a multivariate method for determining the provenance and - jst

Geochemical Journal, Vol. 31, pp. 275 to 288, 1997

A multivariate method

protolith ofan example from

southwestern

for determining the provenance

metasedimentary rocks:

the Fork Mountain Formation,

Virginia Piedmont, U.S.A.

and

PAUL C. RAGLAND,' WILLIAM C. PARKER' and JAMES F. CONLEY2

'Geology Department , Florida State University, Tallahassee, FL 32306, U.S.A. 2Virginia Division of Mineral Resources

, Charlottesville, VA 22903 (retired), U.S.A.

(Received April 22, 1996; Accepted February 20, 1997)

Metasedimentary and metavolcanic rocks within the Smith River allochthon, southwestern Virginia Piedmont, are present in two units, the Bassett and the Fork Mountain Formations. The younger Fork Mountain Formation contains some metabasalt layers but primarily consists of a biotite gneiss and an overlying high-alumina mica schist; the biotite gneiss is wedge shaped and thins to the northwest. Fourteen major-oxide analyses were performed on samples of metasedimentary rocks from the Fork Mountain Formation. Compositions of both gneisses and schists fall on single linear trends on conventional Harker-type scattergrams, which can be explained by sedimentary mixing lines between pure quartz and a pelitic sedimentary assemblage. In addition, the negative correlation between Si02 and K20 is significant because in igneous rocks these two oxides are normally positively correlated. Thus relatively coarse, quartz-rich sediments apparently became the psammitic rocks that formed the

paragneisses, and the finer, clay-rich sediments became the shales that are protoliths to the schists. A simple explanation of these relationships is a relatively fine-grained, deep-water sedimentary facies present in the northwest that transgressed to the southeast through time; the source for these sediments would have been to the southeast. Principal components analysis (PCA), ratio-ratio scattergrams, and t-tests for differences of means,

however, indicate that this two-component. mixing is an over-simplification. Some subtle differences in chemistry between the gneisses and schists exist that cannot be explained by linear mixing alone and may imply more than one source region for the sediments. In addition, PCA and simultaneous solution of mass balance equations estimate the following major rock-forming mineralogy for the pelitic sediments, exclusive of quartz: illite 48%, montmorillonite 20%, chlorite 9%, K-feldspar 20%. This mineral composition is consistent with known patterns of mineral alteration during burial diagenesis. Discriminant function analysis (DFA) was also performed; it suggests that an apparently large com

positional gap is present between the gneisses and schists. Conventional bivariate scattergrams and PCA, however, indicate that a compositional continuum exists for most oxides.

INTRODUCTION

Determining the protolith of a metamorphic

rock has long been of interest for many reasons,

one of which is because reconstructions of regional

geologic histories in metamorphosed terranes is

partly dependent upon knowing something about the pre-metamorphic lithologies of the rocks. In

recent years some aspects of metamorphic petrol

ogy have gravitated toward thermobarometry and

P-T-t paths, but a determination of the protolith

of the metamorphic rock is still an important part

of the discipline. For many regionally metamor

phosed rocks the protolith is obvious, but this is

generally not true, especially in the case of some

gneisses and schists that could have originally been a number of different igneous or sedimentary

rocks. Once the protolith is determined to be a

275

276 P. C. Ragland et al.

sedimentary rock, as in the case of this paper, an

attempt can be made to determine the provenance

of the sediments. This paper will make that at

tempt.

In addition to observing the physical record

where observable (relict mineralogy, textures,

structures, field associations, etc.), the classic ap

proach to protolith identification has been to examine whole-rock chemical trends (e.g., De

LaRoche, 1974; Leyreloup et al., 1977; Floyd et

al., 1989; Muller, 1989; Imeokparia and

Emofuricta, 1991; Maas and McCulloch, 1991;

Slack and Stevens, 1994; Lorenz, 1995). This pa

per will also use whole-rock chemical trends, but it will go a step further and utilize a multivariate

numerical technique, PCA, as well as mass-balance

calculations, in an attempt to determine at least

semi-quantitatively the mineralogy of the protolith.

If the pre-metamorphic mineralogy can be deter

mined with any degree of certainty, perhaps more

can be inferred about the rocks' provenance than

through past efforts that relied on simple element

scattergrams. A necessary caveat is that any metasomatic changes that took place during

metamorphism were so minor that the overall

chemical compositions of the rocks were not

drastically changed. Although this presumption

cannot be proven, the fact that chemical patterns

and compositions observed in these rocks are

consistent with typical sedimentary protoliths

makes the assumption of minimum mobility reasonable.

The rocks on which this study is based are

from the Smith River allochthon in the Inner

Piedmont of southwestern Virginia. The unit is

the Fork Mountain Formation, which consists of

a high-alumina mica schist and a biotite gneiss

with rare amphibolite (metabasalt) interlayers; the biotite gneiss grades laterally into and underlies

the mica schist. Although the protolith of the

gneiss is less certain, the schist was originally almost certainly a pelitic sediment (Conley and

Henika, 1973; Conley, 1989). The questions are:

1) what was the protolith of the gneiss?, 2) are

the two lithologies genetically related?, and 3)

what can we infer about the provenance of the

sediments? A small database of unpublished ma

jor-element analyses is available from the Fork Mountain Formation, which is adequate to dem

onstrate the applicability of the method. The main

purpose of this paper, therefore, is to demonstrate that the multivariate approach coupled with massbalance calculations and ratio-ratio diagrams described herein can yield some information about these rocks that other methods cannot. Obviously, an exhaustive treatment of the petrogenesis of the Fork Mountain Formation would necessitate additional data, such as trace elements, isotopes and thermobarometry. Our primary intent, however, is to use the limited data presented here to demonstrate a new technique based on multivariate analysis.

GEOLOGIC SETTING

The Fork Mountain Formation is located within

a fault-bounded polydeformed, polymetamor

phosed synformal structure named the Smith River allochthon (Fig. 1). The allochthon was emplaced

by movement along the Ridgeway thrust fault,

which bounds the structure, both to the northwest

and to the southeast (Conley, 1989). The Ridgeway fault is truncated on the northwestern side of the

allochthon by the younger Bowen's Creek fault

and on the southeastern side of the allochthon by

the Chatham fault, which is the western border

fault of the Danville (Triassic-age) rift basin. The

allochthon is bounded on the northwest by the

Blue Ridge anticlinorium and on the southeast by

the Sauratown Mountains anticlinorium.

Metasedimentary and metavolcanic rocks that

make up the allochthon consist of two units, the

Bassett and the Fork Mountain Formations. The

overlying Fork Mountain Formation, which is the focus of this study, consists of two units, a biotite

gneiss and an overlying high-alumina mica schist (Conley and Henika, 1973; Conley, 1985, 1989). The contact between the two units is gradational

and intertonguing over short distances. The biotite

gneiss is wedge-shaped and thins to the northwest; along the northwestern boundary of the allochthon

it disappears in outcrop and only the mica schist

Multivariate method for metasedimentary rocks 277

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is exposed. The two units are approximately laterally equivalent and "may represent a change from pelitic sediments to the northwest to

psammitic sediments to the southeast" (Conley, 1989). A major goal of this study is to test this hypothesis. The biotite gneiss is a medium-gray, banded rock that is composed of alternating layers of

quartzo-feldspathic gneiss and garnetiferous twomica gneiss. It primarily consists of approximately

equal amounts of quartz and plagioclase, with varying amounts of microcline, biotite, muscovite,

garnet, and high-Al minerals partially to totally retrograded to sericite. In part, the biotite gneiss is composed of a jumble of angular fragments of

quartzite and calc-silicate quartzite that has been suggested to be a sedimentary melange deposit

(Rankin, 1975; Conley, 1985). The mica schist is a light to medium-grey,

fine to medium-grained, porphyroblastic rock of

variable mineralogical composition. It consists

mainly of muscovite, quartz, garnet, and minor

plagioclase, with locally developed chloritoid

porphyroblasts and anomalously high concentrations of Fe-Ti oxides. Pelitic clasts in a pelitic

matrix are observed only along the northwestern

boundary of the allochthon where metamorphic

grade is at staurolite grade. To the southeast, metamorphic grade is more intense and any pelitic

clasts present have been erased.

RESULTS

Methods

Fourteen representative samples (seven from the biotite gneiss and seven from the mica schist) were chosen for major-element analyses. Samples, typically 20 cm on a side and weighing 20-25

kg, were slabbed, trimmed of weathered material, and crushed. Most analyses were performed by X-ray fluorescence; exceptions were MgO and Na20, which were analyzed by atomic-absorption spectrometry, and ferric iron, analyzed using the colorimetric method described in Shapiro (1975). Calibration curves were prepared using known rock standards, such as USGS standards. Preci

sion was better than 3 percent (for most elements

<2 percent); analyses are given in Table 1.

Mixing lines

Before discussing the results of the multivariate numeric approach, some simple bivariate scattergrams can provide some useful information. A composite diagram showing four scattergrams

is given in Fig. 2. The "best-fit" lines were constructed to pass through the 100 percent Si02 point and the points representing the arithmetic averages for each Si02-oxide pair. The CaO-SiO2 plot is not shown to avoid clutter; it is very similar to the M90-SiO2 plot. The only trend on Fig. 2 that is better fit by a second-order, quadratic curve than a first-order line is the A1203-SiO2 trend; compositions of schists tend to plot above this line, while compositions of gneisses plot below. The possible significance of this observation will be explored in this paper. The presence of sericite in the biotite

gneisses formed during retrograde metamorphism suggests the possibility of alkali mobility, but the fact that Na20 + K20 on Fig. 2 fall on a mixing line with quartz suggests that alkali mobility is not a major factor. The lack of scatter seen in the trends on Fig. 2 can in part be explained by clo

30

20

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40 60 80 100 WEIGHT % S102

Fig. 2. Composite Harker diagram for gneisses and schists from the Fork Mountain Formation. "Best fit" lines are drawn through 100 percent Si02 and the point representing the X and Y-coordinate arithmetic means

for each line. FeO* is total Fe as FeO. The seven gneiss samples contain >54 percent Si02; the seven schist samples contain 554 percent.

280

sure (law of constant sums); however, these trends

can still be viewed as petrologically significant

mixing lines between quartz and a suite of clay

minerals.

If all the trends on Fig. 2 are assumed to be linear, then they are best explained as mixing lines

between two end-members: pure quartz on one end and a pelitic sedimentary assemblage on the other. The most likely mineralogical composition of this

pelitic assemblage will be examined further in the next section. Thus to a first approximation, the differences in composition in gneisses and schists in the Fork Mountain may simply be a function of grain-size variability in the original sediments. The relatively coarse, quartz-rich sediments eventually became the psammitic rocks that formed the

paragneisses, and the finer, clay-rich sediments became the shales that were the protoliths of the schists. These mixing lines imply that ratios among different clay minerals remained the same throughout the entire sequence, which could indicate a single provenance or constant mixing pro

portions from different sources for these sediments. This "scenario" is a working hypothesis that can be examined by utilization of a multivariate numerical technique, principal components analysis

(PCA), coupled with mass-balance calculations.

Results of PCA PCA is one of a number of numerical (rather

than statistical) techniques that allow the researcher to search for structure in a large database involv

P. C. Ragland et al.

ing many variables. It is typically the first step in a search for structure. PCA searches for structure in a dataset by projecting the data points onto axes

of an orthogonal co-ordinate system that is different from the original co-ordinate system of the

raw variables; the main intent here is to redistribute the variances. Given a data array with n variables in n-dimensional space, the linear best-fit line through this array is the first principal component

(or first eigenvector); the next best-fit line, orthogonal to the first, is the second principal com

ponent (second eigenvector), and so on until n

principal components and thus eigenvectors have been calculated. If the data points are projected

onto each of these eigenvectors, the spread (variance) of these projected points measures the length of the eigenvector and is referred to as the eigenvalue of that eigenvector. See Le Maitre (1982) for an insightful, well-written discussion of the basis for PCA and its applications in petrology. The PCA program is included in the software

package SPSS/PC+, version 5.0.1, which is run on an IBM-compatible microcomputer. The pro

gram first standardizes the dataset by calculating Z-scores in order to equalize the contribution of

each variable to the analysis. A Z-score is defined as (xi x)/s, where xi is the numerical value of a

variable; x and s are the mean and standard de

viation, respectively, of all the values measured

for that variable. Then n new variables (the prin

cipal components) are calculated as linear combi

nations of n original variables in such a way that

Table 2. Contributions of original variables and principal components to total variance

Variable v2 CUM (%) PC Eigenvalue CUM (%)

Fe203

MnO

FeO

P205

K20

A1203

MgO

Ti02

CaO

Na20

SiO2

2273.40

1932.97

1226.10

1038.86

995.94

818.85

599.13

493.48

479.78

385.23

283.01

21.6

18.4

11.6

9.9

9.5

7.8

5.7

4.7

4.6

3.7

2.7

21.6

39.9

51.6

61.4

70.9

78.7

84.4

89.1

93.6

97.3

100.0

1

2

3

4

5

6

7

8

9

10

11

5.12855

1.68156

1.31043

1.24218

0.95105

0.34275

0.17833

0.09017

0.05389

0.01932

0.00176

46.6

15.3

11.9

11.3

8.6

3.1

1.6

0.8

0.5

0.2

0.0

46.6

61.9

73.8

85.1

93.8

96.9

98.5

99.3

99.8

100.0

100.0

Multivariate method

the first principal component accounts for the

largest possible percentage of the total variance

(sum of the eigenvalues). Successive principal components have increasingly small eigenvalues

and thus account for increasingly smaller percent

ages of total variance. All the n new variables

account for the same amount of total variance in

the entire dataset as do the n original variables.

In order to approximate the original variables' contributions to the overall variance, V2, the square of the coefficient of variation, is used. The term

V is defined as 100s/x, where s and x are defined as above (recall that the variance is the square of the standard deviation). The term V2 is used rather than variance (s2) because variances of the major oxides, relative to those of the minor oxides such as MnO and P205, tend to dominate the overall variance. As can be seen in Table 2, in

general V2 values for major oxides are not systematically different from those for minor oxides. Table 2 also ranks the coefficients of variation

for the original variables (V2) and compares their

percentage contributions to the overall V2 with the

percentage contributions of the ranked eigenvalues to the overall variance. In Table 2 the first few

raw variables account for considerably less of the

total variance than their counterparts among the

new variables (the principal components or PC

values). Consequently, only a few principal com

ponents are necessary to account for most of the variance in the dataset, as opposed to many more

original variables. Also note in Table 2 that Fe is

considered separately as FeO and Fe203 rather

than total Fe; this is because of the importance of

Fe-Ti oxides as well as ferromagnesian silicates

in these rocks, which will be discussed below. In

addition, Na20 and K20 were considered as

separate variables rather than combining them as

total alkalies.

In order to test the effects of these separations

of some oxide variables on the PCA process, we also analyzed the data in two additional ways: 1)

with Fe203 and FeO combined as total iron, as

well as Na20 and K20 combined as total alkalies, and 2) with Fe203 and FeO combined as total iron

and Na2O and K20 kept separate. With the ex

for metasedimentary rocks 281

ception of the above oxides treated as combined

variables, the results of these additional analyses

were essentially similar to the results of the PCA

described here. We chose to present the results of

the separate-variable analysis because combining

variables decreases the degrees of freedom and

thereby increases the closure effect. Obviously, the

Fe203/FeO ratio is different in these metamorphic

rocks than it was in the original sediments, and

the Na20/K2O ratio may be different as well. As

the PCA results were not very different in any of

the three analyses, increasing the degrees of free

dom was deemed sufficiently important to perform

the PCA analysis in the manner presented in this

paper. Figure 3 shows plots of variable loadings and

sample scores for the first two principal compo

nents (PC1 and PC2), which in this study account for 61.9 percent of the total variance (Table 2).

The variable loadings in Fig. 3A are the coeffi

cients for each variable in the linear equations

necessary to convert the standardized variables to

the sample scores; these scores mark each sample's

position in the new orthogonal co-ordinate system with PC1 and PC2 as the axes (Fig. 3B). Thus

PC I and PC2 for each sample on Fig. 3B are simply linear summations of all eleven standard

ized original variables multiplied by the appropri

ate variable loadings.

Useful information can be obtained by com

paring Fig. 3A with Table 3, as well as Figs. 2 and 3B. For sake of this discussion, variables will

be considered as elements rather than oxides. Note

that Si is strongly negatively loaded on PC1,

whereas the elements that make up the ferromag

nesian silicates are strongly positively loaded on

PC 1. Thus Si and these other variables should be

highly negatively correlated, which is supported

by Table 3. The negative correlation between Si

and K is particularly noteworthy; in igneous rocks

these two variables are generally positively corre

lated. In addition, the very strong negative corre

lation between Si and Al is more indicative of

metasedimentary rocks than metaigneous rocks. Na

and P, however, are not correlated with Si and

are not strongly loaded on PC 1. In addition, it is

282

1

0.5

0

-0.5

-1-1

P. C. Ragland et al.

U i

Na

A. LOADINGS

P

F3

F2

Vi

K

2

1

0

-1

-2

-3

-0.5 0 PC1

0.5 1

N U a

0

B. SCORES

0 ox

O X X

0

x

x

Fig. 3. B, sampl g and scores loaded on are highly g loaded PC]. are marked by x's and the schists by open circles; also on B the the two g "mixing line" and plots f f explanation.

-3 -2 -1 0 1 2

PC1

PCl -PC2 plots for A. variable loadings , and es scores. See text for explanation of loadin

s

. Note that Si is very strongly negatively PCl and most of the remaining variables

positively load on neisses On B the

"sample" represented by + is an average of samples on either end of the

half-way between them. See text or urther

apparent from Fig. 3B that although neither PCI

or PC2 individually distinguish between the com

positions of gneisses and schists, their compositions do fall in different fields on a plot of PC1

versus PC2.

Ragland et al. (1997) have shown that on sample-score plots of principal components such as Fig. 3B, linear-mixing lines behave similarly to analogous lines on simple bivariate scattergrams involving the raw data-in this case major and minor oxides. As an example, a mixing line has been drawn between two compositionally extreme

samples on Fig. 3B. The plus sign (+) marks an artificial sample that is simply the average of the two extreme samples on the mixing line. As this average "sample" represents a 50-50 mixture of the two end-member samples, it should plot on the mixing line half-way between them, and it does, which is further confirmation of the conclusion reached by Ragland et al. (1997). As might be expected for rocks rich in silicates,

PC I (Fig. 3) separates Si02 from the other

chemical components, while PC2 differentiates between those other oxides. A simple linear-mix

ing pattern that can be explained by quartz mixing

with a fixed suite of clay minerals (as suggested

in Fig. 2) is not apparent in Fig. 3B. Ignoring the

anomalous Si-rich gneiss (#3851, Table 1) that

plots on the left at about -2.6 (the left end of the

Table 3. Linear correlation coefficients

Si02 Ti02 A1203 Fe203 FeO FeOr MnO MgO CaO Na2O K20 P205 LOI

SiO2

TiO2

A1203

Fe2O3

FeO FeOr

MnO

MgO

CaO Na2O

K20

P205

LOI

1 -.54

- .97 - .56 - .65 -.94

-.71

- .55 - .76

.04 -.58

-.05

- .55

1

.37

.24

.65

.65

.31

.85

.40

.17

.41-.06

.02

1

.48

.61

.86

.70

.37

.71- .04

.53

.05

.51

1

-.20

.69

.18

.29

.48

-.22

.19- .24

.75

1

.56

.61

.62

.72

-.05

.50- .16

.59

1

.62

.53

.42

.24

.45

.11- .05

1

.28

.59

.02

.36

.33

.48

1

.47

.00

.60

.11

.01

1

.20

.40

.32

.46

1

-.55

.16 - .08

1

.19

-.051 -.05 1

Multivariate method for metasedimentary

mixing line discussed above), a very diffuse trend

exists for the remaining gneisses and schists, but

this is not a mixing trend parallel to PC I with

pure Si02 on one end, in contradiction to Fig. 2. This observation has some petrogenetic signifi

cance and must be explored.

Recall that the working hypothesis derived from the consideration of Fig. 2 is based on a

sedimentary linear-mixing trend between two end

member components: pure quartz and a pelitic

assemblage. This trend could imply grain-size

variations in sediments from a single source area

relatively coarse, quartz-rich sediments (now the

paragneisses), and the finer, clay-rich sediments (now the schists). Further recall that within the Fork Mountain Formation: 1) the schist overlies

the gneiss; 2) the gneiss is wedge shaped and thins

to the northwest; 3) the two units are at least partly

laterally equivalent; and 4) the units are grada

tional into one another and no evidence of a fault

contact between them exists. The hypothesis re

quires the relatively fine-grained, deep-water sedimentary facies to have been present in the northwest and it transgressed to the southeast

through time; the source for these sediments would

have been to the southeast.

The implications of Fig. 3B, however, argue

rocks 283

against such a simple interpretation. There appear

to be some subtle differences in chemistry between

the gneisses and schists that cannot be explained

by the linear-mixing hypothesis outlined above.

As an example, as stated above, no linear-mixing

trend between quartz and a pelitic component is

apparent when Figs. 3A and 3B are considered

together. These subtle differences are explored

further in Table 4, which ranks the oxides in order

of probabilities that their arithmetic means in the

gneisses relative to the schists are not significantly different (results of t-tests for differences of

means). In order for simple mixing between quartz

and a clay component to explain the data in Table

4, Si02 should be significantly higher in the

gneisses (it is) and all other oxides should be significantly lower in the schists (they are not). Using

90 percent (two-tailed significance = 0.10) as a

limit, only the top seven oxides are significantly

different. Subtle differences in accessory heavy-,

mineral suites might account for no differences in

minor oxides such as Ti02 and P205, but they

cannot explain Na2O or MgO. Also recall the ob

servation that A1203 is systematically high in the schists and low in the gneisses relative to the lin

ear-mixing model (Fig. 2). Thus there appear to be some subtle chemical differences between the

Table 4. Comparison of arithmetic means for the two lithologies

Variable Schists Gneisses

std.dev.

Two-tailed significance*

mean std.dev. mean

A1203

SiO2

FeOr

CaO Fe203

LOI

MnO K20

FeO

MgO Ti02

Na2O P205

23.37

49.12

11.46

2.35

6.16

3.97

0.140

4.28

5.89

2.19

1.46

1.80

0.123

2.29

3.81

1.48

0.29

2.19

1.22

0.053

1.17

1.97

0.54

0.25

0.35

0.036

14.23

63.72

7.92

1.77

3.50

2.73

0.091

3.45

4.93

2.02

1.38

1.85

0.119

2.95

7.51

2.15

0.40

1.60

0.94

0.040

1.20

1.83

0.51

0.38

0.39

0.045

.000

.001

.005

.010

.025

.056

.077

.216

.362

.575

.638

.800

.847

*Probability that the means are not significantly different based on t-test that assumes unequal variances

identical to those of the standard Student t-test, which is less conservative and assumes equal variances.. Results are almost


gneisses and schists observation that A1203 is systematically high in the schists and low in the

gneisses relative to the linear-mixing model (Fig. 2). Thus there appear to be some subtle chemical differences between the gneisses and schists that cannot be explained by simple sedimentary mixing of pelitic and psammitic sediments from a single source. As stated above, PC1 (Fig. 3) strongly sepa

rates Si02 from the other oxides, most notably

from A1203 (r = -.97, Table 3), which is at least

partly a result of closure in the data. PC2 (Fig. 3), orthogonal and uncorrelated to PC1, is less af

fected by closure. P205, possibly contained in

apatite within sedimentary heavy mineral suites,

is positively loaded on PC2. Consequently, Fig. 4

is an example of a ratio-ratio plot, in this case

plotting A1203 versus Si02, both normalized

(ratioed) to P205. On this type of ratio-ratio dia

gram linear-mixing trends plot as straight lines. Two distinct linear trends, one for each lithology,

are apparent on Fig. 4, strongly suggesting that a

single linear mixing model for both lithologies is not sufficient. The point near the lower right cor=

ner of the graph that falls off the gneiss trend

represents the anomalous high-Si02 gneiss

sample (#3851; Table 1) on Fig. 3B. Note that

the extremely strong negative correlation between

Si02 and A1203, seen on Fig. 2, is no longer

overwhelming as a result of the normalizing pro

cedure. Possible differences in provenance, as re

flected in apatite contents of different heavy min

eral suites, may account for these two trends. Significant to our discussion here, the PCA results

enabled us to choose the appropriate variables to illustrate this phenomenon. This discussion does

not negate the conclusions drawn above from Fig.

2. The samples do apparently represent some mixing between quartz and a clay mineral suite;

however, additional factors (e.g., differences in

heavy mineral suites and perhaps metasomatic

exchange between K and Na) complicate a simple linear mixing model for these rocks.

In order to at least semi-quantitatively estimate

the clay-mineral assemblage in the original sedi

ments that now make up the schists, and addi

0 N

M 0

Q

400

300

200

100

SCHIST

GNEISS

.

. •

A

0 400 600 800 1000

S102/P205

Fig. 4. Ratio-ratio plots of Si02/P205 versus A1203/ P205 showing two distinct trends for gneisses and schists.

tional PCA was performed. The results are exhibited in Fig. 5, which shows the front (PC1-PC2), top (PC1-PC3), and right-side (PC3-PC2) projections of a three-dimensional PC 1-PC2-PC3 plot. It includes compositions of the schists and some ideal compositions of several minerals that are most likely to occur in pelitic sediments, all of which were recast into cation percents before the PCA was calculated. It was necessary to recast the data in cation percents so fewer assumptions have to be made about solid-solution compositions in the minerals. An example is Mg + Mn + Fe2+ combined to form the single variable ME PC I through PC3 account for 90.1 percent of the total variability in the dataset. Figure 5 can be utilized to estimate semi-quantitatively the mineralogical composition of these pelitic sediments, at least with respect to their major mineralogy. Quartz was not included in the calculations but was probably a mineralogical component of most schist samples; K-feldspar had to be included to obtain a reasonable solution and may be assumed to be primarily detrital in the original sediment, as perhaps can some of the chlorite.

If the schists were derived from sedimentary

rocks that contained a certain set of minerals, then

in PC1-PC2-PC3 space compositions of the schists should fall within the geometric figure (triangle ,

etc.) bounded by compositions of those minerals. Thus the schist compositions should fall within the projections of that figure on each of the three

graphs shown in Fig. 5. On that basis, kaolinite can be omitted as a likely major mineralogical constituent in the original sedimentary rocks. The schist compositions on all three graphs, however, do plot within the triangular projections of the three-phase assemblage chlorite-montmorilloniteK-feldspar (Fig. 5). Likewise, all schist compositions fall within the figure for the four-phase assemblage that includes the three minerals above

plus illite. Which is more likely correct, the threeor four-mineral assemblage? Although it is necessary for a given bulk composition to fall within all orthogonal projections of the geometric figure whose apices represent the compositions of its constituent phases, the reverse situation is not necessarily true; i.e.,. a bulk


2

1 m X schist

x + ave. schist ' o ' „ i Mite

CL m montmorifonite a / \ c chlorite

-2 ~~ f K-feldspar f k kaolinite

-3 -2 -1 0 1 2

PC1

2 2 i f f i

1 1 k zik

U U 0 X m a 0 x is m

CL -1 -1

-2 -2 c

-33 2 -1 0 1 2 -33 -2 -1 0 1 2

PCf PC3

Fig. 5. Front (PC] -PC2), top (PC] -PC3), and side (PC3-PC2) projections of a three-dimensional PCl -PC2-PC3 "scattergram" for the schists and some major rock forming minerals (excluding quartz) that occur in shales, considered likely protoliths of the schists. See text for further explanation.

composition can fall within the orthogonal pro

jections of a figure but not fall in the figure itself. To resolve this problem, we must turn to a numerical solution involving simultaneous solution of several mass-balance equations. Because the variables used in the PCA to prepare Fig. 5 are in cation percent, these mass-balance equations can be written in the form:

flctl + f2ci2 + ... + ffc,1 = Cb,,

where f, is the molar fraction of the j-th mineral, c~~

is cation percent for the i-th cation in mineral j,

and cbi is cation percent for the i-th cation in the

bulk rock. As these variables are in cation percent, some of them can be summed to create composite

variables; e.g., MF = Mg + Fee + Mn and NK =

Na + K. The most pelitic sample has a bulk-rock composition in cation percent: Si = 53%, Al =


30%, MF = 5.3%, and NK = 8.8%. This tech

nique of combining molar variables decreases the

degrees of freedom and thus increases closure, but

is necessary to estimate mineral compositions.

Based on this analysis, solution of four simulta

neous equations for fl through f4 yields: illite

48%, montmorillonite 20%, chlorite 9%, K

feldspar 20% (note that these percentages re

flect the non-quartz portion of the sample only).

All combinations of only three minerals gave im

possible solutions. The cations Ti, P, Ca, and Fe3+ were not included in the mass-balance calculations, although ilmenite, apatite, and especially magnetite are quite common in these rocks. Note the high Fe203 contents of many schist samples in Table 1. Both the PCA and mass-balance calculations were concerned with the major rock-forming rather than accessory minerals, so these three elements were not included in the analyses. Sufficient Ca is

present to account for the 20 percent montmorillonite in the solution. Quartz was also undoubtedly

present in the more silicic shales. No three-phase assemblage is adequate to define quantitatively the major mineralogy of the schists' protolith, but the four-phase assemblage illite-montmorillonitechlorite-K-feldspar (forming the quadrilaterals on Fig. 5) is adequate.

Comparison with other sediments

In order to demonstrate the value of the technique discussed herein and to improve our understanding of potential source(s) of the Fork Mountain Formation protoliths, we have compared the results of our analyses with other mineralogical and chemical analyses of sediments (Pettijohn, 1963, 1975; Clark, 1924). Due to the high-alumina content in the Fork Mountain rocks, clay-rich sediments (e.g., wackes, muds, and shales) are the most reasonable choices for comparison. This decision is confirmed using the geochemical classification diagrams of Herron (1988, log[Fe203/K2O] vs. log[SiO2/A1203]), and Muller (1989, Si02/ A1203 vs. K20/Na2O) in which the schists plot as shales (pelites) and the gneisses plot as shales/ wackes (Herron) or near the juncture of the gray

wacke/arkose/pelite felds (Muller). Using the

method of Nesbitt and Young (1982), a Chemical

Index of Alteration (CIA) of 66 was calculated

for the schists, which reflects a relatively imma

ture shale (average, mature shales range from 70

to 75). As demonstrated by Hower et al. (1976),

diagenesis and burial metamorphism commonly

have little effect on the bulk chemistry of clay

rich detrital sedimentary rocks (other than loss of

CaCO3), but are often associated with mineralogic

changes. Of particular note is the conversion of

montmorillonite + K-feldspar + mica to illite +

chlorite + quartz. Thus the pre-metamorphic min

eral composition, as predicted by PCA, would re

flect partial mineralogic conversion during burial.

The observations presented in Conley (1985)

indicate that the source area for the sediments that

make up the Fork Mountain Formation was to the

east and southeast. The biotite gneiss unit, a unit

with more of a wacke/arkosic composition, would

logically be deposited closer to its source, and the

high-alumina mica schist would be derived from

pelitic sediment swept further out in the basin and deposited further from the source. This is well il

lustrated by the fact that the biotite gneiss thins

rapidly to the northwest within the allochthon and

is replaced along the northwestern boundary of

the structure by the high-alumina schist, which

thickens rapidly in that direction. Our analysis

confirms Conley's (1985) speculations concerning

the protoliths of the metasediments.

Comparison with DFA

Finally, although the main thrust of this paper involves demonstrating the utility of PCA for these types of petrogenetic problems, a brief comparison of PCA and DFA (discriminant function analysis) is informative. In fact, DFA, another numerical method, has probably been used more in petrology and geochemistry than has PCA (e.g., Pearce, 1976; Bhatia, 1983; Roser and Korsch, 1988; Muller, 1989). In DFA sample groups are prechosen by the investigator (hopefully using criteria that have nothing to do with the variables used for the DFA), and the main purpose of the analysis is to project the data points onto a new or


thogonal co-ordinate system in such a way as to maximize the differences between the groups. This co-ordinate system will have one less axis (dimension) than either the number of original variables or number of groups, whichever is smaller. As for PCA, the axes in DFA are eigenvectors, and are referred to as discriminant functions; data

projected onto DF1 best discriminate between the groups, DF2, next best, etc. Figure 6 is a comparison of PCl and DF1

plotted against Si02 using the Fork Mountain database; for DFA the samples are grouped into

gneisses and schists. As there are only two groups, only DF1 was calculated. Note for DF1 the strong

separation between the two lithologic groups; DF1

is positive for the schists and negative for the

gneisses. An apparently large compositional gap between about -4 and +4 is present between the

gneisses and schists. Is this gap real? The trend of PC 1 on Fig. 6, as well as trends on Figs. 2 and

3B, indicate that a compositional continuum exists

and the gap is not real. Figure 5, however, indi

cates that for some oxides such as P205, a gap may

be real. DFA tends to exaggerate differences be

tween groups; in this regard PCA tends to be more

conservative. If two or more groups plot in dif

8

ferent fields on a PC1-PC2 scattergram, one can

be assured that the groups are indeed composi

tionally distinct. If the only purpose is to maxi

mize the ability of a given set of variables to dis

criminate between groups, then DFA is preferred.

We believe, however, that a compositional con

tinuum (such as compositions plotting along a

mixing line in n-dimensional space) for most (but

not necessarily all) components can be more

readily distinguished from two or more distinct

populations by PCA than by DFA.

0 4 a0 Z 0 Q

LL 0 -4

A DF1

PC1

AA

40 50 60 70 80 WEIGHT % S102

Fig. 6. Weight-percent Si02 plotted versus DF1 and PCI. Schist samples all have positive values for DFI, whereas gneiss samples all have negative values. Note the continuum for PC], in comparison with the apparently large compositional gap for DF1 between the

gneisses and schists.

SUMMARY

Major-element geochemical analyses indicate that the biotite gneisses and high-alumina schists of the Fork Mountain Formation were formed from

psammitic (a matrix-rich arenite, like a wacke) and pelitic (probably shale) sedimentary protoliths, respectively. Conventional analyses, using Harkertype plots, suggest that these sediments fall on a linear mixing line between quartz and a pelitic mineral assemblage. PCA and mass-balance calculations reveal two points of interest: 1) the distribution of chemical analyses cannot be attributed to a strictly linear mix, and 2) the composition of the pelitic endmember (exclusive of quartz) can be approximated as illite 48%, montmorillonite 20%, chlorite 9%, and K-feldspar 20%. This shale composition is comparable with that of other Paleozoic and Cenozoic shales that have under

gone burial diagenesis (Hower et al., 1976) and reflects a relatively immature composition (Nesbitt and Young, 1982), which is indicated by the calculated K-feldspar content. The results of the analyses agree well with an origin of the metasediments from the east and southeast. In our opinion, PCA has been, and will continue to be, a

powerful tool for analyzing petrologic and geochemical data.

Acknowledgments-The Virginia Division of Mineral Resources provided the funding for this project. We are indebted to Bill Henika for valuable discussions about the regional geology of this area.


REFERENCES

Bhatia, M. R. (1983) Plate tectonics and geochemical composition of sandstones. Jour. Geol. 91, 611-627.

Clark, F. W. (1924) Data of Geochemistry. 5th edi tion. U.S. Geol. Survey Bull. 770.

Conley, J. F. (1985) Geology of the southwestern Vir

ginia Piedmont. Virginia Div. Min. Resources Pub. 59, 33 pp.

Conley, J. F. (1989) Geology of the Rocky Mount, Gladehill, Penhook, and Mountain Valley quad rangles, Virginia. Virginia Div. Min. Resources Pub. 90, Part C, 15 pp.

Conley, J. F. and Henika, W. S. (1973) Geology of the

Snow Creek, Martinsville East, Price, and Spray

quadrangles, Virginia. Virginia Div. Min. Resources Rpt. of Investigations 33, 71 pp.

Conley, J. F. and Toewe, E. C. (1968) Geology of the Martinsville West quadrangle, Virginia. Virginia Div. Min. Resources Rpt. of Investigations 16, 44 pp.De LaRoche, H. (1974) Geochemical characteristics of metamorphic domains: survival and testimony of their

premetamorphic history. Sci. Terre 19, 103-117.Floyd, P. A., Winchester, J. A. and Park, R. G. (1989) Geochemistry and tectonic setting of Lewisian clas tic metasediments from the early Proterozoic Loch

Maree group of Gairloch, NW Scotland. Precambrian Res. 45, 203-214.

Herron, M. M. (1988) Geochemical classification of terrigenous sands and shales from core or log data . Jour. Sed. Petrol. 58, 820-829.

Hower, J., Eslinger, E. V., Hower, M. E. and Perry, E. A. (1976) Mechanism of burial metamorphism of argillaceous sediment: 1. Mineralogical and chemical evidence. Geol. Soc. Amer. Bull. 87, 725-737.

Imeokparia, E. G. and Emofuricta, W . O. (1991) Protoliths and petrogenesis of Precambrian gneisses from the lgbeti area, SW Nigeria. Chem. Erde 51 , 39 54.

Le Maitre, R. W. (1982) Numerical Petrology. Elsevier , Amsterdam, 281 pp.Leyreloup, A., Dupuy, C. and Andriambololona , R.

(1977) Chemical composition and consequences of the evolution of the French massif central Precam brian crust. Contrib. Mineral. Petrol. 62, 283-300.

Lorenz, W. (1995) Protolith analysis of metamorphicsiliciclastic rocks in the Erzbirge Mts., Germany. Sed. Geol. 97, 43-67.

Maas, R. and McCulloch, M. T. (1991) The provenance of Archean clastic meta-sediments in the Marryer

Gneiss complex, Western Australia: trace element

geochemistry, Nd isotopes, and U-Pb ages for detrital zircons. Geochim. Cosmochim. Acta 55, 1915-1932.

Muller, H. D. (1989) Geochemistry of metasediments in the Hercynian abd pre-Hercynian crust of the Schwarzwald, the Vosges, and northern Switzerland. Tectonophisics 157, 97-108.

Nesbitt, H. W. and Young, G. M. (1982) Early Prot erozoic climates and plate motion inferred from major element chemistry of lutites. Nature 299, 715-717.

Pearce, J. A. (1976) Statistical analysis of major ele ment patterns in basalt. Jour. Petrol. 17, 15-43.Pettijohn, F. J. (1963) Chemical composition of sand

stones-excluding carbonate and volcanic sands. Data of Geochemistry (6th edition). U.S. Geol. Sur vey Prof. Paper 440S, 19 pp.

Pettijohn, F. J. (1975) Sedimentary Rocks. 2nd edition. Harper and Bros., New York, 718 pp.Ragland, P. C., Conley, J. F., Van Orman, J. A. and Parker, W. C. (1997) Principal components analysis as applied to the petrochemistry of the Martinsville igneous complex, SW Virginia, U.S.A. Mineral .

Petrol. (in press).Rankin, D. W. (1975) The continental margin of east ern North America in the southern Appalachians: the opening and closing of the proto-Atlantic Ocean.

Amer. Jour. Sci. 275-A, 298-336.Roser, B. P. and Korsch, R. J. (1988) Provenance sig

natures of sandstone-mudstone suites using dis criminant function analysis of major-element data.

Chem. Geol. 67, 119-139.Shapiro, L. (1975) Rapid analysis of silicate, phosphate ,

and carbonate rocks. U.S. Geol. Survey Bull. 1401, 75 pp.

Slack, J. F. and Stevens, B. P. J. (1994) Clastic metasediments of the Early Proterozoic Broken Hill Group, New South Wales, Australia: geochemistry , provenance, and metallogenic significance. Geochim. Cosmochim. Acta 58, 3633-3652.

a multivariate method for determining the provenance and - jst

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