Data Reduction And Error Analysis For The Physical Sciences

The statistical analysis of compositional data

High-potassium, calc-alkaline I-type plutonism in the European Variscides: northern Vosges (France) and northern Schwarzwald (Germany)

Petrographic, major, trace, and rare earth element compositions of sandstones from the upper Miocene Kudankulam Formation, Southern India, have been investigated to determine their provenance, tectonic setting, and weathering conditions. All sandstone samples are highly enriched in quartz (Q) but poor in feldspar (F) and lithic fragments (L). The major-element concentrations of these sandstones reveal the relative homogeneity of their source. Geochemically, the Kudankulam sandstones are classified as arkose, subarkose, litharenite, and sublitharenite. The CIA values (chemical index of alteration; mean value 44.5) for these sandstones and the A-CN-K diagram suggest their low-weathering nature. Similarly, their Fe2O3* + MgO (mean 2.7), Al2O3/SiO2 ( 0.09), K2O/Na2O ( 2.2) ratios and TiO2 contents ( 0.3) are consistent with a passive-margin setting. The Eu/Eu* ( 0.5), (La/Lu)cn ( 21), La/Sc ( 5.9), Th/Sc ( 1.9), La/Co ( 5.7), Th/Co ( 1.8), and Cr/Th ( 5.3) ratios support a felsic source for these sandstones. Chondrite-normalized REE patterns with LREE enrichment, flat HREE, and negative Eu anomaly also are attributed to felsic source-rock characteristics for Kudankulam sandstones. Total REE concentrations of these sandstones reflect the variations in their grain-size fractions. The source rocks are probably identified to be Proterozoic gneisses, charnockites, and granites of the Kerala Khondalite Belt, which must have been exposed at least since the late Miocene. Finally, the unusual Ni enrichment in the Kudankulam sandstones, unaccompanied by a similar enrichment in Cr, Co, and V, may be related to either the presence of pyrite in the sandstones or, more likely, the fractionation of garnet from the source rocks during transportation.

Geochemistry of Sandstones from the Upper Miocene Kudankulam Formation, Southern India: Implications for Provenance, Weathering, and Tectonic Setting

New multi-dimensional diagrams for tectonic discrimination of siliciclastic sediments and their application to Precambrian basins

Most of the existing major- and trace element-based discrimination diagrams are characterized by major defects such as subjective field boundaries, the constant-sum problem, and inadequacy of samples in creating them. Although major advances toward the solution of all these problems have been recently achieved through major element-based discriminant function diagrams, their applicability to old, altered rocks may be questionable. We present new discriminant function diagrams based on immobile trace elements and log-ratio transformation of the data of basic and ultrabasic rocks. These new diagrams are extremely successful in distinguishing the four tectonic settings (island-arc, continental rift, ocean island, and mid-oceanic ridge) and especially the plate margin (island-arc and mid-ocean ridge grouped together) and intra-plate or plate interior (continental rift and ocean island combined together) settings. The overall success rate for these natural log-transformed ratio-based diagrams using five trace ...

Tectonic Discrimination of Basic and Ultrabasic Volcanic Rocks through Log-Transformed Ratios of Immobile Trace Elements

We present five new discriminant function diagrams based on an extensive database representative of basic and ultrabasic rocks from four tectonic settings of island arc, continental rift, ocean-island, and mid-ocean ridge. These diagrams were obtained after loge-transformation of concentration ratios of major-elements — a technique recommended for a correct statistical treatment of compositional data. Higher % success rates (overall values from ∼ 83 to 97%) were obtained for proposing these new diagrams as compared to those (∼82 to 94%) obtained from the discriminant analysis of the raw major-element concentration data (i.e., without the loge-transformation and without taking ratios of the compositional data, but using exactly the same database to provide an unbiased comparison), suggesting that such a data transformation constitutes a statistically correct and recommended technique. The new diagrams also resulted in less mis-classification of basic and ultrabasic rocks from known tectonic settings than the diagrams obtained from the raw data. The use of these highly successful new discriminant function diagrams is illustrated using Miocene to Recent basic and ultrabasic rocks from three areas of Mexico with complex or controversial tectonic settings (Mexican Volcanic Belt, Los Tuxtlas volcanic field, and Eastern Alkaline Province), as well as older rocks from three areas (Deccan, Malani, and Bastar) of India. Additionally, the major-element data from two ‘known’ continental arc settings are used to show that they are similar to those from the island arc setting. Continental rift setting is inferred for all Mexican cases and for one cratonic area of India (Malani) and an IAB setting for the Bastar craton. The Deccan flood basalt province of India is used to warn against an indiscriminate use of those discrimination diagrams that do not explicitly include the likely setting of the area under evaluation. An Excel template is also provided for an easy application of these new diagrams for discriminating the four settings considered in this work.

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Discriminating four tectonic settings: Five new geochemical diagrams for basic and ultrabasic volcanic rocks based on log-ratio transformation of major-element data

The statistical method of linear discriminant analysis has been applied to distinguish Pliocene to Recent basic rocks on the basis of their major-element composition. Studied basic rock suites are from four tectonic settings: island arc, continental rift, ocean island, and mid-ocean ridge. Field boundaries were derived by computing probability functions replacing the past practice of fitting lines by "eye." Highly successful discrimination diagrams have been obtained. A testing set shows that the rate of correct classification ranges from 76% to 96%, and from 80% to 92% when three and four tectonic groups are considered at a time, respectively. The high potential of this approach to identify different tectonic settings for basic rocks is only reduced by the complex tectonic history shown by a few of the compiled samples, by crustal contamination effects in some basic rock samples, and the similarities of mantle sources tapped in different tectonic settings.

Discriminant Analysis Applied to Establish Major-Element Field Boundaries for Tectonic Varieties of Basic Rocks

Determination of lanthanides in international geochemical reference materials by reversed-phase high-performance liquid chromatography using error propagation theory to estimate total analysis uncertainties

Mirna Guevara

Papers

Tectonic Discrimination of Basic and Ultrabasic Volcanic Rocks through Log-Transformed Ratios of Immobile Trace Elements

Discriminating four tectonic settings: Five new geochemical diagrams for basic and ultrabasic volcanic rocks based on log-ratio transformation of major-element data

Discriminant Analysis Applied to Establish Major-Element Field Boundaries for Tectonic Varieties of Basic Rocks

Determination of lanthanides in international geochemical reference materials by reversed-phase high-performance liquid chromatography using error propagation theory to estimate total analysis uncertainties

DC_BASE: a database system to manage Nernst distribution coefficients and its application to partial melting modeling