Abstract

In sedimentary petrology data are often in the form of measurements of several variables on numerous samples. If the set of data is large and the underlying causal structure obscure, factor and vector analysis can be an important aid in revealing simple patterns in complex information. Mathematically, these approaches treat each variable or each sample as a vector and resolve it into a small number of component vectors. Vectors may represent variables (R-mode) or samples (Q-mode). Factor analysis resolves vectors of raw data into theoretical vectors; vector analysis resolves them into selected data vectors that represent actually observed, compositionally extreme end-member samples (Q-mode) or into variables characterized by the maximum observed linear independence (R-mode). The method has been programmed for various large, high-speed computers. Usefulness of the approach is demonstrated by application to two case histories: heavy mineral provenance studies of Recent sediments in the Gulf of California, and on the Orinoco-Guayana Shelf. Q-mode analysis of these case histories represents quite different but reasonably common situations. In the Gulf of California, most mineral assemblages are derived from nearby, petrographically simple sources and are dominated by only a few minerals. Mixing during transportation is minor, and the system can easily be defined in terms of a few mineralogically distinct end members. Vector analysis of this system yields results similar to those obtained by conventional inspection of the raw data, although more significant detail is revealed and end members are objectively and re-producibly defined. The Orinoco-Guayana Shelf, on the other hand, possesses remote and petrographically complex sources, and mixing of assemblages during long-distance transportation is common. All mineral assemblages are complex and variable and only quantitatively different. Obvious end members are lacking. Vector analysis yields a mineral distribution pattern greatly different from that obtained by inspection of the raw data. The vector pattern appears to be the more meaningful one when interpreted in terms of zones of littoral transportation moving landward during the post-Pleistocene rise of sea level.

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