 0.60 CI (Figures 4a 4c). The 0.50 CI for VAB straddles the original VAB and MORB fields, and VAB are distinguishable from OIB at the 0.70 CI (Figures 4b and 4c). OIB predominantly fall within the OIB discrimination field and overlap with the MORB field at lower Ti abundances Cr-Y [12] The Cr-Y diagram of Pearce [1982] discriminates VAB from MORB and OIB. This diagram is based on the 6of13

7 Figure 9. Probability distribution functions for MORB (solid lines), VAB, (dashed lines), and OIB (dotdashed lines) for each of the seven elements used in the new method. varying degree of partial melting and the subsequent changes in Y abundance expected with increasing degrees of partial melting of a mantle source. MORB only show minimal overlap with the VAB discrimination field at a 0.90 CI (Figure 5a). However, OIB overlap with the VAB discrimination field at the 0.50 CI and the 0.90 CI overlaps with more than half of the VAB discrimination field (Figure 5c). VAB show a much broader range in Y compositions than either MORB or OIB, and are only distinct from them at the 0.50 CI (Figures 5a 5c). Furthermore, the VAB 0.90 CI completely encompasses the MORB 0.90 CI, and the OIB 0.70 CI Ternary Systems Ti-Zr-Y [13] The Ti-Zr-Y diagram of Pearce and Cann [1973] discriminates among MORB, VAB, and OIB. Furthermore, this discrimination diagram divides VAB into IAT and CAB similar to the binary Ti-Zr diagram. The 0.60 CI for MORB lies within the original MORB discrimination field and the 0.90 CI overlies the entire MORB discrimination field, a significant portion of the IAT discrimination field, and lesser amounts of the OIB and CAB fields (Figure 6a). VAB 0.50 CI is centered above the MORB discrimination field, and the 0.90 CI encompasses the total area of all of the discrimination fields (Figure 6b). Furthermore, the VAB 0.60 CI encloses the entire MORB 0.90 CI and intersects the OIB 0.50 CI (Figures 6a 6c). OIB have significantly lower Y abundances relative to Ti and Zr than VAB or MORB; however, the difference is insufficient to discriminate among the three Zr-Nb-Y [14] The Zr-Nb-Y diagram of Meschede [1986] was constructed to discriminate between MORB, EMORB, VAB, and OIB (although as previously mentioned for this study EMORB is grouped into MORB). The MORB 0.50 CI overlaps portions of the EMORB, MORB + VAB, and OIB + VAB discrimination fields, and the 0.90 CI significantly overlies the OIB discrimination field as well (Figure 7a). The VAB 0.50 CI overlies all discrimination fields, encompasses the MORB 0.90 CI, and intersects the OIB 0.50 CI (Figures 7a 7c). Furthermore, the VAB 0.90 CI encloses all of the predefined discrimination fields in addition to encompassing the OIB 0.90 CI. The OIB 0.50 CI completely encloses the original OIB discrimination field, and the 0.90 CI overlies the OIB, EMORB, and OIB + VAB Table 1. Peak Amplitude, Centroid, and Width Values for MORB, VAB, and OIB MORB VAB OIB a1 b1 c1 a1 b1 c1 a1 b1 c1 Ti Hf Nd Zr Nb Pb Gd of13

8 discrimination fields (Figure 7c). OIB and MORB are only distinct at the 0.50 CI on this diagram Ta-Hf-Th [15] The Ta-Hf-Th discrimination diagram [Wood et al., 1979; Wood, 1980] discriminates among MORB, EMORB, VAB, and OIB. The MORB 0.50 CI mimics the outline of the MORB and EMORB discrimination fields with little overlap into other fields (Figure 8a). However, the MORB 0.90 CI encompasses the OIB discrimination field in addition to the MORB and EMORB fields. The VAB 0.50 CI intersects the MORB 0.50 CI (Figures 8a and 8b) and the VAB 0.60 CI intersects the OIB 0.60 CI (Figures 8b and 8c). The VAB 0.90 CI encompasses a very large area of the discrimination diagram, including all of the discrimination fields. 4. A Probabilistic Approach to Discrimination [16] As shown above, previous discrimination diagrams fail to correctly classify most samples with greater than 50 60% certainty. Therefore it is desirable to establish a new method for discrimination that results in more accurate discrimination and an estimate of discrimination quality. [17] Pearce [1987] developed such a system, ESCORT; however, it has not been widely used. Pearce s ESCORT system utilizes mineralogical, geological, petrological, and geochemical data, as well as estimations of volumes of rock erupted since the Paleozoic. The ESCORT classification system analyzed six elements (TiO 2, Zr, Y, Nb, P 2 O 5, and Cr) making it very robust compared to any previous system. However, the nongeochemical constraints that were incorporated proved difficult to quantify and resulted in the method not being widely used. The method described below uses only geochemical data because nongeochemical data (e.g., data for overlying and interbedded strata) are not available in a quantitative format. This approach, although similar to that of Pearce [1987] is different in that it analyzes different elements, does not utilize elemental covariances, and only utilizes geochemical data Theory, Equations, and Method Development [18] Successfully discriminating among basaltic lavas erupted at different plate tectonic settings does not require complete chemical characterization. Pearce [1996] concluded that many elements cannot be consistently analyzed to the necessary accuracy with current instrumentation to be used for discrimination, that many elements do not vary among lavas from different tectonic settings and therefore impede discrimination, and that some groups of elements behave similarly to one another (e.g., the heavy rare earth elements all have similar behavior) and therefore do not provide independent discrimination power. Hence certain elements have much more discrimination power than other elements. In the present study, analysis of probability distribution functions for 42 reliably measured major and trace elements revealed that Ti, Hf, Nd, Zr, Nb, Pb, and Gd have the most discrimination power (where most discrimination power reads the largest separation of probability distribution function peaks) among MORB, VAB, and OIB. [19] The new method presented herein utilizes a priori data from known tectonic settings to generate an a posteriori probability for an unknown sample having formed in a certain tectonic setting. To achieve this, it is necessary to construct Figure 10. Ternary diagrams showing the probability of a sample forming at either a mid-ocean ridge (P MORB ), island arc (P VAB ) or ocean island hot spot (P OIB ). (a) Results of inputting known MORB samples; (b) results of inputting known VAB samples; and (c) results of inputting known OIB samples. These are not discrimination diagrams, but rather a graphical means to show the results of testing the new method. probability distribution functions (PDFs) for the selected elements. Careful analysis of the seven elements chosen for this study reveals that all have approximately lognormal distributions (Figure 9). Therefore the best representation of the data is achieved in lognormal space. However, zero values cannot be used in lognormal space. It is likely, however, that even though some analyses had a measured abundance of 8of13

9 Figure 11. Map showing location of Ontong Java Plateau with magnetic reversal patterns [from Ishikawa et al., 2005]. zero the true abundance is likely some value far below machine detection limits, but greater than zero. Therefore values of 1 ppb were added to all of the reported concentrations to eliminate zero values. The data are then used to construct probability histograms that allow the data to be presented in a probabilistic manner. The best continuous approximation to these histograms is a well-fit (R-squared > 0.98) Gaussian curve f em (x) with the general form " f em ðþ x elem ¼ a elem exp log ð x # elemþ b 2 elem c elem where a elem is the peak amplitude, d elem is the peak centroid, c elem is related to peak width, and x is the abundance of element elem for plate tectonic setting em. The log of x is taken since the curves were fit in lognormal space. A curve of this general form was constructed for each element for each plate tectonic setting em (i.e., one for MORB, VAB, and OIB). Values for a elem, b elem, and c elem are given in Table 1 for each element for each plate tectonic setting. [20] Inasmuch as the Gaussian curve for each element is fit to a probability histogram the equation can be restated as " P em ðþ x elem ¼ a elem exp log ð x # elemþ b 2 elem c elem where P em (x) elem is a particular realization of a sample forming in plate tectonic setting em given abundance x of element elem. This is done for each of the seven elements for each plate tectonic setting (Figure 9). To combine the realizations for each of the seven elements for a given plate tectonic setting, the previous equations for each of the seven elements are multiplied giving P tot;em ¼ Y P em ðþ x elem elem where P tot,em is the product of the realizations for a sample forming in plate tectonic setting em for all x elem (seven in total). In order to translate this into a probability (in ð1þ ð2þ ð3þ equation (3) the sum of P tot for em = MORB, VAB, and OIB is 1) the values are normalized so that they sum to unity. This is accomplished by P final;em ¼ tot;em P Ptot where P final,em is the probability of a sample forming in plate tectonic setting em and where P tot is the sum of the combined realizations for all possible plate tectonic settings (i.e., the sum of P tot,vab, P tot,morb, and P tot,oib ). The final output of this calculation is three probabilities: one for formation at a mid-ocean ridge, one for formation at an island arc, and one for formation at an ocean island. It should be noted that the method presented above is only one possible approach. I have chosen to use multiplicative rule statistics because of the ease of use and approachability. However, there are many other methods that one could utilize (e.g., discriminant analysis) that could also be effectively used for discrimination Testing the Method [21] To construct the PDFs that the method is based upon, 50% of the data were randomly selected using a random number generator. The remaining 50% of the data were used to test the method. In order for a sample to be eligible for testing it must have been analyzed for at least five of the seven selected elements. For testing the model, each analysis was considered to be independent of all other analyses. A classification was considered successful if a sample that formed in tectonic setting em had a P final,em of greater than 50%. Results from model testing are shown in Figures 10a 10c and given below. It should be noted that the ternary diagrams shown in Figures 10a 10c are not discrimination diagrams, but are simply graphical representations of the output probabilities. [22] Classification success rates for correctly discriminating VAB, OIB, and MORB are 83%, 75%, and 76%, respectively. VAB have the highest percentage of correct classifications (Figure 10b), which is a result of having a composition that is generally farthest from that of the other two end-members (Figure 9). [23] The generated output (Figures 10a 10c) can be used in combination with the PDFs shown in Figure 9 to ð4þ 9of13

10 Figure 12. Ontong Java Plateau samples plotted on previous discrimination diagrams. (a) Cr-Y diagram; (b) V-Ti diagram; (c) Zr/Y-Zr diagram; (d) Ti-Zr diagram; and (e) Ta-Hf-Th diagram. 10 of 13

11 rocks if precautions are taken. If a sample is potentially altered it is recommended that the user perform two tests; one with all available data and another excluding elements that are suspected of being nonrepresentative of the original chemistry. If results are drastically different the sample may not be suitable for classification by this method. Figure 13. Ternary diagram showing the probability of Ontong Java Plateau samples forming at either a mid-ocean ridge (P MORB ), island arc (P VAB ), or ocean island hot spot (P OIB ). determine how samples from known tectonic settings are misclassified. Figure 10b shows that VAB samples are most likely to be misclassified as MORB, which is a result of VAB having generally lower abundances of the selected elements than MORB (with the exception of Pb) and much lower abundances than OIB (Figure 9). Alternatively, MORB that are unsuccessfully classified are equally likely misclassified as either VAB or OIB (Figure 10a). Misclassified OIB samples are most often incorrectly classified as MORB because of the stronger overlap between MORB and OIB PDFs than VAB and OIB PDFs (Figure 9). 5. Discussion [24] The method presented above represents a marked improvement over previous systems for geochemical discrimination of basalts. This method is flexible and can be expanded to include any quantitative geochemical data for which requisite databases exist. Also, the new method is probabilistic and thus provides an inherent measure of certainty that was previously unachievable using traditional visual discrimination methods except by the contour intervals presented in this paper. Furthermore, since the model is based upon PDFs, users can still interpret the data independently of the generated output to avoid black-box computations. 6. Chemical Alteration [25] Chemical alteration is a vexing problem when using geochemical data for discrimination and is often difficult to address. The new method presented here, and the classification statistics for its testing, were generated using fresh or unaltered volcanic rocks (i.e., not metamorphosed). However, that does not preclude the possibility of correctly classifying basalts that have been altered by later geologic processes. Most of the elements selected are relatively immobile during greenschist facies metamorphism and beyond, with Pb being the most notable exception. Therefore the model can still discriminate among altered volcanic 7. Test Case: Ontong Java Plateau [26] Large igneous provinces are rare, short-lived features that produce volumes of basaltic lavas unmatched by any other form of basaltic volcanism. They are important not only because of the volume of material erupted, but because of their coincidence in timing with large mass extinction events [e.g., White and Saunders, 2005]. The Early Cretaceous Ontong Java Plateau (OJP) is the world s largest oceanic plateau (Figure 11) with a crustal thickness of km and a total magmatic volume of nearly km 3 [e.g., Gladczenko et al., 1997]. Causal mechanisms that have been suggested for OJP volcanism include: basaltic outpouring attributed to a rising plume head [e.g., Jellinek and Manga, 2004; Larson, 1997; Richards et al., 1989], meteorite collision [Rogers, 1982] and cataclysmic melting of shallow asthenosphere [Anderson et al., 1992]. [27] The purpose of this case study is not to solve the debate on the causal mechanism for OJP volcanism, but instead to compare the results from the new method to results from previous discrimination diagrams. 8. Classification of OJP Samples [28] Data from the OJP were plotted on the Cr-Y, Ti-V, Zr/Y-Zr, Ti-Zr, and Ta-Hf-Th diagrams (Figure 12). Samples plotted on the Cr-Y and Zr/Y-Zr diagrams (Figures 12a and 12c) predominantly fell on the boundaries between MORB and VAB, with only a few samples plotting as OIB on the latter diagram (Figure 12c). Samples plotted on the Ti-V and Ti-Zr diagrams (Figures 12b and 12d) were predominantly classified as being MORB with some overlap into the VAB (Figures 12b and 12d) and OIB fields (Figure 12b). Samples plotted on the Ta-Hf-Th diagram (Figure 12e) fall on the discriminant boundary between NMORB and EMORB. The result of plotting these samples on previous discrimination diagrams indicates a broadly MORB-type trace element affinity and a small likelihood for either a VAB or OIB origin. [29] The new classification method classified 56 of the 57 OJP samples as MORB with a probability greater than 95% (Figure 13). This however, does not imply that they formed by the same tectonic process, inasmuch as different combinations of source compositions and varying extents of partial melting can produce similar characteristics among the trace elements being considered. 9. Conclusions and Future Work [30] The use of large geochemical databases such as GEOROC and PetDB allow for previously unparalleled testing of discrimination diagrams. This study quantitatively demonstrates that the most frequently used diagrams fail to adequately discriminate among MORB, VAB, and OIB. The success of these diagrams is hindered by their limited 11 of 13

12 dimensionality due to visualization requirements and their lack of certainty measurements for interpretations. [31] Advances in computational technology over the last three decades have made it more tractable to utilize large databases to perform the calculations that are necessary for developing quantitative methods for discrimination. The new method presented above was developed from larger databases and utilizes more elements than any other current discrimination tool. Furthermore, the calculations for the new method can be easily computed using various spreadsheet or programming languages. Pseudocode in Appendix A shows the simplicity of implementing the method. [32] Although geochemical discrimination has traditionally been by graphical means, quantitative methods that utilize several elements are needed. Future work in establishing more robust discrimination models should (1) utilize large databases, (2) be N-dimensional and allow for the addition of more elements, and (3) use effective nongraphical techniques. Appendix A [33] The following pseudocode is designed to run the probabilistic discrimination method described above. When possible, all of the variables have remained the same as in the text. For referencing cells within a matrix X, X(M, N) refers to matrix X, row M, column N. A % sign refers to documentation for user reference and not actual code. Versions of this code have been written for various platforms and can be downloaded from the author s Web site % The only input required for this method is matrix X, where the columns in order are the abundances of Ti, Hf, Nd, Zr, Nb, Pb, and Gd, where row 1 is sample 1, row 2 is sample 2, and row N is sample N. Therefore X is a 7 N matrix. load (X) % ii refers to sample number from sample 1 to sample N. Therefore this is a loop that runs N number of times. for ii = 1 to N % The following are for the probability distribution functions for VAB. The values represent a1, b1, and c1 from Table 1 and equations from equation (2). TiVAB(ii) = *exp( ((log(x(ii,1)) 8.725)/0.473)^2) HfVAB(ii) = *exp( ((log(x(ii,2)) )/0.807)^2) NdVAB(ii) = *exp( ((log(x(ii,3)) 2.473)/1.004)^2) ZrVAB(ii) = *exp( ((log(x(ii,4)) 4.303)/0.8635)^2) NbVAB(ii) = *exp( ((log(x(ii,5)) 1.108)/1.793)^2) PbVAB(ii) = *exp( ((log(x(ii,6)) 1.211)/1.265)^2) GdVAB(ii) = *exp( ((log(x(ii,7)) 1.264)/0.5018)^2) % The following are for the probability distribution functions for MORB. The values represent a1, b1, and c1 from Table 2 and equations from equation (2). TiMORB(ii) = *exp( ((log(x(ii,1)) 9.153)/0.403)^2) HfMORB(ii) = *exp( ((log(x(ii,2)) 0.988)/0.5251)^2) NdMORB(ii) = 0.556*exp( ((log(x(ii,3)) 2.347)/0.6661)^2) ZrMORB(ii) = *exp( ((log(x(ii,4)) 4.702)/0.4475)^2) NbMORB(ii) = *exp( ((log(x(ii,5)) 1.523)/1.183)^2) PbMORB(ii) = *exp( ((log(x(ii,6))-( ))/0.7839)^2) GdMORB(ii) = *exp( ((log(x(ii,7)) 1.545)/0.3262)^2) %... The following are for the probability distribution functions for OIB. The values represent a1, b1, and c1 from Table 2 and equations from equation (2). TiOIB(ii) = *exp( ((log(x(ii,1)) 9.734)/0.3644)^2) HfOIB(ii) = 0.115*exp( ((log(x(ii,2)) 1.606)/0.5731)^2) NdOIB(ii) = *exp( ((log(x(ii,3)) 3.541)/0.7696)^2) ZrOIB(ii) = *exp( ((log(x(ii,4)) 5.304)/0.5982)^2) NbOIB(ii) = *exp( ((log(x(ii,5)) 3.431)/1.262)^2) PbOIB(ii) = 0.157*exp( ((log(x(ii,6)) )/1.052)^2) GdOIB(ii) = *exp( ((log(x(ii,7)) 1.895)/0.4416)^2) % The following lines are to equivalent to equation (3) in text. PtotVAB(ii) = TiVAB(ii) * HfVAB(ii) * NdVAB(ii) * ZrVAB(ii) * NbVAB(ii) * GdVAB(ii) * PbVAB(ii) PtotMORB(ii) = TiMORB(ii) * HfMORB(ii) * NdMORB(ii) * ZrMORB(ii) * NbMORB(ii) * GdMORB(ii) * PbMORB(ii) PtotOIB(ii) = TiOIB(ii) * HfOIB(ii) * NdOIB(ii) * ZrOIB(ii) * NbOIB(ii) * GdOIB(ii) * PbOIB(ii) % The following lines are equivalent to equation (4) in text. PfinalVAB(ii) = PtotVAB / (PtotVAB + PtotMORB + PtotOIB) PfinalMORB(ii) = PtotMORB / (PtotVAB + PtotMORB + PtotOIB) PfinalOIB(ii) = PtotOIB / (PtotVAB + PtotMORB + PtotOIB) end [34] Acknowledgments. I would like to thank Jeff Shragge and Kyle Spikes for helping with much of the programming work necessary to generate the confidence intervals and in optimizing some of my often inefficient code. Thanks also go out to Pieter Vermeesch for turning me toward using lognormal space for the confidence intervals and for this method. Also, I would like to thank Gary Ernst for reading and revising an early version of this manuscript and Chris Mattinson for thoroughly editing a revised version. This manuscript has greatly benefited by thorough reviews from Kevin Johnson and Georges Ceuleneer and from the extraordinary efforts of Associate Editor John Mahoney. References Anderson, D. L., Y. S. Zhang, and T. Tanimoto (1992), Plume heads, continental lithosphere, flood basalts, and tomography, in Magmatism and Causes of Continental Break-up, edited by B. Storey, T. Alabaster, and R. J. Pankhurst, Geol. Soc. Spec. Publ., 68, Gladczenko, T. P., M. F. Coffin, and O. Eldholm (1997), Crustal structure of the Ontong Java Plateau: Modeling of new gravity and existing seismic data, J. Geophys. Res., 102, 22,711 22,729. Ishikawa, A., E. Nakamura, and J. J. Mahoney (2005), Jurassic oceanic lithosphere beneath the southern Ontong Java Plateau: Evidence from xenoliths in alnoite, Malaita, Solomon Islands, Geology, 33, Jellinek, A. M., and M. Manga (2004), Links between long-lived hot spots, mantle plumes, D 00, and plate tectonics, Rev. Geophys., 42, RG3002, doi: /2003rg of 13

13 Larson, R. L. (1997), Superplumes and ridge interactions between Ontong Java and Manihiki Plateaus and the Nova-Canton Trough, Geology, 25, Meschede, M. (1986), A method of discrimination between different types of mid-ocean ridge basalts and continental tholeiites with the Nb-Zr-Y diagram, Chem. Geol., 56, Mullen, E. D. (1983), MnO/TiO 2 /P 2 O 5 : A minor element discriminant for basaltic rocks of oceanic environments and its implications for petrogenesis, Earth Planet. Sci. Lett., 62, Pearce, J. A. (1974), Statistical analysis of major element patterns in basalts, J. Petrol., 17, Pearce, J. A. (1982), Trace element characteristics of lavas from destructive plate boundaries, in Andesites, edited by R. S. Thorpe, pp , John Wiley, Hoboken, N. J. Pearce, J. A. (1987), An expert system for the tectonic characterization of ancient volcanic rocks, J. Volcanol. Geothermal Res., 32, Pearce, J. A. (1996), A User s Guide to Basalt Discrimination Diagrams, in Trace Element geochemistry of Volcanic Rocks: Applications for Massive Sulphide Exploration: Geol. Assoc. Can. Short Course Notes, vol. 12, edited by D. A. Wyman, pp , Geol. Assoc. of Can., St. John s, Newfoundland. Pearce, J. A., and J. R. Cann (1973), Tectonic setting of basic volcanic rocks determined using trace element analyses, Earth Planet. Sci. Lett., 19, Pearce, J. A., and M. J. Norry (1979), Petrogenetic implications of Ti, Zr, Y, and Nb variations in volcanic rocks, Contrib. Mineral. Petrol., 69, Richards, M. A., R. A. Duncan, and V. Courtillot (1989), Flood basalts and hot-spot tracks: Plume heads and tails, Science, 246, Rogers, G. C. (1982), Oceanic plateaus as meteorite impact signatures, Nature, 299, Rollinson, H. (1993), Using Geochemical Data: Evaluation, Presentation, Interpretation, 352 pp., John Wiley, Hoboken, N. J. Shervais, J. W. (1982), Ti-V plots and the petrogenesis of modern and ophiolitic lavas, Earth Planet. Sci. Lett., 59, Weltje, G. J. (2002), Quantitative analysis of detrital modes: statistically rigorous confidence regions in ternary diagrams an their use in sedimentary petrology, Earth Sci. Rev., 57, White, R. V., and A. D. Saunders (2005), Volcanism, impact and mass extinctions: incredible or credible coincidences?, Lithos, 79, Wood, D. A. (1980), The application of a Th-Hf-Ta diagram to problems of tectonomagmatic classification and to establishing the nature of crustal contamination of basaltic lavas of the British Tertiary volcanic province, Earth Planet. Sci. Lett., 50, Wood, D. A., J. L. Joron, and M. Treuil (1979), A re-appraisal of the use of trace elements to classify and discriminate between magma series erupted in different tectonic settings, Earth Planet. Sci. Lett., 45, C. A. Snow, Department of Geological and Environmental Sciences, Stanford University, Building 320, Stanford, CA 94305, USA. (casnow@ pangea.stanford.edu) 13 of 13