Petrologic hypothesis testing with Pearce element ratio diagrams: derivation of diagram axes

In petrology, Pearce element ratio (PER) diagrams have been used: i) to determine whether members of a rock suite are co-genetic, ii) to identify the minerals involved in differentiation processes, and iii) to evaluate the extent to which those mineral are involved. The axis coefficients of each diagram are chosen such that sorting of minerals or combinations of minerals will generate unique and predictable trends. Unfortunately, selection of the optimal combination of axis coefficients is a difficult task, especially if the system being investigated has a large number of phases or complicated solid solution minerals. Our work has established a formal set of rules and matrix operations which facilitate the determination of PER diagram axes coefficients. This methodology can be used to determine the unit molar vector displacement caused by the addition or subtraction of a specific mineral, given a set of axis coefficients. It can also be used to create PER diagrams on which minerals have predetermined vector displacements. By designating all vector displacements to be parallel, axis coefficients for assemblage test diagrams can be determined to test the following hypothesis: the observed chemical variation is due to the addition (or removal) of a specific set of minerals. Alternatively, by designating all vector displacements to be mutually perpendicular, phase discrimination diagrams can be created which test whether the observed chemical variations require a specific phase to be involved in differentiation. Phase discrimination diagrams also provide a means to estimate the extent of that involvement. This methodology facilitates construction of powerful yet simple PER diagrams which provide an effective means of testing alternative differentiation hypotheses. Current address: Department of Geological Sciences, Queen's University Kingston, Ontario K7L 3N6, Canada     

Geochemical and Sr–Nd isotopic evidence for the genesis of the Late Cainozoic Almopia volcanic rocks (Central Macedonia, Greece)

Summary ?Major and trace element contents and Sr–Nd isotope ratios of selected volcanics of Pliocene age from the Almopia area, central Macedonia, Greece, have been determined. These rocks are mainly distinguished as two groups based on geographical, petrological and isotopic data: a) the east–central western group (E–CW) and b) the south western group (SW). The absence of contemporaneous basic volcanics in the Almopia area coupled with the considerable scatter of elements in variation diagrams rule out fractional crystallization as the dominant differentiation process. Instead, disequilibrium textures along with the positive correlation of Sr-isotope ratios with differentiation suggest mixing between a basic and an acid component combined with assimilation and fractionation. The spider diagrams of the most silica-poor volcanics show evidence of subduction-related processes, indicating that the parental magmas may have been derived from partial melting of mantle wedge enriched in LILE and LREE by subducted slab-derived fluids. Previous data on the oxygen isotope composition of the same volcanics are consistent with this genetic hypothesis. Lastly, the relatively high ⁸⁷Sr/⁸⁶Sr and low ¹⁴³Nd/¹⁴⁴Nd ratios (0.7080 and 0.512370, respectively) of the volcanic sample inferred to be compositionally the closest one to the parental magma of Almopia rocks suggest that the incompatible element enrichment of the mantle source is old, probably of Proterozoic age. Received December 12, 2001; revised version accepted June 20, 2002 Published online November 29, 2002     

On the Harker Variation Diagrams; A Comment on “The Statistical Analysis of Compositional Data. Where Are We and Where Should We Be Heading?” by Aitchison and Egozcue (2005)

The current theoretical development of the analysis of compositional data in the article by Aitchison and Egozcue neglects the use of Harker’s variation diagrams and other similar plots as “meaningless” or “useless” on compositional data. In this work, it is shown that variation diagrams essentially are not a correlation tool but a graphical representation of the mass actions and mass balances principles in the context of a given geological system, and, when they are used correctly, they provide vital information for the igneous petrologist. The qualitative validity of the “spurious trends” in these diagrams is also shown, when they are interpreted in their proper geological framework. The example previously used by Rollinson to test the usefulness of the log-ratio transformation in the Aitchison and Egozcue article is revisited here in order to fully illustrate the proper use of this tool.     

Application of 55 multi-dimensional tectonomagmatic discrimination diagrams to Precambrian belts

Fifty-five new multi-dimensional diagrams, mostly based on log-ratio transformations, were used to decipher tectonic settings for 17 cases of Precambrian belts in Canada, the USA, Poland, Finland, Jordan, Democratic Republic of Congo and Zambia, China, and India. The results of different sets of diagrams for basic-ultrabasic, intermediate, and acid magmas were generally internally consistent. Possible reasons for some inconsistencies may be related to the use of a sample group of mixed ages because of their uncertainties, extreme element mobility caused by metamorphism especially of high-grade type, analytical data quality, different petrogenetic processes for basic to acid magmas such as mantle versus crustal origin, and some deficiencies that still exist in the multi-dimensional diagrams. To partly overcome the last problem, one new multi-dimensional diagram is proposed and used to discriminate mid-ocean ridge and oceanic plateau settings.     

Geochemical and Sr–O isotopic constraints on magmatic differentiation at Gede Volcanic Complex, West Java, Indonesia

The Gede Volcanic Complex (GVC) of the Sunda island arc (West Java, Indonesia) consists of multiple volcanic centres and eruptive groups with complex magmatic histories. We present new petrological, mineralogical, whole-rock major and trace element and Sr–O isotopic data to provide constraints on the relative importance of fractional crystallisation and magma mixing in petrogenesis, as well as on the role and nature of the arc crust. Banded juvenile scoria from Young and Old Gede provide unequivocal evidence for the (late-stage) interaction of distinct magmas at Gede volcano. However, the relatively small-degree compositional zoning observed in plagioclase phenocrysts of all eruptive groups (up to ~20 mol% An) may be attributed to physical changes in magma properties (e.g. P, T, and PH₂O) rather than changes in melt composition. Major element and trace element variations within each eruptive series are inconsistent with magmatic evolution through simple mixing processes. Instead, mixing of variably fractionated magma batches is suggested to account for the significant scatter in some element variation diagrams. No correlation is observed between textural complexity and/or mineral disequilibrium and whole-rock geochemistry. REE data and geochemical modelling indicate that fractional crystallisation involving amphibole in the mid- to lower crust, and fractionation of plagioclase, clinopyroxene, Fe–Ti oxide ± olivine ± orthopyroxene provide strong control on the geochemical evolution of GVC rocks. Two-pyroxene geothermobarometry provides pre-eruption crystallisation temperatures of 891–1,046°C and pressures of 3.4–6.5 kbar, equivalent to ~13–24 km depth beneath the volcanoes (mid- to lower crust). Low, mantle-like clinopyroxene δ¹⁸O values of GVC lavas and poor correlation of Sr isotope ratios with indices of differentiation precludes significant assimilation of isotopically distinct crust during magmatic differentiation. Therefore, we suggest that the geochemical character of the moderately thick West Javan arc crust is relatively immature compared to typical continental crust. Trace element ratios and strontium isotopes show that the magmatic source composition of the older geographical units, Gegerbentang and Older Quaternary, is distinct from the other GVC groups.     

Exploring self-affine properties in seismograms

Self-affine properties have been observed in a large variety of rough profiles and time series from natural data sets. In this work, seismograms used for oil prospecting, which contain information of distinct subsurface features collected by seismic waves reflected or scattered at their interfaces, are taken into consideration. It is expected that any self-affine property, measured by the Hurst exponent H, depends on the depth. For each seismic trace, H is evaluated locally within a moving window, which is chosen narrow enough to reveal space dependency but also wide enough to display scale invariance. With the use of color code diagrams, it is possible to draw two-dimensional diagrams that show the local dependence of H for the analyzed seismogram. The reliability of the method is tested by the investigation of seismograms that contain ground roll components, as well as multiple reflections. The effect of different kinds of filter in the scaling properties is also investigated. In this case, comparisons are drawn among the diagrams obtained from original seismograms and those subjected to appropriate filter to eliminate spurious components. Work supported by the Brazilian agencies CNPq, FINEP-CTPETRO and Petrobras.     

A new way of interpreting trace element concentrations with respect to modes of mineral formation

The availability of multi-element analyses provides numerous data on trace elements. These data complete petrochemical analyses in general and are often reported as averages although they vary over many orders of magnitude. It can be shown that the variation of trace elements in ores is related to fundamental processes during ore formation. As examples the fractionation of the lanthanoids in Ca-minerals (fluorite, calcite, apatite, phosphorite, etc.), chalcophile elements in sphalerite and Ga, Sc, W, and Fe in cassiterite are discussed. Plotting of analytical data in variation diagrams (fractional index vs. chemical environmental index) help to decipher the mode of mineral formation.The information obtained from trace and minor element fractionation are discussed with respect to the probable origin of hydrothermal solutions.     

Density variations in the thickened crust as a function of pressure, temperature, and composition

Constraints on density as a function of pressure, temperature, and composition are crucial to understand isostatic movements during geodynamic processes. Here, we provide a systematic series of density diagrams extracted from thermodynamic calculations for a variety of crustal compositions within a wide P–T range. We quantify systematic density changes in collisional settings for relevant compositional variations and attempt to simplify the density–composition relationships. Rock densities depend strongly on pressure, temperature, and composition. Densities at some selected pressure–temperature conditions increase linearly with increasing Al₂O₃ as well as MgO/FeO contents in pelitic rocks. Al- and Fe-rich pelites yield the highest densities, which is mostly due to the formation of garnet but also depends on other minerals and changes of reactions. The effect of loading on densities is investigated, and we show that for deep burial, a meta-pelite rich in Fe and Mg yields much larger density changes than a dry basalt and that the burial of such a rock with a composition close to typical lower crust may result in significant negative buoyancy. Metamorphism of hydrous lower crust due to pressurization and heating thus leads to densification of thickened lower crust, while heating of dry crust leads to a decrease in density. Hence, water-loaded isostatic subsidence due to metamorphism of water-saturated lower crust is substantial and increases with the thickness and depth of the reacting layer, while dry compositions show much less or only transient densification and subsidence. The density change due to thermal expansion, an extensively used concept in geodynamic models, predicts uplift under the same P–T conditions and is an order of magnitude smaller than the density variation calculated from petrologically consistent diagrams.     

Application of the discordant outlier detection and separation system in the geosciences

Basically, two main types of statistical methods – robust and outlier-based – are available for handling experimental data; we document here the application of the outlier-based method. Due to the unavailability of a suitable software system for statistically correct application of the outlier-based method, a new computer program, DODESSYS (Discordant Outlier DEtection and Separation SYStem), was written for the application of 33 discordancy test variants to experimental data, constituting contaminated or uncontaminated normal statistical samples. We illustrate the application of the discordant outlier-based scheme by five specific examples; three include univariate data for which this procedure was specifically designed and two are for bivariate data for which this methodology can be easily adopted. We thus report new statistical information on two reference materials (granite G-2 and sediment IAEA-417), bryozoan species from eastern Oman, a new improved Na/K geothermometric equation, and a more significant correlation with water depth of the abundance of meiofauna from the Gulf of Mexico. Recently, two sets of multi-dimensional discrimination diagrams for basic as well as acid rocks have been proposed from statistically correct methodology of natural logarithm-transformation of element ratios; the diagrams also require that these ratios should be normally distributed. We present numerous examples of application of these new diagrams for inferring tectonic setting of Archaean to Recent rocks, both before and after testing the datasets for discordant outliers. We recommend that outlying observations should always be evaluated for their discordancy.     

花岗岩混合问题:与玄武岩对比的启示——关于花岗岩研究的思考之一

最近,花岗岩混合成了花岗岩研究的热点,国内外许多学者探讨了花岗岩混合问题,并尝试用不同端元组分不同比例的混合来解释花岗岩的地球化学变化.本文从花岗岩与玄武岩的对比出发,探讨了花岗岩混合的可能性和局限性.作者认为,花岗岩混合的现象是普遍存在的,但是次要的和局部的.岩浆混合的能力或能干性(competence of mixing)主要取决于岩浆的黏性和温度,而黏性又与硅氧四面体有关.相对于玄武岩,花岗岩的SiO2含量高,温度低,因此,花岗质岩浆的混合能干性很低.玄武质岩浆的混合是mixing(以化学混合为主),而花岗质岩浆的混合通常只是mingling(以机械混合为主),只有在少数情况下才能达到mixing的程度,例如,埃达克岩与地幔混合形成的高镁安山岩或高镁埃达克岩.许多人认为,花岗岩中的暗色微粒包体是花岗质岩浆混合作用最显著、最直接证据.研究表明,花岗岩中的暗色微粒包体大多是闪长质成分的,其初始成分大多是玄武质的.因此,暗色微粒包体不是花岗质岩浆混合作用最显著、最直接证据,而是玄武质岩浆混合能力强过花岗质岩浆的证据.与玄武质岩浆的起源比较,花岗质岩浆从一开始熔融就是不均一的,这源于源区的不均一及熔融过程的复杂性.花岗质岩浆原始均一性的假定是不可能的.花岗岩成分的变化以及在哈克图解中成分点的"连续谱系",主要是由源区不均一性引起的,混合和分异可能有一定的作用,但毕竟是次要的.花岗质岩浆从源区生成、迁移、直至在地表喷出或在浅部定位的全过程,是一个不断均一化和不均一化的过程.但是,由于花岗质岩浆的黏性大,上述过程及岩浆演化的程度和规模都受到限制,也限制了岩浆混合的程度和规模.许多人仅从花岗岩地球化学成分的变化来研究花岗岩的成因,而很少考虑花岗岩物理性质对岩浆演化的制约.对比玄武岩与花岗岩,我们认为,地球化学方法在花岗岩中应用的范围和程度可能远远不及玄武岩,我们应当重新考虑花岗岩的地球化学应用问题.     

Tracking source materials of Phanerozoic granitoids in South Korea by zircon Hf isotopes

Phanerozoic granitoids in South Korea are classified into four primary spatiotemporal groups showing geochemical and isotopic diversity. This study presents the first in situ Hf isotope data for zircons extracted from representative outcrops of each granitoid group. The core‐to‐rim variation in ε_Hf values observed in some zircon grains provides evidence for open‐system processes influenced by the input of more primitive melts or interactions with pre‐existing crustal materials. A general core‐to‐rim decrease in Lu/Hf and Th/U ratios indicates a progressive compositional change in the melts during magmatic differentiation. Contrasting evolutionary paths demonstrated by zircon ε_Hf values suggest that the Neoproterozoic to Palaeozoic crust including the Permian granitoids was recycled during the Cretaceous to Palaeogene magmatism in south‐eastern Korea, whereas the Palaeoarchaean to Palaeoproterozoic crust provided major source material for the Triassic to Jurassic granitoids in central Korea.     

关于岩石微量元素构造环境判别图解使用的有关问题

针对目前应用愈来愈广泛的不同岩石,特别是岩浆岩的微量元素构造环境判别图解使用过程中存在的问题,从这些判别图解建立的原理,介绍了微量元素构造环境判别图解的使用原则。强调指出所采集的样品必须新鲜(无蚀变或极弱蚀变)、非堆晶的岩石;选择的判别图解必须与判别的岩石类型相一致,即对花岗岩类要用花岗岩的判别图解,不能用玄武岩的判别图解;对特殊类型岩石要选择专门用于该类型岩石的判别图解,如碱性花岗岩,钾质火成岩;要应用多种图解综合判断;不能用单个样品,而应作多个样品分析;要注意所选择判别图解的特别说明等。此外,一些构造环境判别图解还能给出岩石的成岩过程和源区。     

Liquid line of descent of a basanitic liquid at 1.5 Gpa: constraints on the formation of metasomatic veins

The metasomatism observed in the oceanic and continental lithosphere is generally interpreted to represent a continuous differentiation process forming anhydrous and hydrous veins plus a cryptic enrichment in the surrounding peridotite. In order to constrain the mechanisms of vein formation and potentially clarify the nature and origin of the initial metasomatic agent, we performed a series of high-pressure experiments simulating the liquid line of descent of a basanitic magma differentiating within continental or mature oceanic lithosphere. This series of experiments has been conducted in an end-loaded piston cylinder apparatus starting from an initial hydrous ne-normative basanite at 1.5 GPa and temperature varying between 1,250 and 980°C. Near-pure fractional crystallization process was achieved in a stepwise manner in 30°C temperature steps and starting compositions corresponding to the liquid composition of the previous, higher-temperature glass composition. Liquids evolve progressively from basanite to peralkaline, aluminum-rich compositions without significant SiO₂ variation. The resulting cumulates are characterized by an anhydrous clinopyroxene + olivine assemblage at high temperature (1,250–1,160°C), while at lower temperature (1,130–980°C), hydrous cumulates with dominantly amphibole + minor clinopyroxene, spinel, ilmenite, titanomagnetite and apatite (1,130–980°C) are formed. This new data set supports the interpretation that anhydrous and hydrous metasomatic veins could be produced during continuous differentiation processes of primary, hydrous alkaline magmas at high pressure. However, the comparison between the cumulates generated by the fractional crystallization from an initial ne-normative liquid or from hy-normative initial compositions (hawaiite or picrobasalt) indicates that for all hydrous liquids, the different phases formed upon differentiation are mostly similar even though the proportions of hydrous versus anhydrous minerals could vary significantly. This suggests that the formation of amphibole-bearing metasomatic veins observed in the lithospheric mantle could be linked to the differentiation of initial liquids ranging from ne-normative to hy-normative in composition. The present study does not resolve the question whether the metasomatism observed in lithospheric mantle is a precursor or a consequence of alkaline magmatism; however, it confirms that the percolation and differentiation of a liquid produced by a low degree of partial melting of a source similar or slightly more enriched than depleted MORB mantle could generate hydrous metasomatic veins interpreted as a potential source for alkaline magmatism by various authors.     

Statistical evaluation of tectonomagmatic discrimination diagrams for granitic rocks and proposal of new discriminant-function-based multi-dimensional diagrams for acid rocks

The four tectonic discrimination diagrams of Pearce et al. [Journal of Petrology, v. 25, p. 956–983] for granitic rocks were first evaluated using the literature cited by these authors as well as from our new database. The first diagram (Y?Nb) cannot discriminate volcanic-arc and collision settings. Both Y?Nb and Yb?Ta diagrams have an overlapping field for within-plate and ocean-ridge granitoids. The remaining two diagrams (Y?+?Nb?Rb and Yb?+?Ta?Rb) use a mobile element (Rb) in their y-axis. Although these diagrams successfully discriminate volcanic-arc and within-plate granites, they perform less well for collision tectonics. Besides, felsic or acid rocks are scarce in ocean-ridge settings, which limits the usefulness of these diagrams for this geological environment. Therefore, using an extensive database, we proposed a set of five new discriminant-function-based multi-dimensional diagrams for acid magmas from four tectonic settings (island arc, continental arc, continental rift, and collision). The very similar tectonic settings of island and continental arcs are discriminated for the first time. These diagrams are based on correct statistical treatment of compositional data, because they use natural logarithm transformation of major-element ratios and linear discriminant analysis (LDA). The use of discordant outlier-free samples prior to LDA improved the success rates by about 3–5%. Success rates of these diagrams as inferred from a testing set were between 76% and 88% for island arc, 60% and 92% for continental arc, and 72% and 84% for both continental rift and collision settings. Finally, application of these new diagrams to case studies not compiled in our initial database used for constructing these diagrams provided the following results: a collision setting for the Himalayas at about 30 Ma; an island arc setting for Quaternary acid rocks from geothermal boreholes in El Salvador; an island- or continental-arc setting for northern Italy at 35–52 Ma; a continental-arc setting for the Italy–Austria border at about 30 Ma; either a rift or a collision setting for northern Nigeria at about 164 Ma; a collision setting for central Nigeria at about 144 Ma and for the Cretaceous Masirah ophiolites of Oman; and an island arc setting for the Cretaceous Semail ophiolites of Oman. In spite of the relative mobility of major elements, these applications suggest utility of the new discrimination diagrams for all four tectonic settings.     

Li-F花岗岩液态分离的稀土地球化学标志

华南和其他国家典型Ｌｉ－Ｆ花岗岩的１１８个稀土分析研究表明,随Ｌｉ－Ｆ花岗岩由早至晚阶段或自下而上不同岩相演化,稀土模式曲线有三种变化类型：①降低变化,②升高变化,③突然变化等类型。①称为正向演化类型,是结晶分异结果;②称为反向演化类型,代表气液分馏为主的液态分离;③称为演化突变类型,是不混溶为主的液态分离形成。因此,不混溶为主的液态分离标志是稀土模式演化突变类型和Ｌｉ－Ｆ花岗岩在ＲＥＥ－（Ｌａ／Ｙｂ）ｎ、Ｌａ／Ｓｍ－Ｌａ（μｇ／ｇ）图解中主演化方向线与次演化方向线或与成分点呈分离特点。气液分馏为主的液态分离标志是稀土模式反向演化类型和Ｌｉ－Ｆ花岗岩在ＲＥＥ－（Ｌａ／Ｙｂ）ｎ、Ｌａ／Ｓｍ－Ｌａ（μｇ／ｇ）图解中主演化方向线,指向图解的右上方等     

平衡热液体系中硫同位素演化的几个图解

根据含硫矿物的同位素组成推断热液矿床成因是很有意义的。 1968年首先由H.Sakai指出热液的温度和pH值可以影响硫化物的同位素组成。接着,1972年H.Ohmoto以及1979年他和R.O.Rye系统讨论了平衡条件下热液的物理化学条件对硫同位素分馏的影响,建立了高温热液系统和低温热液系统的热液流体以及含硫矿物与热液成分和物理化学条件(温度、压力、氧逸度和酸碱度等)之间的数学表达式。     

REE Geochemical Indicatrices of Li—F Granite Liquid Segregation

The results of 118 REE analyses of Li-F granites from South China and other countries indicate that there are three variation types of REE pattern curves with different evolution trends from early to late stages of Li-F granite complex of from lower to upper petrofacies of the Li-F granite body;(1) the decreasing,(2) the increasing,and (3) the saltatory variation types.The first variation type is called the positive evolution type,attributed to crystallization differentiation.The second is called the reversion evolution type.which represents liquid segreation dominated by vapor-liquid distillation.The third is called the saltatory variation type,which is formed from liquid segregation dominated by immiscibilty,Therefore,the indicatices of liquid segregation dominated by immiscibility are the saltatory variation type of REE pattern evolution and the separation of the main evolution trend lines either from the sub-evolution trend lines or from the composition points of Li-F granites in the diagrams of REE-(La-Yb)N and La/Sm-La,The indicatrices of liquid segregation dominated by vapor-liquid fractional distillation are the reverstion evolution type of REE pattern curves and the main evolution trend lines of Li-F granites directing to the upper right-hand on the REE-La/Yb)N and La/Sm-La diagrams.     

论CILa/CISm—CILa图解

通过对分离结晶作用和批式熔融作用C_l^y/C_l^x-C_l^y图解的数学分析,笔者认为,虽然C_l^La/C_l^sm-C_l^La图解在一定程度上能区分这两种不同岩浆作用过程,但是,Treuil等的解释是不完全的。直线的斜率和截距还极大地受参数C_o^x,C_o^y,D_x,D_y的影响。该图解并非总是有效。本文还给出了一般式C_l^y/C_l^x-C_l^y在其它方面的可能应用。     

Phase equilibria modelling of residual migmatites and granulites: An evaluation of the melt‐reintegration approach

Suprasolidus continental crust is prone to loss and redistribution of anatectic melt to shallow crustal levels. These processes ultimately lead to differentiation of the continental crust. The majority of granulite facies rocks worldwide has experienced melt loss and the reintegration of melt is becoming an increasingly popular approach to reconstruct the prograde history of melt‐depleted rocks by means of phase equilibria modelling. It involves the stepwise down‐temperature reintegration of a certain amount of melt into the residual bulk composition along an inferred P–T path, and various ways of calculating and reintegrating melt compositions have been developed and applied. Here different melt‐reintegration approaches are tested using El Hoyazo granulitic enclaves (SE Spain), and Mt. Stafford residual migmatites (central Australia). Various sets of P–T pseudosections were constructed progressing step by step, to lower temperatures along the inferred P–T paths. Melt‐reintegration was done following one‐step and multi‐step procedures proposed in the literature. For El Hoyazo granulites, modelling was also performed reintegrating the measured melt inclusions and matrix glass compositions and considering the melt amounts inferred by mass–balance calculations. The overall topology of phase diagrams is pretty similar, suggesting that, in spite of the different methods adopted, reintegrating a certain amount of melt can be sufficient to reconstruct a plausible prograde history (i.e. melting conditions and reactions, and melt productivity) of residual migmatites and granulites. However, significant underestimations of melt productivity may occur and have to be taken into account when a melt‐reintegration approach is applied to highly residual (SiO₂ <55 wt%) rocks, or to rocks for which H₂O retention from subsolidus conditions is high (such as in the case of rapid crustal melting triggered by mafic magma underplating).     

THE QUANTITATIVE-MINERAL COMPOSITION OF GRANITOIDS AND ITS IMPORTANCE FOR PROBLEMS OF PETROLOGY AND NOMENCLATURE

Compilations of mineral compositional data from several "classical regions of granitoid" rock in the U.S.S.R. are shown on triangular diagrams with quartz, K-feldspar, and plagioclase at the apices. Names, most of which are more or less according to general usage, are applied to different fields within the diagram. It is concluded that location within the compositions of rocks diagrams from the different massives indicate relationships between compositions and certain geological features of coeval masses and also reflects such things as assimilation, hybridization, and "degree of differentiation."--R. V. Dietrich.