De-bugging the millipede porphyroblast microstructure: a serial thin-section study and 3-D computer animation

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1 j. metamorphic Ceol., 1996, 14, 3-14 De-bugging the millipede porphyroblast microstructure: a serial thin-section study and 3-D computer animation S. E. JOHNSON AND K. R. MOORE* School of Earth Sciences, and School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney, New South Wales, , Australia ABSTRACT Seventy-five spatially orientated, serial thin sections cut from a single rock containing millipede porphyroblast microstructure from the Robertson River Metamorphics, Australia, reveal thc three-dimensional (3-Dj geometry of oppositely concave microfolds (OCMs) that define the microstructurc. Electronic animations showing progressive scrial sections of thc 3-D microstructurc arc made available via the World Wide Web. The OCM amplitudes decrease regularly from a maximum in near-central sections to a minimum in near-marginal scctions, whereas the OCM interlimb angles increase regularly from a minimum in near-ccntral sections to a maximum in near-marginal sections. These observations illustrate that the OCMs are noncylindrical surfaces with culminations located in near-central scctions. Because the porphyroblast cores appear to have been present before significant development of the syn-ocm foliation, all of the OCMs were formed by heterogcncous cxtension around thcse cores. The overall gcometry of the OCMs described hcre reflects the strain state, and cannot be used to constrain deformation paths. Keg words: computer animation; computer graphics; crenulation cleavage; mathematica; millipede microstructure: oppositely concave microfolds; porphyroblasts; serial thin sections. INTRODUCTION This paper presents a serial thin-section study, and three-dimensional (3-D) computer-aided reconstruction of the millipede porphyroblast microstructure in plagioclasc porphyroblasts from the Robertson River Metamorphics, Australia (Bell & Rubenach, 1980). The aims of this paper are to clarify the 3-D geometry of this microstructure, and briefly discuss its formation. The millipede microstructure is characterized by inclusion trails and their continuation as an external foliation that form outwardly opening, oppositely concavc microfolds (OCMs) on either side of a porphyroblast (Fig. 1). To clarify the 3-D shape of this complex microstructure, three animations are prescntcd showing progressive serial sectioning of the microstructure in three mutually orthogpnal directions. These animations are available as an electronic supplement through the World Wide Web Home Page of the Jour.nn/ of Met(iiizor.phic Gt.ologj3 ( URL: j. We emphasize that this is only one particular type of OCM, the others being described by Johnson & Bell (1996). SAMPLE CHOICE AND THIN SECTIONING TECHNIQUE The sample described in this paper was chosen because: (1) it comes from the location where the millipede microstructure was originally described; (2) some of the plagioclase porphyroblasts are large enough for 6-12 serial thin sections per porphyroblast, which is a reasonable number for 3-D reconstruction; and (3) inclusion trails and external foliations are generally continuous, allowing accurate tracing of inclusion/ foliation surfaces for 3-D reconstruction. As discussed by Johnson ( 1993a), samples could potentially be Fig. 1. Block diagram showing the relationships between oppositcly concave microfolds (OCMs), porphyroblast inclusion trails. two foliations (S1 and S2) and F2 fold axes. The most useful section for observing thc OCMs is perpendicular to thc two foliations and F2 fold axes. as shown in thc top face of the diagram. OCMs can also be seen on the left-front face of the diagram, owing to the noncylindrical nature of OCMs (explained iii text). 3

2 4 S. E. J O H N S O N & R. R. MOORE studied by photographing serially ground and polished rock surfaces, which would avoid the material loss involved in making thin sections. However, each polished surface is destroyed to produce the next one, whereas serial thin sections allow continual comparison, appraisal and interpretation of microstructures. Furthermore, considerably more microstructural detail can be observed in transmitted light than in reflected light. Before determining the orientations in which to cut serial thin sections, it was necessary to determine the relative orientations of foliations and inclusion trails in the rock. These were evaluated by making three nonparallel saw cuts, from which it was determined that: (1) S1 and S2 are approximately orthogonal through much of the sample (Fig. l), ( 2 ) S1 forms inclusion trails in the plagioclase porphyroblasts (Fig. 1) and ( 3 ) the OCMs are F2 microfolds of S1 (Fig. 1). We decided that the most informative orientation for serial sectioning was perpendicular to S1 and S2, providing a profile view of F2 microfolds, and therefore the OCMs, at their culminations (clarified below). This orientation corresponds to the top face of Fig. 1. Fig. 2. Set of six serial thin sections through a single plagioclase porphyroblast with well-developed OCMs. The section orientation corresponds to the top face of Fig. 1. Line diagrams are shown in Fig. 3. Crossed polars; long axes of all photomicrographs 23 mm.

3 DE-BUGGING THE 'MILLIPEDE' PORPHYROBLAST MICROSTRUCTURE 5 Because we used lines traced from serial thin sections to reconstruct the 3-D shape of the foliation and inclusion surfaces, it was necessary to cut sections in one orientation only. However, the reconstructed geometry was checked by cutting a second set of sections parallel to S2, corresponding to the left-front face of Fig. 1. OCMs are also seen in this section orientation, because the F2 OCMs in the top face of Fig. 1 are noncylindrical, which will be explained in a later section. Seventy-five serial thin sections were cut in the two orientations described above; 69 perpendicular to S 1 and S2, and six perpendicular to Sl and parallel to S2. To control the spacing of individual thin sections, lines were marked at 1-mm intervals on the sides of the thin-section blocks. Sections were cut from the Fig. 3. Interpretative line diagrams of photomicrographs in Fig. 2. Inclusion trails are equivalent to matrix S1, and the OCMs of S1 formed during the development of S2. The shaded areas represent plagioclase porphyroblasts ~ the larger, central porphyroblast is of most interest here.

4 6 S. E. JOHNSON & R. R. MOORE blocks with an eight-inch-diameter, continuous-rim diamond blade with a 0.5-mm kerf. After each section was cut, the block was prepared for the next section, and the position of the prepared surface relative to the marked 1-mm intervals noted. Sections were generally spaced at approximately 1.5-mm intervals, although some were spaced as little as 1.0 mm and as much as 2.0 mm apart. Twenty-nine complete porphyroblasts were intersected during serial thin sectioning parallel to the top face of Fig. 1. A set of serial thin sections through one of these porphyroblasts, which shows the internal morphology of porphyroblasts with OCMs, is illustrated in Fig. 2. Twelve thin sections were made through the porphyroblast in Fig. 2; however, six photomicrographs were removed to allow the set to be printed at a reasonable size on one page. Line diagrams of Fig. 2(a-f) are shown in Fig. 3(a-f) to help clarify the microstructures. Figure 4 shows OCMs seen in a section corresponding to the left-front face of Fig. 1. Fig. 4. OCMs of S1 sew in thin section cut parallel to S2, corresponding to the Icft-front face of Fig. I. SI and OCM pattcrii ninrkcd. Crossed polars: long axis of photomicrograph 28 mm. MICROSTRUCTURES These OCMs occur in and around plagioclase porphyroblasts in a matrix of quartz and muscovite (e.g. Figs 2-6). The matrix has two well-developed foliations, which we will call S1 and S2 for convenience only; see Bell & Rubenach (1983), Reinhardt & Rubenach (1989) and Davis (1995) for more information about the structural history. Both Sl and S2 are differentiated crenulation cleavages, and the porphyroblast inclusion trails are S1 (Figs 2-6). All porphyroblasts examined are composed of a core in which inclusion trails are invariably straight, surrounded by a narrow rim in which inclusion trails curve into the matrix, forming the characteristic OCMs (e.g. Fig. 5a). The core/rim boundary is marked by a change in the number of inclusions, the core being inclusion-rich relative to the rim (e.g. Fig. 5a-c). The boundary is also marked by a sharp change in anorthite content, cores having a range of An,,-An,,, rims An,,-An,, (Bell & Rubenach, 1980). It is unclear whether or not the cores were present before S2 began to form, or whether they grew during D2. The invariably straight trails in the cores suggest that, if they did grow during D2, they grew during its very early stages. Growth timing of the rims is clearer. the curvature of inclusion trails indicating growth during D2. The spacing between S1 cleavage domains is considerably greater in the matrix affected by S2 than in the porphyroblasts (e.g. Figs 2c & 5a-c), showing that extension continued after cessation of porphyroblast growth. Mica grains in S1 cleavage domains and quartz grains in S1 microlithons are elongate parallel to S1, both within porphyroblasts and in adjacent matrix unaffected by D2 (Fig. 5c). However, in areas affected by D2, the matrix S1 has been strongly modified in the following two ways, depending on the concentration of mica in S1 cleavage domains (Fig. 7). (1) In mica-poor S1 cleavage domains, mica grains that were aligned approximately parallel to S 1 have commonly been nearly homogeneously rotated towards alignment with S2 (e.g. Figs 5b, c & 7). In S1 microlithons, quartz grains have been flattened and recrystallized, so that they are elongate parallel to S2, and new mica grains have grown parallel to S2 (e.g. Figs 5b & 7). (2) In mica-rich S1 cleavage domains, rotation of mica grains is heterogeneous, defining an S2 crenulation cleavage with cleavage domains and microlithons (e.g. Figs 5a-c & 7). In S2 microlithons, mica grains are still aligned parallel to S1, and quartz grains have relatively equidimensional shapes, resulting presumably from a combination of shortening and recrystallization during D2 (e.g. Figs 5b & 7). These two types of areas merge continuously without noticable anastomosing or deflection of S2 cleavage domains. suggesting that approximately the same amount of shortening was accommodated by each (Fig. 7). This requires that the S2 cleavage domains are zones of relatively high strain

5 DE-BUGGING THE MILLIPEDE PORPHYROBLAST MICROSTRUCTURE 7 compared to zones of the same width in the areas in which S2 crenulations did not form. Quartz has been lost from S2 cleavage domains, which are now entirely white mica. Numerous examples of quartz enrichment in the pressure shadows of porphyroblasts may represent some of this quartz (e.g. Figs 2b-d & 5a,c), but it is unclear whether D2 involved volume loss or gain, on the thin section scale. However. the proportion of quartz in the matrix appears to be similar to that preserved in porphyroblasts, and in local matrix largely unaffected by D2 (e.g. Fig. 5c), suggesting that any volume change on the thin-section scale was probably not large. The sample used to make serial thin sections contained the hinge and one limb of an F2 fold of S1 (Fig. 8). In areas where strain was relatively low in the hinge during D2, S2 crenulations are commonly symmetrical, and S2 cleavage domains at early stages of their development commonly contain very tight to isoclinal microfolds of S1 cleavage domains. This contrasts with zones in the hinge where strain was relatively high during D2, in which one of the crenulation limbs has ruptured. the isoclinal microfolds of S1 have been destroyed and new mica grains have grown parallel to S2, forming an asymmetrical crenulation cleavage (e.g. Fig. 5a-c). Strain appears higher and S2 crenulations are generally more asymmetrical in the limb of the F2 fold. Where developed, the asymmetry of S2 crenulations is consistently sinistral in all thin sections, regardless of where they occur in the fold in Fig. 8. As with S2 crenulations, OCMs in the F2 hinge are relatively symmetrical (e.g. Figs 2 & 5a-c), whereas those in the limb are variably asymmetrical (e.g. Fig. 5d). 3-D COMPUTER-AIDED RECONSTRUCTION To reconstruct the OCMs shown in Figs 2 & 3, we traced the outlines of three intersected plagioclase porphyroblasts, as well as five inclusion-foliation surfaces (Fig. 9). Two of these surfaces were chosen for reconstruction because they were the most widely spaced, oppositely concave surfaces in the central section through the porphyroblast (Figs 2c & 3c). A third surface was chosen to correspond approximately to the median or central inclusion surface. The two remaining surfaces were chosen to provide intermediate sections between the median surface and the strongly curved surfaces at the margins of the porphyroblast. Because S1 is a differentiated crenulation cleavage with variable but reasonably consistent spacing betwcen individual cleavage domains, it was relatively easy to identify the same five inclusion-foliation surfaces in each of the 12 serial sections. The tracings of porphyroblasts and inclusionfoliation surfaces were scanned and redrawn with the polygon tool in the program CanvasTM. The Canvas files were then imported into the program, in which the various curves representing porphyroblasts and foliations were redefined as functions with a fitting routine. These functions were then connected with a separate set of functions to form 3-D surfaces corresponding to each of the three porphyroblasts and five inclusion-foliation surfaces. The reconstructed porphyroblasts and surfaces were then correctly positioned relative to one another and scaled to form the final image. Five successive slices of equal thickness were then removed from the image to show the full 3-D geometry more clearly (Fig. 10). The reconstruction method is similar to that used by Moore & Johnson (1993) and Johnson & Moore ( 1993) to reconstruct spiral-shaped inclusion trails in garnet porphyroblasts (Johnson, 1993a,b). Mathematica allows the 3-D image to be viewed in any orientation, and it can be sectioned in any orientation to any depth, as shown, for example, in Fig. 10. Mathematica also has an animation capability allowing movies to be generated, which greatly helps to clarify the 3-D shapes of complex surfaces or groups of complexly interconnected surfaces. We have sectioned the image in three mutually orthogonal orientations, corresponding to the left-front, right-front and top faces of Fig. 1, and presented the sectioning process as QuickTimeTM movies (referred to here as Fig. lla-c), which are available as an electronic supplement through the World Wide Web Home Page of the Journal of Metcimorphic Geology ( ). Fig. 5. (see overleaf) Photomicrographs of OCMs in and around various plagioclase porphyroblasts. See interpretative linc diagfims in Fig. 6 for clarification. All photomicrographs are shown looking in the same direction as those in Fig. 2, and the fold profile in Fig. 8. (a) Very symmetrical OCMs. Pressure shadows form the cores of these OCMs, and individual quartz grains are elongate parallel to matrix S2. Detail shown in (b). Crossed polars, long axis 17.5 mm. (b) Enlargement of upper-right portion of (a) clearly showing several of the features described in the text and in Fig. 7. A marked decrease in the concentration of quartz grains at the right margin of the porphyroblast defines the core-rim boundary. Crossed polars, long axis 10 mm. (c) OCMs in and around two scgments of a single plagioclase porphyroblast. The lower area between the two segments contains gently folded SI. This area has been largely protected from the effects of D2, and demonstrates that quartz and mica grains were elongate parallel to S1, and quartz grains were approximately the same size as those inside porphyroblasts, prior to D2. Crossed polars. long axis 13.5 mm. (d) OCMs in and around a plagioclase porphyroblast from the limb of the F2 fold in Fig. 8. Although OCMs arc apparent at the top and bottom of the porphyroblast, inclusion trails exiting the main body of the porphyroblast are clearly folded with a sinistral asymmetry into alignment with matrix SI, which runs diagonally from the lower left to the upper right. Crossed polars. long axis 10 mm.

6 8 5. E. JOHNSON & R. R. MOORE

7 Fig. 6. Interpretative line diagrams of the photomicrographs shown in Fig. 5. DE-BUGGING THE 'MILLIPEDE' POKPHYKOBLAST MICROSTRUCTURE 9

8 10 S. E. JOHNSON & R. R. MOORE I S1 Fig. 7. Diagram showing the two different styles of D2 deformation, depending on the concentration of mica in S1 cleavage domains. (a) Pre-D2 configuration showing S1 cleavage domains as dark layers with elliptical quartz grains between. (b) Post-D2 configuration. Where mica concentrations are relatively rich, strain during D2 is very heterogeneously distributed, most of the strain localized in S2 clcavage domains. In the S2 microlithons. mica grains are still largely parallel to S1 and quartz grains are relatively equant. Where mica concentrations arc relatively poor, D2 deformation is taken up more homogencously. quartz grains are variably elongate parallcl to S2. mica grains in S1 cleavage domains have rotated towards alignment with S2 and new mica grains have grown parallel to S2. This diagram illustrates microstructures that can be seen in Figs 2 & 5. I S1 13 cm 3-D SHAPES OF OCMS Fig. 8. Geometrical relationships between Sl and S2 in the hand sample used to make serial thin sections. Folded S1 partially defines an F2 fold. The fold profile is shown looking in the same direction as the photomicrographs in Figs 2 & 5. Interlimb angles of the ocms increase regularly in successive serial sections from near-central sections through the porphyroblasts, outward through their margins into the matrix, whereas the OCM amplitudes decrease. For example, consider the two microfolds at the left and right margins of the porphyroblast in Fig. 9(f). Moving in either direction through the porphyroblast, towards (a) or (l), interlimb angles increase and amplitudes decrease. The regular changes of interlimb angles and amplitudes can be seen in three dimensions in Fig. 10, and particularly in Fig. ll(a) as

9 DE-BUGGING THE 'MILLIPEDE' PORPHYROBLAST MICROSTRUCTURE 11 Fig. 9. Porphyroblasts and inclusion/foliation surfaces traced from photomicrographs of 12 serial thin sections through the central porphyroblast in Fig. 2. Sections (a), (b). (d), (i), (k) and (I) were excluded from Fig. 2. These 12 sections are spaced at approximately 1.5 mm, and were used in the 3-D reconstruction in Figs 10 & 1 I. the movie loops back and forth. These regular changes demonstrate that the microfolds are noncylindrical, as seen in Fig. 12. The shapes of OCMs seen in sections parallel to S2 (Fig. 4) result from their noncylindrical nature. These OCMs can be seen around the porphyroblast in Fig. 3 by running the movie in Fig. 1 I (b). The noncylindrical nature of the microfolds can also be seen from a different perspective by running the movie in Fig. 11 (c). This movie sections the microfolds perpendicular to the direction of maximum finite elongation on S2 (parallel to the right-front face in Fig. l), revealing closed foliation loops like those seen in sections through sheath folds. The locations of culminations in an OCM pair relative to one another depend on the shapes and orientations of porphyroblasts relative to the thinsection plane. If the extreme ends of a porphyroblast do not lie in the thin-section plane, the culminations of the two microfolds also lie in different thin-section planes. In the example shown in Fig. 9, the culminations of both OCMs are very close to section (f), indicating that the extreme ends of the porphyroblast are approximately in this section.

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11 ~ DE-BUGGING THE MILLIPEDE PORPHYROBLAST MICROSTRUCTURE 13 Fig. 11. Computer animations ( movies ) showing progressive serial scctioning in three mutually orthogonal directions of the 3-D image in Fig. lo(a). In these movies the plagioclase porphyroblasts are green, and the five inclusion-foliation surfaces are variably coloured depending on their orientations. Numbers along the margins indicate true dimensions (mm). These movies can be accessed directly at the WWW address below. and further descriptions and instruction can be found there. (a) Sectioning parallel to top face of Fig. I, and X-Z plane of finite strain. (b) Sectioning parallel to left-front face of Fig. I, and X-Y plane of finite strain. (c) Sectioning parallel to right-front face of Fig. 1, and Y-2 plane of finite strain. (URL: contents/l996.html) Fig. 12. The right-end S1 foliation surface in Figs 3,9, 10 & I I, illustrating the noncylindrical shape of the folded surface. The orientation of the surface has been changed relative to its orientation in the above figures to illustrate its shape more clearly. The bulge in the middle of the surface points out towards the reader. the dark region to the left being a valley. FORMATION OF THESE OCMs Because the porphyroblast cores were present before detectable development of S2, the OCMs formed during D2 by heterogeneous extension of S1 around these cores. Bell & Rubenach (1980) and Bell (1981) interpreted these OCMs as indicating bulk coaxial shortening, at least on the scale of individual OCMs. However, Johnson & Bell (1996) have demonstrated that such OCMs can form by heterogeneous extension around rigid objects during any deformation path between, and including, bulk coaxial shortening and bulk simple shearing. Thus, these OCMs reflect the strain state only, and cannot be used as indicators of specific deformation paths. ACKNOWLEDGEMENTS We acknowledge support for this project by the Australian Research Council in the form of a Queen Elizabeth I1 Research Fellowship (to S.E.J.), Grant number A , ARC Small Grants from Macquarie University, and a research agreement with the Digital Equipment Corporation. T. H. Bell and M. J. Rubenach are thanked for the sample from the Robertson River Metamorphics. T. H. Bell, D. W. Durney, D. Robinson and R. H. Vernon are thanked for comments on the manuscript. W. D. Means and M. L. Williams are thanked for their thoughtful reviews. We especially thank the editors of the Journal of Metunzorphic Geology for their enthusiastic support as we prepared our movies for the WWW. Fig. 10. Three-dimensional representation of the three porphyroblasts and five inclusion/foliation surfaces in Fig. 9. In (b)-(f), slabs of equal thickness have been sequentially removed from the full image in (a), parallel to the top face of Fig. 1, to illustrate the microstructural details more clearly. Numbers along the margins indicate true dimensions (mm). Plagioclase porphyroblasts are green, and the five inclusion-foliation surfaces are variably coloured depending on their orientations.

12 14 S. E. JOHNSON & R. R. MOORE REFERENCES Bell. T. H., Foliation development: the contribution, geometry and significance of progressive bulk inhomogeneous shortening. Tec,ronoph! sic.s, 75, Bell, T. H. & Rubenach, M. J., Crenulation cleavage development - evidence for progressive, bulk inhomogeneous shortening from millipede microstructures in the Robertson River Metamorphics. Trc,tonoplz! sic.s, 68, T9-T15. Bell, T. H. & Rubenach, M. J., Sequential porphyroblast growth and crenulation cleavage development during progressive deformation. Tecfonopkysics, 92, Davis, B. K Regional-scale foliation reactivation and re-use during formation of a macroscopic fold in the Robertson River Metamorphics, north Qucensland, Australia. Tr.tonopk!.sic,.s, 242, Johnson, S. E., 1993a. Unraveling the spirals: a serial thin section study and three-dimensional computer-aided reconstruction of spiral-shaped inclusion trails in garnet porphyroblasts. Jourmil of Mcftrmorphic Gwlogy, 11, Johnson, S. E., 1993b. Testing models for the development of spiral-shapcd inclusion trails in garnet porphyroblasts: to rotate or not to rotate, that is the question. Journul of hfetuwwl phi~ G eologj.. 11, Johnson, S. E. & Bell. T. H., How useful are millipede and other similar porphyroblast microstructures for determining synmctamorphic deformation histories? Jourriul of Meramorplzic~ Geology, 14, Johnson, S. E. & Moore, R. R., Surface reconstruction from parallel serial sections using the program Mathematica: example and source code. Computrrs & Geosciences, 19, Moore, R. R. & Johnson, S. E., Reconstructing inclusion surfaces within metamorphic garnet crystals. The Mtrtherizuticu JOUUIU~. 3, Reinhardt, J. & Rubenach, M. J., Temperature-time relationships across metamorphic zones: evidence from porphyroblast-matrix relationships in progressively deformed metapelitcs. Tectonophysics, 158, Receicerl 28 Jurir 1995: recision ucc,epted 30 July