deformed graptolites, finite strain and volume loss during cleavage formation in rocks of the...

Deformed graptolites, ®nite strain and volume loss during cleavage

formation in rocks of the taconic slate belt, New York and Vermont,

U.S.A.

ARTHUR GOLDSTEIN*, JONATHAN KNIGHT and KARI KIMBALL

Department of Geology, Colgate University, Hamilton, NY 13346, U.S.A.

(Received 17 February 1997; accepted in revised form 14 July 1998)

AbstractÐAn analysis of graptolites in the Taconic slate belt of eastern New York and western Vermont(U.S.A.) shows that they are nearly ideal strain markers. For the three species used in this study, Orthograptuswhit®eldii, Orthograptus calcaratus and Climacograptus bicornis, the spacing of thecae is constant except forthe ®rst ®ve or so thecae in the proximal part of the fossil rhabdosome. Further, the thecal apertures are per-pendicular to the long axis of the stipe. Observations of the thecal spacing in deformed rocks leads to a deter-mination of extension (e= (lfÿl0)/l0) and a measure of the angle between thecal aperture and stipe axis yieldsa direct determination of angular shear strain. In practice, we ®nd it is most straightforward to use lengthchanges to determine the magnitude of principal strains. In Taconic slates, e1 ranges from 1.0 to 0.24, e2ranges from 0.23 to ÿ0.43 and e3 ranges from ÿ0.56 to ÿ0.74. Thus, we ®nd that the absolute ®nite strain inthese slates is constrictional at three sites, plane strain at another and a true ¯attening at only one site. Anexamination of volume changes based on strain results in determinations of between 81% volume loss and 7%volume gain, with volume losses between 28% and 81% in 9 out of 10 calculations. These conclusions are inaccord with previous determinations of volume loss based on reduction spot analyses and are consistent withthe observation that pressure dissolution was a common grain scale deformation process in cleavage formationbut that these slates lack abundant veins, ®brous overgrowths or other identi®able sites of reprecipitation.# 1998 Elsevier Science Ltd. All rights reserved

INTRODUCTION

The determination of ®nite strain is one of the princi-pal goals of structural geology. The magnitude andorientation of the ®nite strain ellipsoid is critical forconstraining, for example, fold mechanisms, displace-ment across ductile shear zones and volume changesduring deformation. Most strain measurement tech-niques (reduction spots, Rf-f, center-to-center, Fry,etc.) return ®nite strain ratios which are useful formany applications. However, there are some appli-cations for which absolute ®nite strains are required.Measurement of absolute ®nite strains requires objectsof known pre-deformation size whereas strain ratiosmay be determined if rocks contain objects of knownshape or distribution. In this regard, the use ofdeformed graptolites has been under-utilized as astrain measurement technique.Determination of volume changes is one case for

which absolute ®nite strains are preferable to strainratios. The amount of volume change which may ormay not accompany slaty cleavage formation is a topicwhich has been debated for nearly 150 years. Sorby(1853) suggested nearly 60% loss of material based onstudy of reduction spots in Welsh slates. Although helater re®ned that estimate downward to approximately20% (Sorby, 1908), numerous other workers have con-cluded that large volume losses (approximately 50±

60%) have accompanied cleavage formation (e.g.Goldstein et al., 1995; Wright and Platt, 1982; Beutnerand Charles, 1985; Henderson et al., 1986; Wright andHenderson, 1992; Jenkins, 1987). Others have foundlittle evidence for volume loss (e.g. Wintsch et al.,1991; Erslev and Ward, 1994; Kanagawa, 1991;Waldron and Sandiford, 1988; Tan et al., 1995).Considering the lack of agreement between workersand the potential magnitude of mass transfer impliedby up to 60% volume loss, the subject of volumechanges during deformation is one which needs ad-ditional study. Interestingly, of the small number ofpapers which have utilized graptolites to determinestrain, several have made contributions to the volumeloss issue. Wright and Platt (1982) used samples ofOrthograptus in the Martinsburg shale to concludethat approximately 50% volume loss had accompaniedslaty cleavage formation. Jenkins (1987), using samplesof a species of the graptolite Didymograptus, showedthat the strain in rocks of the Llanvirn series ofAbereiddi Bay (Wales) had experienced 56% reductionin volume during deformation. Tan et al. (1995) com-bined measurements of deformed Oncograptids fromshales in Gisborne, Victoria (Australia) with measure-ments of pyrite framboid pressure shadows to concludethat no change in volume had a�ected those rocksduring cleavage formation. Other work on graptolitedeformation has been done by Hills and Thomas(1944) and Cooper (1970, 1990) although thoseworkers have not made reference to volume changes.

Journal of Structural Geology, Vol. 20, No. 12, pp. 1769 to 1782, 1998# 1998 Elsevier Science Ltd. All rights reserved

0191-8141/98/$ - see front matterPII: S0191-8141(98)00083-2

*E-mail: [email protected]

1769

Goldstein et al. (1995) relied on strain ratios inTaconic slates to conclude that large heterogeneousvolume loss had accompanied the deformation ofthose rocks, but they were unable to determine absol-ute strains. The reliance on strain ratios rather thanabsolute strains resulted in uncertainties about volumeloss and Goldstein et al. (1995) based their con-clusions, in part, on reasoning. In this paper we pre-

sent absolute ®nite strains based on graptolitedeformation as well as textural evidence both of whichare indicative of large mass loss during cleavage for-mation. We show that calculated volume changesrange from +7% to ÿ81% and that most of theobserved strains demand signi®cant volume reductions.We also compare ®nite strains determined by analysisof deformed graptolites with other ®nite strain deter-

Fig. 1. Photographs of graptolites used in this study. (a), (c) and (e) are all undeformed specimens used to determineundeformed thecal spacings and (b), (d) and (f) are deformed specimens. (a) and (b): Orthograptus whit®eldii; (c) and (d):

Climacograptus bicornis; (e) and (f): Orthograptus calcaratus.

A. GOLDSTEIN, J. KNIGHT and K. KIMBALL1770

minations, especially those from measurement of press-ure shadows, and speculate on some of the factorswhich might control whether volume loss accompaniesdeformation or not.

STRAIN MEASUREMENT FROM GRAPTOLITEDEFORMATION

Graptolites are two-dimensional impressions of threedimensional colonial organisms which lived during theLower Paleozoic Era. They are commonly preserved aseither carbon ®lms in black shale and slate or as awhite or pale green ®lm (Fig. 1) which may be associ-ated with pyritization of the fossil. Despite some reser-vations (Underwood, 1992), most workers haveconsidered graptolites to be almost ideal strain indi-cators (Wright and Platt, 1982; Jenkins, 1987; Tan etal., 1995; Cooper, 1970, 1990) because they have regu-lar morphological characteristics which are di�erent indeformed and undeformed states. Graptolites are pre-served as long, thin stipes which may bear small, saw-tooth-shaped thecae on either or both sides (Figs 1 &2). Using fossils preserved in early lithi®ed, uncom-pacted rocks, paleontologists have determined that thethecae were the sites at which individuals in the colonylived. In life, the animals grew by adding thecae at thedistal end of the stipe (Fig. 2) and these thecae wereadded with a regular spacing. Thus, observations ofthe thecal spacing in the deformed state yield theextension parallel to the stipe:

e � lf ÿ l0� �=l0 �1�with l0 represented by the undeformed thecal spacingand lf represented by thecal spacing in the deformedstate (Fig. 3).

The geometry of two-dimensional ®nite strain issuch that extension and shear strain are functions ofthe angle that a line makes with the directions of prin-cipal ®nite strains (Ramsay and Huber, 1983; pp. 127±149). The relationship between orientation and exten-sion is especially useful for working with graptolites.Ramsay and Huber (1983) show that the relationshipcan be de®ned by the following equation in whichchange in length of a single graptolite is expressed asquadratic extension (l = (1 + e)2):

l0 � l01�cos2 y0� � l02�sin2 y0� �2�in which l1' and l2' are the reciprocal principal quad-ratic elongations and y' is the angle between the maxi-mum principal extension direction and the graptolite.This equation can be rewritten in the following form:

l0 � l01 � �l02 ÿ l01� sin2 y0: �3�This formulation can be graphed with l' as theabscissa and with sin2y' as the ordinate producing alinear arrangement of strain states (Fig. 4). Two ad-vantages arise from such a formulation of theequations of strain. First, the statistics of linear re-gression are more accessible than are those for curve®tting and these statistics are, in general, more robust.These include not only the ability to ®t lines to dataarrays but also the ability to determine statisticalvariability. Such statistics are available on most gen-eral use data analysis software packages. The secondadvantage is that the principal strains plot at sin2y' of1.0 and 0.0, making it fairly simple to determine themfrom the graphs. Because some species of graptoliteshave thecal apertures which are perpendicular to thestipe, the angle between thecal aperture and the stipein the deformed state yields a direct measurement ofangular shear strain (Figs 1b, 2 & 3). Thus, one couldexamine graptolite strain in Mohr circle spacealthough, in practice, determination of principal strains

Fig. 2. Sketch of graptolite showing morphological elements referredto in this paper.

Fig. 3. Deformation of graptolites results in a change in the spacingof thecae as well as a change in angle of the thecal aperture. Forsamples of the three species used in this study the undeformed thecalapertures are perpendicular to the stipe so that measurement of theangle in the deformed state leads to a determination of angular shear

strain parallel to that graptolite.

Deformed graptolites, ®nite strain and volume loss 1771

is more straightforward if one uses only lengthchanges.

THE TACONIC SLATE BELT

The area used for this study is the slate belt of thenorthern Taconic allochthon (Fig. 6). The Taconicallochthons are large slices of Cambrian throughmiddle Ordovician ®ne-grained rocks originally depos-ited on the paleo-eastern passive margin of northAmerica. During the middle Ordovician Taconic oro-geny these rocks, along with slices of crystalline base-ment, were thrust westward on top of shelf carbonatesof equivalent age. It is widely accepted that this defor-mation occurred during the collision of the earlyPaleozoic North American passive margin with thewest-facing Taconian subduction zone (e.g. Stanleyand Ratcli�e, 1985). In addition to thrusting, the rockswithin the thrust sheets were isoclinally folded and apervasive slaty cleavage formed parallel to the axialplanes of the folds. The region has been used exten-sively for commercial slate quarrying and the slateshave been the subject of a number of structural investi-gations (Goldstein et al., 1995; Wood, 1974; Hoak,1992; Pickens, 1993; Cushing and Goldstein, 1990;Crespi and Byrne, 1987; Bosworth and Vollmer, 1981;Bosworth and Rowley, 1984) as well as serving as amodel for interpreting the origin of mountain belts inthe context of plate tectonics (e.g. Bird and Dewey,

1970; Jacobi, 1981; Rodgers, 1970; Rowley and Kidd,1982; Stanley and Ratcli�e, 1985).

Graptolites have been found in two formations ofthe Taconics, both black, rusty-weathering slates. Inthe Hatch Hill Formation the graptolites are neitherabundant nor useful for strain analysis. However, theyare reasonably widespread in the Mount MerinoFormation and are almost ideal for strain studies. TheMount Merino is the youngest stratigraphic memberof the Taconic sequence and is only locally overlain bymiddle Ordovician ¯ysch, which was deposited over aregional angular unconformity. Within the MountMerino Formation, the graptolite-bearing unit is thestratigraphically highest (Rowley et al., 1979) resultingin its preservation only in the deepest synclines.

ABSOLUTE FINITE STRAINS

Three species of graptolites which are abundant inthe Mount Merino Formation have been utilized forthis study: Orthograptus whit®eldii (Fig. 1a & b),Orthograptus calcaratus (Fig. 1c & d) andClimacograptus bicornis (Fig. 1e & f). For these threespecies, early formed thecae are slightly more closelyspaced than are later formed thecae and the stipewidens progressively for the ®rst few thecae (Fig. 1b &d). We note that once the stipe has achieved its`mature' width the thecae maintain a constant spacing.Further, the thecal aperture is perpendicular to thelong axis of the stipe in the undeformed state (Figs 1

Fig. 4. Illustration of the method used for determining principal strains from deformed graptolites. (a) ®ve graptolites inthe undeformed state; (b) ®ve graptolites from (a) deformed with one principal shortening and one principal elongation;(c) strain recorded by the ®ve graptolites in (b) plotted according to equation (3); (d) strain recorded by ®ve graptolitesin (b) graphed according to equation (3) but with the reciprocal quadratic elongation (l') converted to quadratic

elongations.


& 2) and the change in angle of the thecal apertureyields the angular shear strain (Fig. 3). Undeformedthecal spacings for the three species were obtained bymeasuring the dimensions of graptolites in samplesborrowed from the Smithsonian Institution (Figs 1a, c,e & 5). These samples (Fig. 1), collected by JamesHall, are from exposures of middle Ordovician rocksnear Albany, N.Y. and were deposited closely in spaceand time with the graptolites of the Taconics.Undeformed thecal spacings were obtained by measur-ing the spacing between thecae for 10±15 thecae oneach of between 3 and 6 individual graptolites. Thesespacings were used to determine a mean and standarddeviation spacing between thecae (Fig. 5). We reportthese spacings as the distance between 10 thecae andthese values are in good agreement with measurementsby other workers (e.g. Elles and Wood, 1918).

Graptolites were found at eight localities in thenorthern Taconic allochthon in su�cient numbers andwith su�ciently good preservation to be measured(Fig. 6). The fossils are found on bedding planes aswhite, two-dimensional replacements of the originalanimal remains. Rocks of the Taconics have been iso-clinally folded so that on limbs of folds bedding andcleavage are parallel. Because graptolites lie parallel tobedding, when they lie on cleavage surfaces one cansee that bedding is exactly parallel to cleavage. Thehinges of the folds are very sharp and the limbs arelong so that most exposures in the Taconics displayparallel bedding and cleavage. Of the eight sites welocated, ®ve are on limbs of folds, two are at hingesand one is intermediate between the two (Table 1). Ateach site, oriented blocks were collected and were splitalong bedding until well preserved graptolites werefound. The spacing of between 5 and 10 thecae foreach graptolite was measured either by photographingand measuring from the photographic print or bydirect measurement under the microscope. Thecal spa-cings were converted to quadratic elongations andwere plotted as a function of orientation (Fig. 7). Thedata were statistically analyzed by linear regressionand the variability of that regression was also deter-mined to the 95% level of con®dence (Fig. 7). Allerrors reported in strains are at that statistical level.We believe that most of the variation in graptolitestrains determined by using this method re¯ect thevariation in original, undeformed thecal spacing(Fig. 5).

The data in Table 1 summarize the results of strainmeasurements and the data are shown in Fig. 7. Thegraphs (Fig. 7) display strains as quadratic elongation(1 + e)2 whereas the principal strains in Table 1 areshown as extensions (e) because such values are moreeasily interpreted. Five sites located on limbs have par-allel bedding and cleavage and, thus, yield determi-nations of the X±Y principal strains. At hinges, wherebedding is perpendicular to cleavage, the Z principalstrain is determined and the strain perpendicular to

Fig. 5. Determination of undeformed thecal spacings. Theca number,plotted along the x-axis, is an arbitrary designation and does not referto theca number in the paleontological sense. Data were all derivedfrom measurement of thecal spacings far from the proximal end of thestipe. Average spacings between 10 thecae along with standard devi-ation are shown for each species. (a) Orthograptus calcaratus, (b)

Climacograptus Bicornis and (c)OrthograptusWhit®eldi.


that, parallel to the bedding-cleavage intersection, is anon-principal strain. This is because the X direction ofstrain is not perpendicular to fold hinges but rakesfrom 408 to 908 southward on the cleavage plane andis marked by a prominent mineral elongation lineation.The ®nal site does not record principal strains but ishelpful in constraining the values of principal strain,especially Z.

An examination of Table 1 reveals considerable het-erogeneity in the principal strains. X (e1) varies from100%28% elongation to 22%24% elongation (note:all errors are 295% con®dence limits). Y (e2) valuesrange from 1%28% elongation to 43%210% short-ening. One of our cleavage-parallel sites yields a Yvalue of near zero (plane strain) whereas the otherfour all record shortenings. Statistically, the Y valuefor site THS could also be a shortening but none ofthe variability in principal strain determination for theother sites allows for Y being an elongation. Our twohinge sites both record large amounts of shortening,56%213% and 74%226%. The remaining site, in-termediate between hinge and limb, also records largeamounts of shortening, 52%210%. Although this isnot a principal strain, the minimum principalelongation (Z) must be smaller (more shortening) thanthis value suggesting that the large amounts of short-ening recorded at the hinges are reasonable.

COMPARISONS OF GRAPTOLITE STRAINSWITH OTHER STRAIN RESULTS

It is of interest to compare our strain results withother strain measurements made in the Taconics.Previous workers have determined strain in slates ofthe northern Taconics using reduction spots (Fig. 8)and pyrite framboid and porphyroblast pressure sha-

Fig. 6. Geologic maps of the study area. (a) Geologic map of theWhitehall, N.Y. region, modi®ed from Fisher (1984). SR refers to asmall region in which ®ve sites are located, shown on (b). Sample lo-calities QHR, P1, RR and THS are shown. (b) Geologic map of the

Stoddard Road area showing location of sampling sites.


dows (Fig. 9). Goldstein et al. (1995), Hoak (1992) andWood (1974) all reported strains recorded by reductionspots in the same region from which graptolites wereobtained, although the reduction spots are foundlower in the stratigraphy in a di�erent formation thanare the graptolites. All three studies reported similarresults, strains which lie in the ®eld of apparent ¯atten-ing (Fig. 8). It is di�cult to compare these resultsdirectly with the data reported here because reductionspots record sedimentary compaction whereas grapto-lites do not. Further, reduction spots yield only strainratios and one must assume either constant volume orsome speci®c volume change in order to derive absol-ute strains (Goldstein et al., 1995). The shape of re-duction spots, highly ¯attened, is suggestive of a strainstate with two principal ®nite elongations and oneshortening. However, the graptolites clearly show thatstrain is a ®nite ¯attening at one site, is plane strain atanother and is a ®nite constriction at the remainingthree. Despite this, strain states displayed on a Flinndiagram (Fig. 10) show only two sites which plot asapparent constrictions (close to plane strain) whereasthe other three all plot within the ®eld of apparent ¯at-tening. These plots have been made by using the aver-age Z from sites SR2 and SR5 combined with X andY from the ®ve sites on limbs of folds. The error barsrecord the variation in strain ratios at the 95% con®-dence limit. The error in the Y/Z ratio is large becausewe used the statistical variation in both of the hingesites yielding an average Z which ranges from 43% to99% shortening. Two factors account for the lack ofcorrespondence between absolute principal strains andthe positions on the Flinn diagram (Fig. 8). The ®rst isthat we believe that a signi®cant volume change hasa�ected these rocks (see below) so that the strain stateis best described as a ®nite constriction plus a volumeloss. The other factor is that reduction spots recordburial compaction whereas graptolites do not.Graptolites exist as three dimensional tubes (e.g.Climacograptus) or boxes (e.g. Orthograptus) which arecompressed during burial. This vertical shorteningdoes not alter the original thecal spacing so that grap-tolites record only the tectonic components of strain.If one adds an additional component of compaction

(volume loss through porosity reduction) to graptolitestrains, they plot well into the ®eld of reduction spotstrains so that we believe that the reduction spotsrecord the true strains. Goldstein et al. (1995) notedthat reduction spot strain was highly heterogeneous ata variety of scales and they used this observation tosuggest large volume losses. We do not see the hetero-geneity which those workers found. This is because re-duction spots are only a few millimeters to a fewcentimeters in size and each spot can be consideredindependently whereas many graptolites must be usedat a single site to determine an average site strain, thusobscuring any site-scale heterogeneity. Site-to-site het-erogeneity (Fig. 8) indicates greater variability in Y/Zvalues than in X/Y values, similar to that seen in re-duction spots.

Comparing graptolite strains to other strain determi-nations from Taconic slates is also possible (Fig. 9).The magnitude of elongation in X may be derivedfrom pyrite framboid and porphyroblast pressure sha-dows. Cushing and Goldstein (1990), Pickens (1993)and Chan and Crespi (personal communication, 1996)have all investigated this phenomenon in the northernGiddings Brook slice with comparable results. Cushingand Goldstein (1990) reported an average elongationof 101% from 24 framboid pressure shadows at onesite; Chan and Crespi (personal communication, 1996)noted framboid pressure shadow elongation values offrom 110% to 140% at ®ve sites and Pickens (1993)found an average of 95% elongation from porphyro-blast pressure shadows at seven sites. Despite the goodagreement between these studies, none of them agreeswith the lower strains determined from graptolites(Fig. 9 and Table 1). Pressure shadow strains have notyet been determined for the same sites used for grapto-lite strain measurements and we have only a single sitewhich records an extension as high as those indicatedby pressure shadows. At this time it appears thatpressure shadow strains may be overestimating thetrue elongation.

One may determine the Z component of strain inthe Taconics by observing buckled beds at hinges offolds, where bedding and cleavage are perpendicular orwith rare ®ndings of buckled veins. We have found

Table 1. Summary of principal strain values determined from graptolite deformation. n is the number of graptolites measured at each site;e1,2,3 are principal strains determined using the average thecal spacing for undeformed graptolites; efax is the strain recorded parallel to thefold axis; and e* is a non-principal strain which lies within bedding and perpendicular to the fold axis. BXC is the angle between bedding and

cleavage. All errors are reported at the 95% con®dence level

Site n e1 e2 e3 efax e* B�C

SR1 39 0.2420.06 0.4320.10 08QHR 23 0.3220.08 0.3820.16 08THS 25 0.6220.07 0.0120.08 08RR 10 1.020.08 0.2320.07 08P1 39 0.2220.04 ÿ0.1120.07 08SR2 9 ÿ0.5620.13 0.0620.07 908SR5 23 ÿ0.7420.26 ÿ0.0320.03 908SR3 38 ÿ0.0320.06 ÿ0.5220.10 658


four examples of these phenomena and the amounts of

shortening average approximately 50% (Fig. 9). This issomewhat lower than the 56% and 75% shortening

determined from graptolite measurement, but is muchcloser than the di�erence in X values.

Finally, we note that graptolites provide the only

accurate method of determining Y in these, and mostother, slates. Reduction spots, so common in red

slates, are of little use in this regard because, as dis-cussed above, they yield only strain ratios. We observe

Fig. 7. Data derived from measurement of graptolites at each site. Data are shown as dots, the solid line is the linear re-gression ®t to the data with R2 noted; dotted lines are the 95% con®dence limits for each regression determination.


that there is no indication in any of the other strainmeasurements made of Taconic rocks that Y is ashortening (Fig. 9).

VOLUME CHANGE CALCULATIONS

If the graptolite data are accepted as providing goodmeasurements of principal ®nite strains, then thesevalues can be used to constrain volume changes whichmay have a�ected these rocks. Such a determinationrelies on the mathematical relationship determined byRamsay and Wood (1973):

ln�1� D� � ln�1� e1� � ln�1� e2� � ln�1� e3� �4�in which D is the volume change (positive for gainsand negative for losses) and e1, e2 and e3 are principal®nite extensions. Because we have not been able todetermine all three principal strains at one locality, itis necessary to combine principal strains from di�erentlocalities. We have ®ve sites which yield XY principalstrains and two which yield Z. For each site there issome variability in the principal strains derived whichwe interpret to be due to natural variability in unde-formed thecal spacings. This is expressed, we believe,in the 95% con®dence limits for the linear regressions(Fig. 7 and Table 1). We have combined strains suchthat the volume change for each site (Table 2) is basedon the strains at that site (XY) and the Z value at thetwo hinge sites, SR2 and SR5. The error in these site-level determinations is expressed by showing thevolume change which would be derived by using the95% con®dence limits for the strains at that site.

The volume changes using this method are listed inTable 2. Using the best-®t linear regression to thestrain data (Table 1 and Fig. 7) we note that volumelosses are indicated for all sites with the sole exceptionof site RR which yields a slight increase in volumewhen the XY values for this site are combined with theZ value for site SR2. If the Z value for site SR5 is

Fig. 8. Flinn diagram of strains derived from reduction spotmeasurements (from Goldstein et al., 1995). Site average strains fromGoldstein et al. (1995) are shown as triangles, data from Hoak(1992) are shown as open circles and data from Wood (1974) areshown as open squares. The range of data collected by Wood (1974)for slates from Wales and the Taconics is shown with a dashed lineand the range of data collected by Hoak (1992) is shown with a solid

line.

Fig. 9. Comparison of principal strain from this study with strain de-terminations from Taconic slates derived using other methods.Strains from reduction spots have been calculated assuming novolume loss. These values would change if one were to assume a

volume change.

Fig. 10. Flinn diagram of strains from each site with parallel beddingand cleavage combined with an average shortening of 65%. Errorbars show the variation in strain ratios if the 95% con®dence limitsare used. The ellipse shows the general region of reduction spot

strain measurements.


used, the calculations yield volume losses for all siteswith value ranging from 35 to 81% volume loss. If oneconsiders the statistical ranges of the principal strains(Min and Max in Table 2) two of the ®ve limb sitessuggest volume gains using the Z value for site SR2but only site RR yields volume gains for Z from SR5.Thus, we interpret these results as strongly suggestiveof large volume losses for most of the sites within theTaconic slate belt.A question of some signi®cance is to what extent the

statistical ranges of volume change are a re¯ection ofreality. In other words, exactly how much of thevolume loss or gain which has been calculated isreasonable? The extremes go from 40% volume gainto 99% volume loss. The very large volume losses cal-culated using the 95% con®dence limits for site SR5derive from the inability to de®ne an appropriate mini-mum for e3 at that site (Fig. 7). The linear regressionis strongly a�ected by a range of strains parallel to orat a low angle to the bedding-cleavage intersection(sin2y'10). Thus, the lower intercept for the 95% con-®dence envelope is negative, a result which has no sig-ni®cance in the context of strain. Thus, we do notconsider the very large volume losses to be accurate.Similarly, we have some concern about the determi-nations of volume gain in these rocks. We note belowa number of observations which are consistent withvolume losses for Taconic slates but we know of noobservations which are in any way indicative ofvolume gains. If a rock has experienced true volumegain one should be able to see abundant veining orother evidence of precipitation of mineral matter. Wedo not ®nd these features in the slates of the Taconics.Thus, we contend that the volume changes derived byusing the linear regression y-intercepts are more re-liable than those derived by using the statistical rangesof possibilities. This yields determinations of volumechange which range from near 80% for some sites tonear zero for others, with an average of approximately44% for the region studied.In order to use this method we must accept that the

least principal strain (Z) value determined at foldhinges is close to that on fold limbs, where XY valueshave been determined. Because cleavage does notappear to vary in intensity from limb to hinge webelieve that the shortening measured at hinges is close,

if not identical, to shortening which would bemeasured on limbs, if appropriate strain markers werepresent. In one site located on a fold limb we havefound an early vein which is buckled and intersectscleavage at 558. The shortening measured from thatvein is 56% and the principal shortening must begreater than that (i.e. more shortening). We do notbelieve that strain would be homogeneous on the scaleof a fold and the degree of heterogeneity would becontrolled, for the most part, by the folding mechan-ism and the post-folding strain history. Severalworkers have determined that folding in the Taconicswas a reasonably early structural event and that theslaty cleavage was superimposed on already foldedrocks (Rowley et al., 1979; Goldstein et al., 1991;Crespi and Byrne, 1987). Such conclusions are based,in part, on the observation that cleavage cuts uni-formly across the folds without displaying cleavagerefraction or a fanning geometry. We assume that overa scale of several meters (the distance from hinge tolimb) cleavage-related (post-folding) strain was fairlyhomogeneous. What may not be homogeneous is thestrain related to folding. Di�erent fold mechanismswill result in di�erent strain patterns (e.g. Ramsay andHuber, 1987, pp. 445±473) and given only two dimen-sional strain markers, such as graptolites, it is notpossible to uniquely determine this pattern. It is likely,however, that using two dimensional, bedding-parallelstrain markers may make the problem more tractablethan otherwise. The rocks of the Taconics are domi-nantly clay-rich with very few beds of other lithologieswhich could have acted as rigid, stress-bearing plates.Thus, buckling fold mechanisms may not generallyapply to the Taconics. Crespi and Byrne (1987)suggested that folding was accomplished by ¯exural¯ow and that hinges were pinned. In this case, onewould expect fold-related strain to be zero at the hingeand that strain on the limbs would approximate thestrain in a shear zone with bedding acting as shearzone boundaries (Ramsay and Huber, 1987). In such acase the bedding will be a plane of no ®nite strain, aswould any shear zone parallel plane in a homogeneousshear zone. Thus, graptolites may well not record anyof the folding-related strain. For all these reasons wefeel con®dent in using strain values from hinges as anapproximation of shortening on fold limbs.

Table 2. Volume changes calculated from equation (4). Principal strains from sites with parallel bedding and cleavage have been combinedwith Z values from the two sites at which bedding and cleavage are perpendicular. The value of the strains determined from linear regressionare listed as `Mean' and the statistical ranges using the 95% con®dence limits around the regression are listed as `Min' and `Max'. Volume

losses are shown as negative numbers and volume gains are listed as positive numbers

SR2 SR5Site Mean Min Max Mean Min Max

SR1 ÿ68% ÿ83% ÿ50% ÿ81% ÿ99% ÿ54%QHR ÿ65% ÿ83% ÿ39% ÿ78% ÿ99% ÿ43%THS ÿ28% ÿ56% +5% ÿ56% ÿ98% ÿ4%RR +7% ÿ31% +26% ÿ35% ÿ98% +40%P1 ÿ52% ÿ70% ÿ31% ÿ71% ÿ99% ÿ36%


DISCUSSION

The volume loss determined from graptolite strainvalues is in good agreement with other volume changedeterminations from the Taconics and other slate belts.It has been common for volume losses of between40% and 60% to be proposed for slates (e.g.Goldstein et al., 1995; Wright and Platt, 1982; Beutnerand Charles, 1985; Henderson et al., 1986; Wright andHenderson, 1992; Jenkins, 1988). In particular,Goldstein et al. (1995) suggested that volume loss forthe Taconic slates was heterogeneous varying, at aminimum, from 0% up to 55%. Because these con-clusions were based on reduction spots they had allthe problems and uncertainties of strain studies basedon strain ratios. In particular, Goldstein et al. (1995)had to assume that the site which had the lowest strainstate had experienced zero volume change and thevolume change for other sites was calculated fromthat. Considering that even the lowest strain site ishighly strained and probably had experienced somevolume loss, Goldstein et al. (1995) suggested that anaverage of between 50% and 60% loss of volume wasreasonable for the Taconic slate belt. Erslev and Ward(1994) studied a single thin section from the Taconicsand concluded that no volume change had a�ectedthat sample. They based that conclusion on theassumption that their sample had started with a com-position similar to an average shale and, since it stillhad that composition, no signi®cant volume changeshad a�ected that sample. We do not agree with theassumption of initial composition and, rather, chooseto interpret the data presented by Erslev and Ward(1994) as re¯ective of considerable elemental mobilityand loss of approximately 50% volume.Other observations suggest that volume loss has

a�ected the slates of the Taconics. The slaty cleavageis marked by concentrations of illite separatingdomains rich in quartz, chlorite and minor amounts ofcalcite and albite (Fig. 11). The concentrations of illitehave formed by dissolution of the other minerals leav-ing an insoluble residue of clays. We ®nd little evi-dence of reprecipitation of any of these dissolvedminerals. Fibrous overgrowths are exceptionallyuncommon, although very small volumes surroundpyrite framboids and porphyroblasts. Crespi and Chan(1996) have observed syn-tectonic fringes of mineraliz-ation on the edges of pre-tectonic veins, but thesefringes are small compared to the volume of early veinmaterial. No quartz-mica beards on quartz grains havebeen observed as they have been in many other slates.Similarly, veins are very uncommon in the Taconics.Even when veins are present, they can be shown tohave formed either pre-cleavage or post-cleavage. Verylittle syn-tectonic mineralization can be found in theserocks and considering the evidence for pressure dissol-ution we feel that it is entirely consistent that we de-rive large volume losses from our strain analyses.

For large volume losses to be possible there musthave been an appropriate hydrologic system. Fluidsmust have moved through the rock in such a way thatthe elements that are being dissolved do not reach sat-uration or dissolution will cease. The tectonic settingof the Taconic orogeny provides an appropriate paleo-hydrological scenario. During the middle Ordovicianthe paleo-eastern margin of North America contactedthe west-facing Taconic subduction zone and it wasprobably this collision which stopped subduction.During the collision the rocks deposited on the passivemargin of North America were imbricated and incor-porated with the Taconic accretionary complex(Stanley and Ratcli�e, 1985). An examination of mod-ern accretionary complexes shows that they are en-vironments in which large volumes of water arepassing through rock (e.g. Elder®eld et al., 1990;Moore and Vrolijk, 1992; Kastner et al., 1991). This isseen in the common occurrence of submarine springsand mud volcanoes on the surface of accretionarycomplexes. Some workers have estimated the annual¯uid discharge from accretionary complexes at 10 s to100 s of m3 per year for each meter of length of sub-duction zone (Kastner et al., 1991). The scale of this¯uid ¯ow system is su�cient to entirely recycle theworld's oceans in approximately 500 Ma (Kastner etal., 1991). Apparently, loss of pore water occurs atshallow depths after incorporation into the prism butstructural water held in smectite and opal-A is notreleased until much deeper (Moore and Vrolijk, 1992).This water passes upward through the accretionarycomplex and, at shallow depths, is focused along faultsand fracture zones. At greater depths, ¯uid pressuresare probably quite high (Moore and Vrolijk, 1992),perhaps equal to or greater than lithostatic stress,making it possible for pervasive, di�use ¯uid ¯ownecessary to accomplish the widespread dissolutionsuggested here. It is exactly this kind of hydrologic set-ting at which we might expect large volumes of dissol-ution and volume reduction. Thus, we can imaginethat some slates were deformed in settings where thepaleohydrology allowed major dissolution withoutmuch reprecipitation whereas others may have beendeformed in setting which lacked the proper hydrogeo-chemical setting. From this perspective, we believe thatit is entirely reasonable to ®nd that some slates havelost volumes of 50±60% whereas others have lostessentially no volume at all.

An examination of modern accretionary prismssuggests an answer to the question invariably asked ofthose proposing large volume losses: ``Where has itgone?''. In modern accretionary prisms material dis-solved at depth is transported upward with advectingwater and discharged into the oceans. A similar situ-ation might well have existed during the TaconicOrogeny. As long as a su�ciently vigorous ¯ow systemis operating it is possible that ¯uids never reached sat-uration, explaining the general lack of widespread syn-


tectonic mineralization in the Taconics and helping toexplain the large volume losses derived from strainanalysis.

CONCLUSIONS

1. The three species used for this study are nearlyideal strain indicators as they have regular thecalspacings and angles between the stipe and thecalapertures which are 908 in the undeformed state.Determination of principal strains is most straight-forward if one uses length changes only.

2. The absolute ®nite strain for the Taconic slate belt

is best described as a ®nite constriction plus a

volume loss. Three out of ®ve sites which de®ne e2show it to be a shortening which varies from 010%

to 040% shortening, one site de®nes near plane

strain and only one site shows e2 to have been an

elongation. If one considers the e�ect of sedimen-

tary compaction, strains determined from grapto-

lites agree well with those from reduction spots.

Graptolite strains, however, record lower extensions

in X than do measurements of pyrite framboid and

porphyroblast pressure shadows, suggesting that

Fig. 11. Backscattered image of slaty cleavage and a ball of volcanic ash from the Indian River Formation in the Taconicslate belt. Slaty cleavage (S2) cuts horizontally across the image and the pre-cleavage fabric (S1) is seen in the strainshadow around the ash ball. Note the evidence for pressure dissolution as well as the general lack of ®brous overgrowths.

Note scale bar in lower right of photo.


perhaps these values are overestimating true strainmagnitudes.

3. Volume changes calculated from graptolite strainvary from 7% volume gain to 81% volume loss.Most combinations of strains result in large volumelosses. Whereas some sites may have experienced novolume loss or even very slight volume gain, we®nd the calculations of large volume gain or verylarge volume loss to be at odds with observationsof rock texture. The determinations of volume lossare in agreement with previous suggestions basedon reduction spot measurement, textural obser-vations and the general lack of syntectonic mineral-ization.

AcknowledgementsÐCharles Mitchell (SUNY Bu�alo) providedinvaluable assistance with graptolite identi®cation and morphology.Backscattered image was collected by Nancy Brauer. This work wassupported by a grant from the National Science Foundation (EAR94-18200). Reviews by Mike Williams, Richard Lisle, Dave Grayand Bock Tan signi®cantly improved the manuscript. Barry Doolankindly guided the authors to some sampling sites. Joe Amatosuggested the rearrangement of the strain equations.

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