Porphyroblast rotation during crenulation cleavage ...€¦ · Porphyroblast rotation during...

Porphyroblast rotation during crenulation cleavage development:an example from the aureole of the Mooselookmeguntic pluton,Maine, USAS. E . JOHNSON, M. E. DUPEE AND C. V. GUIDOTTIDepartment of Earth Sciences, University of Maine, Orono, ME 04469-5790, USA ([email protected])

ABSTRACT In the low-pressure, high-temperature metamorphic rocks of western Maine, USA, stauroliteporphyroblasts grew at c. 400 Ma, very late during the regional orogenesis. These porphyroblasts,which preserve straight inclusion trails with small thin-section-scale variation in pitch, were subsequentlyinvolved in the strain and metamorphic aureole of the c. 370 Ma Mooselookmeguntic pluton. Theaureole shows a progressive fabric intensity gradient from effectively zero emplacement-relateddeformation at the outer edge of the aureole !2900 m (map distance) from the pluton margin to thedevelopment of a pervasive emplacement-related foliation adjacent to the pluton. The development ofthis pervasive foliation spanned all stages of crenulation cleavage development, which are preserved atdifferent distances from the pluton. The spread of inclusion-trail pitches in the staurolite porphyroblasts,as measured in two-dimensional (2-D) thin sections, increases nonlinearly from !16! to 75! withincreasing strain in the aureole. These data provide clear evidence for rotation of the stauroliteporphyroblasts relative to one another and to the developing crenulation cleavage. The data spread isqualitatively modelled for both pure and simple shear, and both solutions match the data reasonablywell. The spread of inclusion-trail orientations (40–75!) in the moderately to highly strained rocks issimilar to the spread reported in several previous studies. We consider it likely that the sample-scalespread in these previous studies is also the result of porphyroblast rotation relative to one another.However, the average inclusion-trail orientation for a single sample may, in at least some instances,reflect the original orientation of the overgrown foliation.

Key words: contact metamorphism; crenulation cleavage; deformation mechanism; pluton emplacement;porphyroblast rotation.

INTRODUCTION

This paper examines the kinematic behaviour ofstaurolite porphyroblasts during crenulation cleavagedevelopment in the strain aureole of the Moose-lookmeguntic pluton, Maine Appalachians, USA(Fig. 1). The pluton intruded a pelitic/psammiticturbidite sequence c. 30–35 Myr after regional defor-mation and metamorphism had ceased, and theemplacement-related strain aureole preserves a com-plete sequence of crenulation cleavage developmentculminating in an intense, margin-parallel foliationadjacent to the pluton. Staurolite porphyroblasts thatgrew very late during the regional deformation typic-ally preserve straight, consistently oriented inclusiontrails. These porphyroblasts are overprinted by theemplacement-related deformation, and inclusion-trailorientation data show progressively increasing scatterwith increasing strain in the aureole, providing anunequivocal example of porphyroblast rotation relat-ive to one another and to the developing crenulationcleavage.

Porphyroblasts in metapelitic rocks commonly pre-serve trails of mineral inclusions that are remnants of

planar and linear fabrics present in the rock at the timeof porphyroblast growth. In some instances, thesetrails can be unequivocally correlated with fabrics stillpresent in the surrounding matrix. In other instances,extensive deformation and recrystallization of thematrix after porphyroblast growth has left only theinclusion trails as records of previous structuralfabrics. Porphyroblasts are therefore of centralimportance because they are generally the only featuresin multiple-deformed metapelites that preserve infor-mation about the deformation history beyond whatcan be extracted from the matrix microstructure(Zwart, 1960, 1962; Vernon, 1978, 1989; Bell et al.,1986; Williams, 1994; Johnson & Vernon, 1995; Karl-strom & Williams, 1995; Chan & Crespi, 1999; John-son, 1999; Hickey & Bell, 2001; Holcombe & Little,2001; Timms, 2003). Of equal importance, porphyro-blast microstructures show characteristics that shouldmake them useful for: (1) determining deformationkinematics (Rosenfeld, 1968; Simpson & Schmid, 1983;Bell, 1985; Busa & Gray, 1992; Passchier et al., 1992;Johnson, 1993), (2) quantifying elongation strain(Johnson & Williams, 1998), (3) quantifying shearstrain and shear strain rate (Christensen et al., 1989,

J. metamorphic Geol., 2006, 24, 55–73 doi:10.1111/j.1525-1314.2005.00621.x

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1994; Busa & Gray, 1992; Vance & O’Nions, 1992;Barker, 1994; Holcombe & Little, 2001; Biermeier &Stuwe, 2003), (4) quantifying vorticity (Passchier,1987; Beam & Fisher, 1999; Holcombe & Little, 2001),(5) evaluating the effects of strain localization on rigidobject behaviour (Ildefonse & Mancktelow, 1993;Marques & Coelho, 2001; Paterson & Vernon, 2001;ten Grotenhuis et al., 2002; Mancktelow et al., 2002;Johnson, 2006), (6) examining pluton emplacementmechanisms (Paterson et al., 1991; Davis, 1993; Mor-gan et al., 1998), and (7) investigating folding mecha-nisms (Ramsay, 1962; Visser & Mancktelow, 1992;Solar & Brown, 1999; Williams & Jiang, 1999; Hickey& Bell, 2001; Stallard & Hickey, 2001; Timms, 2003;Evins, 2005).

The potential of porphyroblast microstructures isclear, but there is uncertainty surrounding their inter-pretation. In particular, the kinematic behaviour ofporphyroblasts during deformation is not fullyunderstood. Without a clear understanding of por-phyroblast kinematics, many of the topics above aredifficult to address with any confidence. Since 1989,

numerous papers have been published using inclusion-trail orientation data to argue that porphyroblastshave undergone little or no rotation during ductiledeformation, relative to a fixed external referenceframe such as geographic coordinates. These studieshave commonly shown that the statistical peaks of thedata remain consistently oriented over areas ranging insize from sample- and outcrop-scale folds (e.g. Stein-hardt, 1989; Bell & Forde, 1995; Jung et al., 1999;Evins, 2005) to tens or hundreds of square kilometres(e.g. Fyson, 1980; Johnson, 1990, 1992; Aerden, 1995;Ilg & Karlstrom, 2000). These data are impressive, andthe general lack of microstructures that record historyin deformed and metamorphosed rocks makes them allthe more important. However, the relatively largespread (commonly 40–80!) in inclusion-trail orienta-tions at the sample scale, typically measured as pitchesin two-dimensional (2-D) thin sections, has not beensatisfactorily addressed and requires attention. Severalexplanations for this sample-scale variation might besuggested, including variable rotation of porphyro-blasts of different shape and orientation (e.g. Passchier

Fig. 1. Regional geological setting of study area within thenorthern Appalachians, USA and Canada – after Bradleyet al. (2000).

56 S . E . JOHNSON ET AL .

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et al., 1992), original variation in the orientation of thefoliation overgrown by the porphyroblasts (e.g. Bellet al., 1992), object interaction where objects are clo-sely spaced (Ildefonse et al., 1992), measurement error(Steinhardt, 1989; Timms, 2003), late brittle–ductiledeformation (Aerden, 1995), or heterogeneous distri-bution of strain at the thin-section scale (Ilg & Karl-strom, 2000; Paterson & Vernon, 2001).

The problem that there is noway to demonstrably andrigorously explain the sample-scale spread in these dataunless the initial, pre-deformation orientation of theinclusion trails can be determined, remains. In thispaper, a rare situation is described in which we can inferthe original orientation of porphyroblast inclusion trailsprior to emplacement-related deformation and com-plete destruction of the original matrix fabric in theaureole of the Mooselookmeguntic pluton. By measur-ing inclusion-trail orientations across a complete andclearly defined strain gradient, it is possible to examineprogressive kinematic behaviour of the porphyroblaststhrough all stages of crenulation cleavage developmentleadingultimately to apervasive new foliationparallel tothe margin of the pluton. Our results settle a 20-year-olddebate, but as is often the case they raise importantquestions that require further investigation.

GEOLOGICAL SETTING

The study area covers an approximately 20-km2 por-tion of the wall rocks east of the Mooselookmegunticpluton, in the Central Maine Belt of the northernAppalachians (Fig. 2). The distributions of strati-graphic units, structures and metamorphic zonesthroughout the area of interest are well known fromthe regional mapping and structural studies of Moench(1966, 1970, 1971), Moench & Hildreth (1976), Brown& Solar (1998a,b, 1999) and Solar & Brown (1999,2001) and the petrological and microstructural work ofGuidotti (1970a,b, 1974), Conatore (1974), Solar &Brown (1999, 2001), Guidotti & Johnson (2002) andJohnson et al. (2003). The pluton is generally consid-ered to have a gently east-dipping contact, a conclu-sion based both on geological observations (e.g.Moench & Zartman, 1976; Guidotti et al., 1996), drill-hole intersections (Guidotti, 1970a) and gravity data(Carnese, 1981; Brown & Solar, 1998b). Consequently,the pluton’s contact metamorphic aureole is verybroadly developed in map view, extending c. 5 km ormore to the east (Moench & Zartman, 1976; Guidotti& Johnson, 2002). The deformation aureole is alsobroadly developed in map view (Moench, 1970;

c.

Fig. 2. Geological map of study area showing the major lithological units and primary structural patterns and features (after Moench& Hildreth, 1976). Metamorphic zones after Conatore (1974) are separated by dashed lines (isograds) defined by discontinuousreactions (see Henry et al., 2005, for descriptions of assemblages and reactions). Filled circles show sample localities from presentstudy. Localities for Figs 3, 6, 7, 8 and 9 are shown.

PORPHYROBLAST ROTAT ION DURING CRENULAT ION CLEAVAGE DEVELOPMENT 57


Moench & Zartman, 1976), extending c. 3 km to theeast (our own data, presented below).

The area of interest was affected by two prominentmetamorphic episodes referred to by Guidotti (1970a)as M2, the peak regional metamorphism, and M3, thecontact metamorphism associated with the pluton. Athorough summary of these two metamorphic events,as they were originally defined, can be found inGuidotti & Johnson (2002), and a more recent assess-ment of the M2 phase equilibria is provided by John-son et al. (2003). The peak M2 regional metamorphismwas reached at c. 405–400 Ma, late during the Devo-nian Acadian deformation (Smith & Barreiro, 1990;Solar et al., 1998; Johnson et al., 2003), and wascharacterized by the assemblage And + St + Bt± Grt (abbreviations after Kretz, 1983). The Devo-nian deformation resulted in macroscale tight foldingwith associated steeply dipping, NE–SW trending axialsurface foliation. M2 metamorphic microstructuresshow a progressive thermal evolution in relation to theregional deformation (e.g. Solar & Brown, 1999), withsyntectonic biotite and garnet porphyroblasts over-

grown by very-late syntectonic staurolite porphyro-blasts (Fig. 3). Because of the very late growth ofstaurolite relative to the regional deformation, theseporphyroblasts typically preserve straight inclusiontrails that are continuous with the external matrixfoliation, exhibiting only slight margin deflection(Fig. 3). The regional foliation overgrown by theseporphyroblasts shows a remarkable consistency inorientation throughout the region of interest (Fig. 2;Moench & Hildreth, 1976; Solar & Brown, 1999,2001). Consequently, the staurolite inclusion-trail or-ientations on the outer edge of the pluton aureole arealso consistent, providing a control microstructure thatcan be tracked into the aureole.TIMS U/Pb zircon and monazite geochronology in-

dicate crystallization of the granite and associated M3contact metamorphism at c. 370 Ma (Smith & Barreiro,1990; Solar et al., 1998; Tomascak et al., 2005). Thus, itpost-dates the waning stages of the Acadian deforma-tion by c. 30–35 Myr. The M3 metamorphic grades inthe area range from upper garnet zone to lower silli-manite zone (Fig. 2), and detailed estimates for the

Fig. 3. Photomicrographs well outside of the pluton aureole illustrating the progressive nature of M2 metamorphism, and the very latepeak timing relative to regional strain accumulation. (a) Section cut perpendicular to the regional foliation (SR) and mineral elongationlineation. M2 garnet and staurolite porphyroblasts, with staurolite very late relative to SR and showing no deflection of SR at theporphyroblast margins. (b) M2 garnet and staurolite porphyroblasts. Note that garnet porphyroblasts have well-developed strainshadows, having grown well before the staurolite. Staurolite porphyroblasts show minor deflection of the matrix foliation at theirmargins. Plane-polarized light, long dimension of both photomicrographs 5.9 mm.



aureole temperatures by Henry et al. (2005) range from535!C in the upper garnet zone to 610!C in the lowersillimanite zone. During M3 metamorphism, bothprograde and retrograde pseudomorphism of M2 por-phyroblasts occurred (Guidotti & Johnson, 2002). Thetype of pseudomorph and degree of development isdirectly related to the rock’s position within the M3metamorphic gradient, and therefore to its proximity tothe pluton. Of relevance to the present study, M2staurolite was stable only in the transition zone betweenM3 staurolite and lower sillimanite zones (Fig. 2).Down grade from this transition zone, M2 staurolitewas pseudomorphed by chlorite and muscovite, andupgrade from this zone the pseudomorphs containmuscovite and some biotite. The transition zone is thusthe only zone in the aureole in which M3 staurolitegrew; the rest of the staurolite in the aureole is of M2origin. As a result, M2 staurolite porphyroblasts in thetransition zone commonly show M3 growth rims(Guidotti & Johnson, 2002).

As noted by Guidotti & Johnson (2002), and dis-cussed further below, the M3 rims that grew on M2staurolite porphyroblasts in the transition zone (Fig. 2)overprint the pluton-related foliation that wraps theM2 grains, and there is no evidence for measurablestrain accumulation that post-dates rim growth. Inaddition, M3 pseudomorphs of M2 porphyroblaststypically retain euhedral shapes, and the individualminerals that comprise the pseudomorphs are unde-formed (Guidotti & Johnson, 2002). The lack of strainaccumulation after the growth of M3 sturolite rimsand the M3 pseudomorphism of M2 porphyroblastsindicate that the thermal peak at any point in theaureole lagged behind the emplacement-related de-formation at that point (Moench & Zartman, 1976). Italso suggests that most or all regional strain accumu-lation in this area had terminated prior to emplace-ment of the pluton, or at least that it did not affect thearea of Fig. 2 in any significant or measurable way.

MICROSTRUCTURAL ANALYSIS

Sample collection and preparation

Spatially oriented samples were collected primarilyalong a series of east–west transects through theaureole (Fig. 2). These transects were chosen becauseprevious mapping (Moench & Hildreth, 1976) andreconnaissance field trips indicated long tracts ofexposed rock running approximately perpendicular tothe pluton contact. Additional short sampling trans-ects were located on ridges, rivers and roads whereoutcrop was previously reported (Moench & Hildreth,1976) or suspected. Sample spacing varied withproximity to the pluton contact, with samples spacedmore closely near the pluton where emplacement-related deformation is the most pronounced.

In cutting thin sections, there were two objectives: (i)to evaluate the progressive evolution of the micro-

structures in relation to crenulation cleavage develop-ment, and (ii) to quantify the average three-dimensional (3-D) orientation of inclusion trails fromeach sample. To achieve these aims, two non-parallelthin sections (!A" and !B") were produced from eachsample (Fig. 4). The A-sections were cut perpendicularto the intersection lineation between the regional foli-ation and emplacement-related crenulation cleavage(Fig. 4). The B-sections were cut parallel to thisintersection lineation and approximately perpendicularto the regional foliation.

Microstructural observations

Preliminary microstructural observations confirmedthe presence of a progressively developed crenulationcleavage, with fabric intensity increasing towards thepluton contact. Moench (1966, 1970) was the first todescribe this crenulation cleavage and he recognized itsspatial and genetic relationship to the Mooselookme-guntic pluton. Along this deformation gradient, therange of inclusion-trail orientations in staurolite por-phyroblasts also increases towards the pluton. Afterdetailed microstructural work, the Mooselookmegun-tic aureole was divided into five zones based on thestages of crenulation cleavage development (Fig. 5).The divisions between these zones are not intended torepresent precise boundaries. Heterogeneous strainand fabric development in the aureole lead to someoverlap among the zones, but dividing the aureole inthis way proved useful for the following descriptions.

Zone 1

Rocks in zone 1 represent the microstructures presentoutside the pluton strain aureole. The dominantstructural fabric in these rocks is a regional schistosity

Intersection lineation

Crenulationcleavage

SR‘A-section’ ‘B-section’

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Fig. 4. General strategy for cutting thin sections. The A-sectionswere cut orthogonal to the intersection lineation, providing aprofile view of the crenulations and inclusion trails. The B-sec-tions were cut parallel to the intersection lineation and typicallyat a high angle to the A-sections.



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(SR) defined by the preferred orientation of muscovitelaths and elongate quartz and plagioclase grains. Onthe outcrop to map scale, SR is a steeply dipping, NE–SW-trending foliation that forms the axial surface tomoderately NE-plunging, tight folds found throughoutthe region. In these rocks, euhedral staurolite por-phyroblasts are commonly present in the metapeliticlayers, and reach sizes of 15–20 mm. These M2 por-phyroblasts overgrew SR, resulting in straight inclusiontrails that are continuous with the surrounding matrixfoliation (Fig. 3). Typically, there is slight deflection ofthe matrix fabric at the margins of the staurolite por-phyroblasts because of strain accumulation during/after porphyroblast growth (Fig. 3). This microstruc-ture is consistent over a large area, and is used as acontrol to evaluate crenulation cleavage developmentand porphyroblast kinematics in the aureole. Near itsboundary with zone 2, zone 1 hosts a population ofbiotite grains related to the M3 metamorphic eventthat cross SR in a consistent orientation (Fig. 6a).These grains are small relative to the regional M2biotite grains, and they define a plane that isapproximately parallel to the crenulation cleavage

developed at higher strain in the aureole (e.g. Fig. 6b).Further discussion of the microstructures found inzone 1 rocks, and more regionally in western Maine,can be found in Solar & Brown (1999, 2001).

Zone 2

Rocks in zone 2 show a moderate crenulation of theregional foliation (Fig. 6b), analogous to stage 2 ofcrenulation cleavage development defined by Bell &Rubenach (1983). This deformation is observedalmost exclusively in the phyllosilicate-rich metapelitelayers, with little visible strain recorded in the quartz-rich metapsammitic layers. As in zone 1, the inclusiontrails in zone 2 staurolite porphyroblasts are straightand defined by elongate quartz, plagioclase andilmenite grains. Inclusion trails in this zone are con-tinuous with the surrounding matrix foliation, butthere is a clear deflection of the matrix foliation at theporphyroblast boundaries. Zone 2 also hosts thecross-cutting population of biotite grains that areelongate parallel to the axial surfaces of the crenula-tions (Fig. 6b).

Fig. 6. Photomicrographs showing characteristic microstructures of the zone 1/zone 2 transition and zone 2. (a) Zone 1, near theboundary with zone 2. M2 staurolite at bottom of view preserves a foliation that had wrapped around an earlier M2 garnet por-phyroblast. The matrix in the upper-right quarter is gently crenulated, and a new generation of M3 biotite grains are alignedapproximately parallel to the axial surfaces of the folds. (b) Zone 2 showing the early stages of development of a crenulation cleavage.At this stage, the cleavage is only locally developed around M2 staurolite porphyroblasts. Plane-polarized light, long dimension of both(a) and (b) 5.9 mm.



Zone 3

Rocks in zone 3 show a well-developed crenulationcleavage (Fig. 7), analogous to stage 3 of Bell &Rubenach (1983). Where the microfolding is asym-metric, the long limb of each microfold is mica-rich andthe short limb is rich in quartz and feldspar (plagioclasein this case). These limbs correspond to what are typi-cally referred to in the literature as phyllosilicatedomains (P-domains) and quartz–feldspar domains(QF-domains), respectively (e.g. Passchier & Trouw,1996). In zone 3, it is still possible to trace a single SRsurface across P- and QF-domains. Staurolite por-phyroblasts are subhedral to euhedral with extensivequartz and ilmenite inclusions. Although the SR matrixfoliation is strongly deflected at the porphyroblastmargins, it is still continuous with the inclusion trails(Fig. 7).

Zone 4

Rocks in zone 4 show a strongly developed crenu-lation cleavage (Fig. 8a), analogous to stage 4 of Bell& Rubenach (1983). Mineralogical differentiation

becomes increasing more developed towards thepluton with most, if not all, of the quartz and pla-gioclase eventually being removed from P-domains,presumably migrating to the neighbouring QF-domains. New biotite and muscovite laths appear tohave nucleated in the P-domains further enhancingthe mineralogical differentiation. SR is preserved inthe P- and QF-domains, but an individual surfacecannot be traced from one P-domain to anotherthrough the intervening QF-domain. Staurolite por-phyroblasts are subhedral to euhedral and stillcommonly show straight inclusion trails, but there isno longer continuity between these trails and SR(Fig. 8a). The crenulation cleavage wraps each por-phyroblast, and the mica-caps effectively truncate theinclusion trails.A common observation in zone 4 is that the mica-

caps around staurolite porphyroblasts have beenovergrown by M3 rims of inclusion-poor staurolite(Fig. 8b). Solar & Brown (1999) recognized M3 rimovergrowths on M2 staurolite and garnet porphyro-blasts in the thermal aureole of the pluton, and Gui-dotti & Johnson (2002) placed these overgrowths in thecontext of the metamorphic zones and strain aureole.However, Moench (1966, p. 1452) appears to havebeen the first to recognize the relations among em-placement of the pluton, development of the strainaureole and overgrowth of the emplacement-relatedfoliation by M3 porphyroblasts. We have found littleor no evidence for deformation following the growthof these rims, suggesting that emplacement-relateddeformation was effectively complete before growth ofthe peak contact metamorphic minerals occurred inthese rocks (Moench & Zartman, 1976; Guidotti &Johnson, 2002).

Zone 5

Closest to the pluton, zone 5 shows a transition from adifferentiated cleavage to a pervasive foliation adjacentto the pluton (Fig. 9), analogous to stages 5 and 6 ofBell & Rubenach (1983). This cleavage differs from thecrenulation cleavage in zone 4 in that the biotite andmuscovite in the former QF-domains are sub-parallel tothe fabric in the P-domains. Closer to the pluton, themineralogical differentiation is progressively reducedleading to a pervasive fabric in which biotite and mus-covite laths are distributed relatively evenly throughoutthe rock (Fig. 9). Staurolite porphyroblasts in zone 5 aresubhedral to anhedral with lengths typically c. 2 mm.These staurolite are smaller than those in zones 1–4, andsome grains show apparent resorbsion textures relatedto staurolite-consuming reactions in the thermal aureole(Guidotti & Johnson, 2002).

Summary

Staurolite porphyroblasts throughout the study areaovergrew a regionally pervasive, NE–SW-trending,

Fig. 7. Photomicrograph showing characteristic microstructureof zone 3. In this example, a well-developed crenulation cleavageformed around a single M2 staurolite porphyroblast, whichoccupies a QF-domain. Plane-polarized light, long dimension5.9 mm.



steeply dipping, regional foliation (SR) and typicallypreserve this foliation as straight inclusion trails. Inrocks unaffected by the pluton-related crenulationcleavage, the inclusion trails are continuous with thematrix, showing little deflection at porphyroblastmargins. In the outer part of the strain aureole,inclusion trails can be traced from porphyroblasts tothe matrix but are deflected at the porphyroblastmargins. In the inner aureole, progressive strainduring crenulation cleavage development resulted inloss of continuity between inclusion trails and SR.Throughout the aureole, staurolite porphyroblastsare generally elongate parallel to their inclusiontrails. Thus, in the A-sections cut perpendicular tothe intersection lineation between SR and the cren-ulation cleavage, the long dimensions of stauroliteporphyroblasts typically lie at a high angle to theoverprinting crenulation cleavage. Using the orien-tations of inclusion trails from the uncrenulatedrocks as a reference, the kinematic behaviour ofporphyroblasts in rocks at different stages of crenu-lation cleavage development were evaluated, as dis-cussed in the following section.

INCLUSION-TRAIL ORIENTATION ANALYSIS

The preservation of a complete deformation gradientin the pluton aureole, combined with the known ori-ginal orientations of inclusion trails in M2 stauroliteporphyroblasts, provides a rare opportunity to exam-ine porphyroblast kinematics in relation to fabricdevelopment. To rigorously determine the true spreadof inclusion-trail orientations in the aureole, it wouldbe necessary to measure the 3-D inclusion-trail orien-tation in each individual porphyroblast in each sample.Although this is possible using computed X-raytomography (e.g. Ketcham, 2005), the method of datacollection outlined below is sufficient for our purposes.The average 3-D orientation of the planar fabricincluded in the porphyroblasts was determined bymeasuring the pitches of inclusion trails in two non-parallel thin sections from each sample (Fig. 10). Thepitch for each staurolite porphyroblast was measuredwith respect to a horizontal datum (a strike linemarked on the thin section). These pitch data werethen processed using FitPitch developed by Aerden(2003). FitPitch calculates the deviation of the pitch

Fig. 8. Photomicrographs showing characteristic microstructure of zone 4. (a) Well-developed, emplacement-related crenulationcleavage wrapping around M2 staurolite porphyroblasts. P- and QF-domains are well developed and single folia can no longer betracked across them. (b) M2 staurolite porphyroblast with M3 rim overgrowth along its top edge. This rim grew over the emplacement-related foliation that wraps the M2 core of the staurolite. Plane-polarized light, long dimension of (a) 5.9 mm, (b) 2.95 mm.



orientation from a model plane, iteratively minimizingthe deviation and then returning a best-fit planethrough the data.As discussed by Timms (2003), the total uncertainty

involved in the inclusion-trail orientation data is thesum of the uncertainties of: (i) sample collection(< ±3!), (ii) reorientation using a sand box (< ±3!),(iii) transfer of the orientation from the sample to thethin-section billet (±1!), (iv) transfer of the orientationfrom the billet to the thin section (±1!) and (v)uncertainty of orientation measurements using amicroscope (of order 1!). The compounding of errorscould possibly lead to total errors of ±9!. However,these potentially large errors are applicable only to theaverage inclusion-trail orientations (Fig. 5). In con-trast, errors in orientation measurements using themicroscope are the only ones relevant when evaluatingthe spread of inclusion-trail pitches from a single thinsection. Although Timms (2003) lists an error whenmeasuring inclusion-trail pitches on the order of 1!, thedegree to which these measurements are representativedepends largely on how straight and well-defined theinclusion trails are in each porphyroblast. The inclu-sion trails in the staurolite porphyroblasts studied hereare typically straight and well-defined but, as aconservative estimate, error related to pitch measure-ments are considered to be c. ±1!.After the best-fit plane was calculated using FitPitch,

the data were plotted on a lower hemisphere,equal-area projection using Stereonet developed byAllmendinger (Cornell University). The pitch datawere plotted with the best-fit planes to show the spreadof inclusion-trail orientations from the average

Fig. 9. Photomicrograph showing characteristic microstructureof zone 5. Well-developed, emplacement-related foliation wrapsaround M2 staurolite porphyroblasts. Note that all mica grainsare now elongate parallel to the new foliation, and mineralogicaldifferentiation is much less pronounced than in zone 4. Plane-polarized light, long dimension 5.9 mm.

Fig. 10. Diagram showing how an average inclusion-trail orientation is determined from pitch data in different thin sections (Aerden,2003). (a) Shows how inclusion-trail pitches are plotted on a lower hemisphere projection, and how a best-fit plane is determined. (b)The final lower hemisphere projection showing the average inclusion-trail orientation, the thin-section orientations and the inclusion-trail pitches.



(Fig. 5). The spread of inclusion-trail pitch data ineach sample were then plotted against map distancefrom the pluton contact (Fig. 11a). The A-sections(Fig. 4) were used for this exercise because they are

approximately perpendicular to the intersection linea-tion between the crenulation cleavage and SR. Thissection orientation provides minimum error of pitchspread associated with apparent dip, yielding values as

Fig. 11. (a) Diagram showing the spread of inclusion-trail pitch data against distance from the pluton margin for those 29 samplesindicated in Fig. 5. Approximate zone boundaries shown. (b) Diagram showing strain distribution in the pluton aureole. Datapoints for shortening profile include assumed zero shortening strain at 2900 m from the pluton margin, and six shortening valuesmeasured from crenulation cleavage. Five of these measurements come from zone 3, and one from zone 4. Ellipticity calculated fromshortening profile. (c) Single dashed curve shows calculated spread in pure shear, as shown in the inset diagram. / values of ±7! fromthe shortening direction were used for ellipses of axial ratio 2. Single solid curve shows calculated spread for dextral simple shear, asshown in inset diagram. / values of ±8! from the normal to the shear plane were used for objects of axial ratio 1 (circles) and 2 (ellipses).



close as possible to the true spread of the inclusion-traildata. Single-section pitch data from the outer aureole(zone 1) show a tight clustering with the averageinclusion-trail orientation approximately equal to SR(Fig. 5). As shown in Fig. 11(a), the total data spreadfor this zone is 14–19!, which we suggest reflects theinitial variation in the orientation of SR prior to beingpreserved in the staurolite porphyroblasts. Withincreasing strain in the aureole, the spread of single-section pitch data increases progressively to a maxi-mum of 75! near the pluton margin (Fig. 11a).

It is important to note that the effect of apparent dipin the 2-D thin section probably increases as theinclusion-trail pitch spread increases about the averageorientation, because of non-orthogonal intersectionsbetween the inclusion trails and the thin-section plane.As a result, the measured spread of pitches will becomeincreasingly larger than the true spread of the inclu-sion-trail planes. It is not possible to quantify the dif-ference between the measured and true spread,although we suspect that it is small. The differencewould be dependent on the 3-D shape and orientationof each individual porphyroblast, and the initialorientation of the inclusion trails in each, regardless ofthe strain path (e.g. Freeman, 1985). Nevertheless,Fig. 11(a) clearly shows a nonlinear increase in thespread of inclusion-trail orientation with proximity tothe pluton. This nonlinear increase is a key observationthat allows us to link porphyroblast kinematics to totalstrain accumulation in the aureole, as well as to strainaccommodation processes at different stages of cren-ulation cleavage development. In order to model thesepitch data to better understand their origin, a model offinite strain in the aureole is needed, which is developedin the following section.

AUREOLE STRAIN ANALYSIS

To test whether or not the inclusion-trail spread in theaureole is consistent with spreads predicted by theequations of motion derived for rigid particles in aviscous medium, a strain model is needed for theaureole. Metapelitic rocks generally lack the markersrequired for quantitative strain analysis. However,Johnson & Williams (1998) showed that crenulatedmica-rich folia can provide a minimum estimate ofshortening strain. In this technique, the length of acrenulated surface is used as the initial length and thefinal length is measured perpendicular to the trace ofthe crenulation cleavage (Fig. 12). We assume planestrain and accordingly took the measurements fromthin sections cut perpendicular to the intersectionlineation between the crenulation cleavage and SR(A-section in Fig. 4). The assumption of plane strain isprobably an inaccurate description of the strain in theaureole, but the only published strain data collectedfrom crenulation cleavage (Johnson & Williams, 1998)suggest that it provides a reasonable estimate ofshortening. The shortening calculation is made using

the standard expression for change in the length of aline:

e ¼ l# l0l0

! "ð1Þ

where e is finite elongation, l0 the length of the cre-nulated surface, and l the length measured perpendi-cular to the trace of the crenulation cleavage (Fig. 12).To generate a strain distribution, thin sections were

used to identify the effective outer limit of the strainaureole, which was placed !2900 m from the plutonboundary. The technique of Johnson & Williams(1998) was then applied to six samples midway throughthe aureole, as close as possible to the pluton, whilestill using the technique. The analyses resulted inshortening values ranging from 41% to 57% (Fig. 12),which are plotted against distance from the plutonmargin in Fig. 11(b). These data points, and the zero-strain point 2900 m from the pluton, are used toestablish a linear approximation to the shorteningstrain distribution in the aureole. Although a linearapproximation is an unsatisfactory representation ofthe detailed shortening strain distribution in the aure-ole, it is consistent with detailed 3-D strain analyses inother pluton aureoles (e.g. Johnson et al., 1999,fig. 11), and adequate for our purposes here. The bulk-shortening distribution could not vary dramaticallyfrom that plotted in Fig. 11(b). Stains continues toincrease with proximity to the pluton as illustrated bythe obvious increase in fabric intensity, but the increaseis unlikely to be more than slightly nonlinear becauseof the unrealistically large strains associated withshortening values between 85% and 100%.From the shortening strain distribution, combined

with the assumption of plane strain, ellipticity is cal-culated from:

ellipticity ¼ 1þ e11þ e2

¼

ffiffiffiffiffik1k2

s

ð2Þ

where e1 and e2 are the principal finite elongations, andk1 and k2 the principal quadratic elongations. Theellipticity is plotted in Fig. 11(b), with a maximumvalue of 48.

MATHEMATICAL MODELLING OFINCLUSION-TRAIL PITCH SPREAD

The nonlinearly increasing spread in the inclusion-trailpitch data with proximity to the pluton strongly sug-gest rotation of porphyroblasts relative to one anotherduring ductile deformation. Given the qualitativemodel of strain distribution in the aureole (Fig. 11b),the equations of motion derived by Jeffery (1922) wereused to test whether or not the pitch spread in theaureole is consistent with the calculated rotation ofellipsoids in a linear viscous matrix. The intention hereis to provide a first-order test only. The manyassumptions inherent in this type of analysis preclude a



quantitative result, but we believe that it is a usefulexercise because of the unique nature of the data set.

For this analysis, the following important assump-tions are made: (i) the deformation is plane strain, (ii)the material exhibits linear viscous behaviour, (iii) therotation occurs in the plane perpendicular to theintersection lineation between the crenulation cleavageand SR, (iv) the porphyroblasts are axisymmetric, and(v) the porphyroblasts are spaced sufficiently far apartthat the disturbed velocity fields around individualporphyroblasts do not strongly interfere with oneanother. It is also assumed that the inclusion-trailorientations reflect the orientations of the long axes ofthe staurolite porphyroblasts in the evaluated plane.Although the microstructural observations indicatethat there are exceptions to this geometric relationship,the assumption holds in general and is consistent withdata presented by Solar & Brown (1999, fig. 4) whoshowed that the staurolite porphyroblasts in our zone1 (near Coos Canyon) are strongly to moderatelyaligned in the SR plane.

Analytical solutions for the equations of Jeffery(1922) for total rotation of isolated ellipses of knownoriginal orientation in two dimensions have beenprovided for pure shear (e.g. Gay, 1966, 1968), simpleshear (e.g. Reed & Tryggvason, 1974), and combinedpure and simple shear (e.g. Ghosh & Ramberg, 1976).Gay (1966, 1968) showed that principal quadraticelongations can be used to relate the total rotation ofobjects of known axial ratio to total shortening strainin pure shear by the following equation:

ln cot /0 ¼ ln cot /þ a2 # b2

a2 þ b2

! "ln

ffiffiffiffiffik2k1

s

ð3Þ

where /¢ is the final orientation of the object long axisrelative to the shortening direction, / the initial ori-entation of the long axis, and a and b the lengths ofthe semi-major and semi-minor axes of the objectrespectively. Similarly, Reed & Tryggvason (1974)showed that principal quadratic elongations can beused to relate the total rotation of objects of known

Fig. 12. Tracings of crenulated, mica-rich foliation domains used to approximate shortening strain in the aureole using the methodof Johnson & Williams (1998). Short vertical lines in each example represent the trace of the crenulation cleavage. Shorteningstrains (e) are indicated for each sample. The upper-left sample is used to illustrate the technique, and the upper-right sample isaccompanied by a photomicrograph illustrating the relationship between the microstructure and the traced foliation. Photomicrographin plane-polarized light.



axial ratio to total shortening strain in simple shear bythe following equation:

tan /0

¼ a

btan

2ab sinh 0:5 lnffiffiffiffiffiffiffiffiffiffiffiffik1=k2

p$ %

a2 þ b2þ cot

b

atan /

! "2

4

3

5

ð4Þwhere all parameters are defined above.

Figure 11(c) shows one curve calculated for pureshear (Eq. 3) that illustrates the predicted spread oflong-axis orientations for objects of axial ratio 2 thathave an initial orientation of 7! either side of theshortening direction. This curve is superimposed onthe inclusion-trail pitch data across the aureole,showing that the pitch data are broadly consistent withthe analytical results. Our microstructural observa-tions indicate that porphyroblasts in single thin sec-tions generally show axial ratios between 1 and 2, andonly rarely >2. Thus, the solution for axial ratio 2 issufficiently representative of the possible total spreadsfor the specific starting geometry.

Figure 11(c) also shows a single curve for simpleshear (Eq. 4). This curve was calculated by determiningthe maximum spread of porphyroblast long axes(inclusion trails) in a rock containing objects with axialratio between 1 and 2, starting out with their inclusiontrails at ±8! from the normal to the shear plane (inthis case assumed to be parallel to the east-dippingpluton contact and developing crenulation cleavage).The analytic solution for combined pure and simpleshear given by Ghosh & Ramberg (1976) predictablyprovides a fit between those for pure and simple shear.

DISCUSSION

The understanding of rigid object behaviour in aniso-tropic media is incomplete, and our analysisincorporates many assumptions: therefore, the mod-elling results of Fig. 11(c) must be treated with caution.However, given the assumptions and initial startingconditions, the results do suggest that a significantincrease in the inclusion-trail spread is not expecteduntil shortening strains reach values greater than c. 50–60%. This is a useful result because even though themicrostructural observations clearly indicate a pro-gressive increase in strain towards the pluton, theinclusion-trail spread does not appear to increase untilmidway through zone 4. In addition, the averageinclusion-trail orientations do not begin to varymarkedly until approximately this same position in theaureole (Fig. 5). A number of published studies showremarkably consistent average inclusion-trail orienta-tions over areas ranging in size from sample- andoutcrop-scale folds (e.g. Steinhardt, 1989; Bell &Forde, 1995; Jung et al., 1999; Evins, 2005) to tens orhundreds of square kilometres (e.g. Fyson, 1980;Johnson, 1990, 1992; Aerden, 1994, 1995; Ilg & Karl-

strom, 2000; Hickey & Bell, 2001). The question re-mains as to whether or not these data preserve, even ina crude way, the original orientations of foliationspresent in the rock during porphyroblast growth.Unfortunately, the answer is unlikely to be clear exceptin cases where the original orientation of the preservedfoliation is known. Many of these studies (e.g. John-son, 1992) show sample-scale variations up to 80!, andwe suggest that this probably reflects rotation of por-phyroblasts relative to one another. Nevertheless, thedata in Figs 5 and 11 suggest that, given certain initialconditions and deformation paths, the total spread ofinclusion-trail orientations, and the average orienta-tion in each sample, can remain effectively unchangedup to shortening strains of 50–60%, and so the averageinclusion-trail orientations in some of the studies citedabove probably do reflect original foliation orienta-tions, particularly where the porphyroblasts have axialratios close to 1.0 and the deformation path was highlycoaxial (e.g. Evins, 2005).An alternative approach to evaluating the data in

Figs 5 and 11 is to consider how strain is accommo-dated during crenulation cleavage development, andattempt to interpret the data in this context. In theearly stages of crenulation cleavage development(zones 1–3), cleavage-parallel stretching is accommo-dated primarily by mass transfer between P- andQF-domains (e.g. Cosgrove, 1976; Marlow & Ether-idge, 1977; Gray, 1979; Gray & Durney, 1979;Schoneveld, 1979; Johnson, 1990; Williams et al.,2001). In these early stages, there is little reduction inthe width of QF-domains, and little or no wrapping ofSR around the porphyroblasts (Fig. 13a,b). Underthese circumstances, it is highly unlikely that porphy-roblast kinematics would follow the idealized formu-lations above for viscous flow, but we would stillexpect the spread of inclusion trails to remain largelyunchanged during these early stages, consistent withthe data (Fig. 11a).When progressive cleavage development reaches

zone 4, the shortening and stretching can no longer beaccommodated primarily by mass transfer between P-and QF-domains, because all of the quartz and feld-spar have been removed from the P-domains. At thisstage, the primary strain-accommodation mechanismmust change to some combination of dislocation creepand diffusion creep. As a result, the width of QF-do-mains is reduced and SR begins to wrap around theporphyroblasts (Fig. 13c). This is the most likely partof the strain history in which the porphyroblasts wouldfollow viscous-flow rotational paths, because of thehigher probability of a viscous-like shear–stress coup-ling between the wrapping foliation and the porphy-roblast margins.In zone 5, the new fabric no longer resembles a

crenulation cleavage, but is instead an intense newfoliation. It is possible that shear strain preferentiallypartitioned into this narrow zone adjacent to the plu-ton margin. This might be expected near the primary



rheological interface, and shear strain would be easilyaccommodated by the new foliation. This might pro-vide at least a partial explanation for the markedvariations in average inclusion-trail orientations inzone 5 (Fig. 5), but we have no corroboratingmicrostructural evidence, such as asymmetric strainshadows, shear bands, or mica fish to suggest highlynon-coaxial deformation during the emplacement-related deformation.

Another possible explanation for marked variationsin average inclusion-trail orientations in zone 5 isprovided by the study of Brown & Solar (1998a) andSolar & Brown (2001). These authors have dividedwestern Maine into alternating domains in which theregional lineation is either weaker (apparently flatten-ing) or stronger (apparent constriction) than the re-gional tectonic foliation. One of their proposeddomain boundaries runs through the northern half ofFig. 5, parallel to the regional NE trends, betweensamples WM5 and WM3. Rocks to the west of thisboundary are assigned to an apparent constrictionaldomain, and these authors have argued that theregional foliations are less consistently oriented fromone locality to another within these domains. Thus, theNW portion of Fig. 5 lies in a zone of apparent con-strictional strain, as defined by Brown & Solar(1998a,b) and Solar & Brown (2001), and this mayprovide a partial explanation for the increased varia-bility in average inclusion-trail orientations for those

samples that lie to the west of sample WM5. In con-trast, the samples that show marked variation from theregional trends (e.g. D3-060, D3-056, D2-014) are veryclose to the pluton margin, so the variation mayinstead reflect the higher emplacement related strainsthere. Although the cause of variability in the averageinclusion-trail orientations in the more highly strainedrocks is open to question, the systematic sample-scaleincrease in the inclusion-trail spreads (Fig. 11a) isunlikely to reflect position of the sample relative to theproposed flattening/constriction boundary. At thescale of a thin section, foliations defined by muscoviteand quartz in all rocks are moderately to stronglydeveloped (e.g. Solar & Brown, 1999), and in the sev-eral thousand thin sections we have access to, they aretypically sub-planar. We therefore conclude thatvariations in regional fabric type and intensity havelittle if any effect on the systematic, nonlinear increasein inclusion-trail spread (Fig. 11a).

There are clearly a number of potential complica-tions to consider when interpreting the data in Figs 5and 11, and along with the discussion above we notethe following three additional considerations. First, itis known that porphyroblasts intersected in theA-sections do not, in general, have semi-major andsemi-minor axes that lie precisely in this plane.Therefore, the problem becomes one of rotation inthree dimensions. Although the equations for 3-Drotation in pure shear and simple shear are straight-

Fig. 13. Diagram showing how shape-con-trolled porphyroblast rotation may havebeen largely responsible for the increasedinclusion-trail pitch spread with increasingstrain in the aureole. Strain from (a) to (b) isaccommodated primarily by dissolution–precipitation mass transfer. Continuedshortening and stretching causes thedeforming matrix to wrap around the rigidporphyroblast (c). The resulting stress cou-ple between the porphyroblast and deform-ing matrix causes the shape-controlledrotation of the porphyroblasts.



forward (e.g. Gay, 1968; Reed & Tryggvason, 1974;Freeman, 1985), such an analysis would requireassumptions or knowledge regarding the 3-D shapesand orientations of all porphyroblasts intersected, andit is unclear what gains would be made over the 2-Danalysis conducted here.

Another possible consideration has to do with theno-slip boundary condition inherent in the viscousformulations for rigid-object behaviour. Johnson(1990, 2006) has suggested that the boundaries ofporphyroblasts in deforming mid-crustal rocks may bepartially lined by phases that allow strain localizationat the object interface, effectively violating the no-slipboundary condition and leading to kinematic beha-viour that is not predicted by the equations of motionderived by Jeffery (1922). Strain localization at theboundaries between rigid objects and viscous orMohr–Coulomb matrix materials has been investi-gated in several analog and numerical studies (e.g.Ildefonse & Mancktelow, 1993; Marques & Coelho,2001; ten Grotenhuis et al., 2002; Mancktelow et al.,2002; Ceriani et al., 2003; Johnson, 2006), and it isclear that such localization provides an additionalcomplication that may render the kinematic history ofporphyroblasts more difficult to extract. In general,such localization will tend to stabilize orientations andtherefore reduce the amount of spread.

Finally, there remains some ambiguity, thoughsmall, as to the original spread of the pre-emplacementinclusion-trail orientations in the rocks that now makeup the pluton aureole. However, even if there weremoderate pre-emplacement variation in the initial,sample-scale orientation spread, it would not effect theconclusion reached from the data in Fig. 11. The sys-tematic, nonlinear increase in orientation spread inrelation to increasing strain in the aureole is convincingevidence for the rotation of porphyroblasts relative toone another.

CONCLUSIONS

Microstructural observations and porphyroblastinclusion-trail analysis in the aureole of the Moose-lookmeguntic pluton show that staurolite porphyro-blasts rotated relative to one another duringcrenulation cleavage development. Thus, this paperputs to rest the 20-year-old debate about whether ornot porphyroblasts can rotate relative to one anotherduring crenulation cleavage development and ductiledeformation, and provides a sensible explanation forthe sample-scale variation typically seen in deformedmid-crustal rocks.

The amount of rotation in the strain aureole, asindicated by the nonlinearly increasing spread ofinclusion-trail pitch data, is broadly consistent withplane-strain analytical solutions of rigid object rota-tion in a linear viscous matrix. However, there are anumber of complexities and variations from ideal vis-cous behaviour associated with the 3-D deformation of

rocks, and the analytical solutions should only beconsidered useful for a first-order, qualitative analysisof porphyroblast kinematics. Among these complexit-ies are: (i) variation in deformation mechanismsresponsible for fabric development and strain accom-modation at different stages of crenulation cleavagedevelopment, which can affect the nature and magni-tude of the stress couple at porphyroblast interfaces;(ii) possible partitioning of shear strain near the marginof the pluton during emplacement and fabric devel-opment in the aureole, which would require a spatiallyvarying and possibly strain-dependent analytical for-mulation for rotation calculations; (iii) lack of know-ledge of the 3-D shapes and orientations of individualporphyroblasts in each sample, which limits the accu-racy of 2-D calculations; and (iv) the effective violationof the no-slip boundary condition at porphyroblastmargins partially lined by phases that are relativelyweak in shear.Although much controversy has revolved around the

rotation of porphyroblasts relative to one another orsome arbitrarily chosen reference frame (see Johnson,1999 for review), there has been much less discussionabout the usefulness (or otherwise) of average inclu-sion-trail orientations. Our results suggest that, givencertain initial starting conditions and deformationpaths, the average inclusion-trail orientations in por-phyroblasts overprinted by a later deformation eventmay be useful indicators of the original foliationorientation, particularly if shortening strains do notexceed 50–60%. The spread of inclusion-trail orienta-tions (40–75!) in the moderately to highly strainedrocks is similar to the spread reported in several pre-vious studies. We consider it likely that the sample-scale spread in these previous studies is also the resultof porphyroblast rotation relative to one another.More studies are needed before firm conclusions can bedrawn, and in particular data are required across straingradients in highly non-coaxial shear zones that over-print porphyroblasts with known initial inclusion-trailorientations.

ACKNOWLEDGEMENTS

We gratefully acknowledge support for this work fromthe National Science Foundation, grants EAR-0207717 and EAR-0440063. We thank N. Mancktelowand G. Solar for constructive comments that helped usto improve the manuscript, and D. Whitney for edi-torial assistance.

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Received 24 July 2005; revision accepted 25 October 2005.



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