This paper presents a detailed field characterization of boudinage in a high-strain zone several kilometers wide in Northern China to establish relationships between boudin types and rheological contrasts between different parts of migmatites during the migmatization process. This zone contains nearly all types of boudins: foliation boudins, blocktorn boudins, pinch- and- swell structures, tapering boudins, object boudins, and modified boudins. These boudinage structures record the different stages of melt-involved and solid-state deformation.
The boudinage of migmatites is significantly controlled by the evolving rheological contrasts between the leucosome and melanosome. During the melting stage, the deformation and boudinage of rocks are controlled by the melt fraction. Migmatite strength progressively decreases with increasing melt fraction. The occurrence of melt-filled foliation boudins and melanosome block boudins suggests that the residuum and melanosome are more competent than the leucosome. During solid-state deformation after crystallization, the existence of recrystallized solid-state leucosomes and the intrusion of pegmatites cause the migmatite strength to increase. The relationship is reversed: the leucosome is much more competent than the melanosome. The type and geometry of boudins and pinch- and- swell structures are correlated to the fraction of leucosome in the migmatites. The mechanical strength and strain localization of migmatites after crystallization depend on the presence and volume fraction of the different mineral phases, as well as the mineral grain size. The type and geometry of boudins suggest that the effective viscosity of migmatite can be ranked, from high to low, as: quartz veins; coarse-grained, thick pegmatite; coarse-grained, diatexite migmatite; medium-grained leucosome; and fine-grained melanosome.
While experiencing partial melting and migmatization, a rheologically homogeneous protolith is turned into two dominant lithologic domains: a competent diatexite migmatite domain and an incompetent melanosome migmatite domain. Spatially, with the increasing leucosome fraction in migmatites, the migmatite rheology of rock changes from homogeneous to heterogeneous and anisotropic, and then back to homogeneous. The strain distribution likewise changes from uniform to partitioned, and then back to uniform. This evolutionary process of strength and rheological properties of rocks during migmatization may promote strain localization at mid-crustal conditions.
As the most common product of in situ partial melting of solid rocks, migmatites can help us understand the ways that melts are generated, as well as the subsequent segregation/migration pathways of melts moving between and within different crustal levels (Cavalcante et al., 2016). Critical aspects of these processes of melt generation and migration center around the rheological transitions that occur at the initiation of anatexis. In heterolithic, layered rock masses undergoing anatexis, melting, neocrystallization, and recrystallization are spatially and temporally heterogeneous. This heterogeneity is reflected in the evolving rheological contrasts between different parts of a migmatitic rock and complex strain partitioning that occurs during migmatization. An example of this is the emplacement of leucosomes and pegmatites, which typically causes compositional and grain-size changes that are recorded in banded gneisses. Within these gneisses, the overall structural evolution and coeval spatially and temporally varying modification of rheological contrasts between different parts or layers are well recorded in synmigmatitic boudinage structures (Ghosh and Sengupta, 1999).
Boudinage of outcropscale migmatites has been observed in the Tolstik Peninsula, Russia (Brown, 2001); the southern Eyre Peninsula, South Australia (Pawley et al., 2013); the Aus granulite terrain, southern Namibia (Diener and Fagereng, 2014); the Karakoram Shear Zone, NW India (Weinberg and Mark, 2008); the Chotanagpur Gneissic Complex, East India (Ghosh and Sengupta, 1999; Samanta and Deb, 2014); and the Espinho Branco anatexites of southeastern Brazil (Cavalcante et al., 2016). The common occurrence of boudinage in these and other migmatites indicates that significant strain partitioning commonly occurs during migmatization and suggests that principles established from the study of boudinage (Ramberg, 1955; Sen and Mukherjee, 1975; Mandal et al., 1992, 2000, 2001, 2007; Passchier and Druguet, 2002; Treagus and Lan, 2004; Goscombe et al., 2004; Arslan et al., 2008; Schmalholz et al., 2008; Marques et al., 2012; Abe and Urai, 2012; Samanta and Deb, 2014; Dabrowski and Grasemann, 2014; Duretz and Schmalholz, 2015; Peters et al., 2015, 2016) may be usefully applied to understand the rheological evolution of rocks undergoing anatexis. In general, field observations of migmatites indicate that the melanosome is stronger than the leucosome during progressive anataxis, and that the leucosome becomes more competent than the melanosome once the leucosome has fully crystallized during retrogression (Ghosh and Sengupta, 1999; Diener and Fagereng, 2014; Cavalcante et al., 2016). Experimental investigations of anatexis indicate that the rheological evolution of partially molten rocks and magmas is a function of the proportion and distribution of the melt fraction (Rutter and Neumann, 1995; Rosenberg and Handy, 2005; Vanderhaeghe, 2009). To date, neither experimental nor field investigations have documented the impact of migmatite heterogeneity (in terms of types and composition differences) on the evolution of rheological contrasts and the resulting strain partitioning that occurs during migmatization. Observations of boudins that formed during migmatization may help to fill this gap.
Boudins that form during migmatization are potentially useful strain gauges and rheological indicators (Mandal et al., 2007), because the geometry of boudins is dependent on the competence contrast between the boudinaged layer and the embedding matrix, the flow type, and the amount of layerparallel extension (Ramberg, 1955; Rodrigues and Pamplona, 2018; Dabrowski and Grasemann, 2019). This paper presents a detailed field characterization of boudinage in a deformation zone with a width of several kilometers in Northeast China. The zone contains nearly all types of boudins classified by Goscombe et al. (2004), including foliation boudins, blocktorn boudins, pinch- and- swell structures, tapering boudins, object boudins, and modified boudins. Some of the boudins formed during the melting stage, while some of them developed after crystallization in the solid-state deformation stage. These boudinage structures consequently record the history of melt-involved and solid-state deformation. The differences in their types, geometry, and the locations where they developed may reveal the rheological property differences in different parts of migmatites, as well as the changes in rheology that occur during the migmatization. To test this idea, we quantify the geometry of boudins that occur in this high-strain zone and then use these geometries to establish relationships between boudin types and the rheology of migmatites. Our goal is to use the strain partitioning revealed by boudinage structures to better understand the spatial and temporal evolution of the rheological properties of migmatites during the migmatization process. Of particular interest is the dependence of effective viscosity on the fraction of leucosome in the migmatites.
The basement rocks in the eastern zone of the North China Craton are composed predominantly of Archean gneisses and syntectonic granitoids (Zhao et al., 1998). A wide variety of boudinage and mullion structures (Li et al., 2017; Wan et al., 2020) are present in the Taili syntectonic migmatite deformation zone of North China, one of many high-strain zones located along the northeastern margin of the North China Craton (Fig. 1). We examined several square kilometers of scattered exposures in the Xingcheng-Taili region of the western Liaoning province in northeastern China. Rocks in the study region include rare, mafic lamprophyre dikes, but primarily comprise three distinct granitic units: (1) late Neoarchean gray granitic gneiss (2522 ± 21 Ma, zircon U-Pb; Zheng, 2009), (2) Late Triassic dark biotite adamellite (ca. 220 Ma, zircon U-Pb; Li et al., 2013), and (3) Late Jurassic light granite (ca. 153 Ma, zircon U-Pb; Li et al., 2013). The late Neoarchean granitic gneisses consist of quartz (~20–35%), microcline (~25–40%), plagioclase (~15–35%), and biotite (~5%), with accessory amounts of epidote, zoisite, and magnetite (Cai et al., 2014). The biotite adamellite rocks exhibit a porphyritic texture. The large phenocrysts are composed of alkali feldspar and quartz, whereas the matrix is composed of fine-grained minerals: quartz (~25–35%), microcline (~30–40%), plagioclase (~25–30%), and biotite (~5%), with accessory amounts of zircon, garnet, magnetite, and apatite (Li et al., 2013).
The intrusion of biotite adamellite into the late Neoarchean granitic gneisses caused partial remelting and migmatization at the contact zone. Strong ductile deformation occurred due to the emplacement of Late Triassic granitic magma (Li et al., 2017). In the deformation zone, a dominant foliation is striking NE, with a general trend of 320–345° and dip of 66–88° (Liang et al., 2015a). An ENE-trending sinistral shear zone developed and shows the deformational characteristics of shallow ductile crust, which reflects apparent thinning and decratonization of the North China Craton continental crust (Liang et al., 2015a, 2015b).
FIELD DESCRIPTION AND MEASUREMENT METHOD
Coordinate Frame for Field Description and Measurement
Boudins and pinch- and- swell structures are deformation structures that form in mechanically layered rocks under normal shortening and parallel extension of layers (Ramberg, 1955; Marques et al., 2012). Their three-dimensional shape is rarely well exposed on the outcrops, so key aspects of their geometry usually appear differently and thus yield different measurements in variously oriented, two-dimensional observation planes.
In the study area, the foliations in both the late Neoarchean granitic gneiss and the Late Triassic dark biotite adamellite show almost the same strike and dip: the average strike is 071° and the average dip is 73° (Figs. 2A and 2B). Pegmatite has almost the same consistent attitude (Fig. 2C). The quartz and feldspar grains in gneiss are aligned to form a penetrating mineral lineation, which is parallel to the extension direction of boudinaged layers. All mineral lineations show a very low plunge, ranging from 8° to 18°, with an average of 13° (Fig. 2D).
Mineral lineations and boudin structures suggest a layer-parallel extension in just one direction. The blocked boudins show rodlike geometries in three dimensions, with no shortening or extension along their long axes, which indicates that the finite strain state is plane strain. Kinematic vorticity values from electron-backscatter diffraction (EBSD) and finite strain measurements suggest a general shear-dominant ductile deformation (Liang et al., 2015b). Therefore, quantitative measurements constraining boudin geometries can be obtained and systematically compared if they are collected in the XZ-section of the finite strain ellipsoid.
To systematically describe the deformation characteristics of boudin structures and accurately measure their shapes, all observations need to be made perpendicular or close to perpendicular to the foliation or layering and parallel to the mineral lineation at the field outcrops (Fig. 3). Observation and estimation of the volume of leucosome and melanosome were also performed on this same observation plane. In the observation coordinate frame, the X-axis is parallel to the foliation and mineral lineation, the Y-axis is oriented along the long axes of the boudins and is parallel to the foliation and perpendicular to the mineral lineation, and the Z-axis is perpendicular to the foliation and mineral lineation. The observation plane is on the XZ-plane.
All of the outcrops with the steep foliation and approximately horizontal lineation in the study area are well exposed on the beach, so most observations and measurements can be readily carried out on the defined observation surface. Because the length measurement (Lm) in the direction parallel to the lineation is sensitive to the orientation (α) of the observation plane in which we measured, we made corrections to L in cases where α was greater than 10°. In these cases, the corrected length (L) is given by: L = Lm·cos(α). In the field, whenever possible, we made sure the angle α was less than 10° before choosing a feature to measure. Hence, the error for length-measurement parallel to the lineation direction is limited to ~1%.
Classification and Measuring Method of Boudin Geometry
A great many geological strain and viscosity indicators have been described in detail in the literature (e.g., Ramsay and Huber, 1983; Passchier, 1988; Treagus and Lan, 2004; Passchier and Trouw, 2005; Bürgmann and Dresen, 2008). A variety of relationships between geometry, effective viscosity, and strain of boudins is already inferred from previous field and modeling work (e.g., Ramberg, 1955; Smith, 1975, 1977; Passchier and Druguet, 2002; Goscombe et al., 2004; Treagus and Lan, 2004; Mandal et al., 1992, 2001, 2007; Schmalholz et al., 2008; Marques et al., 2012; Schmalholz and Maeder, 2012; Gardner et al., 2015; Peters et al., 2015, 2016; Samanta et al., 2017; Dabrowski and Grasemann, 2019). Generally, the geometric type of boudinaged structures is largely controlled by the contrast in viscosity between the boudinaged layers and the embedding matrix, the flow type (kinematic vorticity number), the angular relationships between the layer and the deformation (kinematic) axes, and the shear strain (Goldstein, 1988; Abe and Urai, 2012; Rodrigues and Pamplona, 2018). For example, when embedded in an identical matrix, boudin that is angular in shape is mechanically stronger than a lensoid-shaped boudin (Abe and Urai, 2012; Peters et al., 2015, 2016; Samanta et al., 2017). In this same matrix, the most competent layers formed the most rectangular boudins, whereas the less competent layers developed pinch- and- swell structures (Ramberg, 1955).
The wide variety of boudin shapes and styles in the Taili deformation zone provide a unique opportunity to infer how the relative effective viscosity of migmatites varies with different melt or leucosome fractions. In this paper, the geometric description and measurement of boudinage structures are based on the classification of boudin types by Goscombe et al. (2004; Fig. 4):
Foliation boudinage refers to the disruption of foliation planes in a foliated rock devoid of distinct competent layers (Ghosh and Sengupta, 1999; Goscombe et al., 2004) and is also called foliation boudinage structure (Arslan et al., 2008).
A single competent layer embedded in a less competent host forms single-layer, isolated boudins by extension fracturing and forms pinch- and- swell structures by continuous necking without separation (Ramberg, 1955; Smith, 1977; Ghosh and Sengupta, 1999). They are subdivided into torn boudins and drawn boudins by Goscombe et al. (2004). Torn boudins are completely isolated, have sharp inter-boudin surfaces, and experienced apparently “brittle” failure, whereas drawn boudins have no inter-boudin surfaces, are curved in shape, and usually experienced apparent “ductile” stretch of the layer. These can also be called necked boudins, as the boudin blocks are still connected by a neck zone, and tapering boudins, which are either completely isolated or tenuously connected by particularly long and thin necks (Goscombe et al., 2004).
Both isolated boudins and pinch- and- swell structures are well developed in the study area. The pinch- and- swell structures are also called necked boudins and are defined as one type of drawn boudin in the classification by Goscombe et al. (2004). In this paper, to facilitate the use of unified geometric parameters for measurement and comparison, torn and drawn boudins were selected for geometric measurement, and the pinch- and- swell structures were described as one type of drawn boudin.
Shear-band boudins are asymmetric, with rounded rhomb to tapering lens shapes, and typically have relatively high aspect ratios. These are called asymmetric pinch- and- swell structures (Passchier, 1991; Goscombe et al., 2004; Passchier and Trouw, 2005).
Multilayered boudins are the result of boudinage that has occurred in a multilayer as a whole, whereas composite boudins are composed of boudinaged sublayers within a boudinaged packet of layers, which results in nested boudins of different scales (Ghosh and Sengupta, 1999).
Object boudins occur when isolated, competent objects undergo what Goscombe et al. (2004) referred to as “object boudinage.”
Some types of boudins experienced a continued deformation, including progressive, coaxial, layer-parallel extension, sequential shearing, and layer-parallel shortening, to form folded boudins and bone-type boudins, etc., which are called modified boudins by Goscombe et al. (2004), but the mechanism and intensity of the continued deformation varies spatially.
The geometry of a boudin margin can give us important clues about the viscosity contrasts among the boudin, interboudin, and matrix material (Samanta et al., 2017). To estimate the change and evolution of effective viscosity during both the melting deformation stage and the post-crystallization, solid-state deformation stage, we used a series of parameters to quantify and compare the geometry of boudins in the study area (Table 1, Fig. 5). For torn boudins and tapering boudins, Lb and Wb denote the length and thickness of boudin segments, respectively, and Ln denotes the length of the thinned part of the boudins. For the pinch- and- swell structures, Lb and Wb denote the wavelength and maximum thickness, respectively, and Ln denotes the half length of necked zones. The aspect (Rn) and thinning ratios (Rt) of boudin neck zones are indicators of the strain difference and contrast in viscosity between the boudinaged layers and the incompetent host. For torn boudins, when the competence contrast is increasing, the inter-boudin face is straighter. For rectangular boudins with straight inter-boudin faces, the length Ln and width Wn of the boudin neck zone are equal to 0, and the edge angle θ is equal to 90°, which indicates a relatively high competence contrast. For necked boudins, the length of the neck zone Ln is less than half the length of the boudin block, and the thinning ratio of the neck zone is less than 1. This geometry indicates that the boudinaged layer has a relatively higher effective viscosity and has experienced a smaller stretch than the pinch- and- swell structures in which Ln is equal to half the length of the boudin block.
Almost all boudinaged layers are parallel to the foliations and generally show a symmetric geometry in this study area; therefore, the impact of the flow type and the initial orientation of the layers on the geometry of boudinaged structures was not considered in this study.
Field Observation and Volume Proportion Estimate of Migmatites
Throughout this paper, the description of migmatitic rocks and determination of melting stages are based on the book of Sawyer (2008) and guide of Pawley et al. (2013), which provide systematic terminology definitions, a classification scheme, and guidance on relating the transition of stages to critical melt fractions (Fig. 6). Sawyer (2008) and Pawley et al. (2013) report that a migmatite is a rock found in medium- and high-grade metamorphic areas, it can be heterogeneous at the microscopic to macroscopic scale, and it consists of two or more petrographically different parts, which are petrogenetically related to one another, and to their protolith, through partial melting or segregation of the melt from the solid fraction (Sawyer, 2008; Pawley et al., 2013). The palaeosome is the part that was not affected by partial melting, and the neosome comprises the parts that are newly formed by, or reconstituted by, partial melting of the protolith (Sawyer, 2008).
The first-order division of migmatites into meta-texites and diatexites is considered a function of the fraction of melt and the properties of the solid grains in the partially melted rock (Sawyer, 2008). Metatexites are migmatites that preserve coherent, pre-partial melting structures in the palaeosome and residuum. The neosome is generally segregated into leucosome and melanosome. Based on the synanatectic strain, Sawyer (2008) describes four main second-order divisions of metatexite:
Patch metatexite. In the incipient stages of partial melting, melting occurs at discrete sites to form small, scattered patches of non-foliated, in situ neosome.
Dilational metatexite. The leucosomes occur within dilatant sites, such as boudin necks, pressure shadows, or fractures in more competent layers.
Net-structured metatexite. Leucosomes occur in two or more systematic sets that intersect to form a net-like pattern.
Stromatic metatexite. This is composed of numerous thin and laterally continuous bands of leucosomes that are oriented parallel to the major plane of anisotropy in the palaeosome, which are typically layered or occur as a solid-state foliation.
Diatexites are dominated by pervasive neosome and have lost structural coherency. Based on transitional stages, Sawyer (2008) describes four main second order divisions of diatexite: nebulite migmatites, schollen (raft) migmatites, schlieren migmatites, and diatexite migmatites. Diatexite migmatites are gradational from schollen and schlieric migmatites through an increase in melt fraction and from nebulitic migmatites through an increase in synanatectic strain (Sawyer, 2008; Pawley et al., 2013; Fig. 6).
Previous field examples have been used to illustrate that boudinage of mafic layers with melt ponding in the boudin neck and the formation of foliation boudins by melt flow in extensional shear bands occurred during partial melting (e.g., Pawley et al., 2013; Diener and Fagereng, 2014). In contrast, boudinage and folding of leucosomes and pegmatites has been determined to occur during the solid-state deformation stage (Ghosh and Sengupta, 1999; Diener and Fagereng, 2014; Cavalcante et al., 2016). In the field, these relationships helped us distinguish the various generations of boudins and pinch- and- swell structures that formed during different stages.
We use the area ratio of leucosome and melanosome on the observation plane to represent the proportions of their volume. The estimate of area is based on photographs in which the view direction is perpendicular to the defined observation plane. It is assumed that the rock type mainly changes along the observation plane perpendicular to the foliation, and that the spatial distribution and volume of leucosome and melanosome does not change significantly on the plane of foliation.
TYPES AND CHARACTERISTICS OF BOUDINAGE STRUCTURES
A variety of boudinage structures occurs in the syntectonic migmatite deformation zone, including foliation boudins, blocktorn boudins, pinch- and- swell structures, tapering boudins, object boudins, and modified boudins (e.g., folded boudins and bone-type boudins). Some of these boudins formed during the melting stage, while some of them developed in the solid-state deformation stage that followed crystallization.
In the study area, the foliation boudins only occur in the foliated lithologic domains with no competent layers, where the rock does not contain melanosome and leucosome layers with a clear contrast in effective viscosity.
Foliation Boudins in Palaeosome
Melt patches are locally preserved in melanosome and show feathery margins that can be traced into the foliation in the host (Figs. 7A and 7B). Other workers have suggested that these features form during the early stage of partial melting, when the melt is moving along the foliation planes and migrates into dilational, low-pressure sites represented by shear bands (Brown, 2013; Pawley et al., 2013). The shear bands suggest local derivation of the melt, and a weak folding of the foliations often occurs near the shear bands, forming foliation boudins with only faint thinning of the neck zones. The leucocratic melt localized into the dilatational shear zones is incompetent in comparison to the host palaeosome (Figs. 7A and 7B), and foliation boudins that develop in these rocks are typically asymmetric. Melt pools within the dilatational shear zone can fold during continued flattening perpendicular to the foliation (Fig. 7B), while mafic dikes (e.g., lamprophyre) that are more competent than the host palaeosome develop into blocky boudins.
Foliation Boudins in Melanosome
Within the melanosome domain, most of melt has been extracted from its source, and the leucosome volume proportion is generally less than 10 vol%. In these circumstances, there is no distinct competent layer in the melanosome domain, and the competence of the overall rock mass is nearly uniform. Under continued coaxial stretching after crystallization, a pervasive foliation forms. Where the foliated melanosome contains few in situ leucosomes, it is slightly more competent than the whole rock and is deformed into foliation boudins most likely during foliation-parallel stretching (Figs. 7C and 7D).
Foliation boudins in the melanosome are typically asymmetric and contain quartz-filled extension fractures in the neck zones (Figs. 7C and 7D). The foliation is deflected toward these central quartz veins, and compared to the feathery margins of the melt-filled shear bands, these late quartz veins show a sharp margin. These quartz-filled extension fractures in the neck zones are typically perpendicular to the foliations. Both the elongation and thinning are very slight within the neck zones of these boudins, which suggests that ductile thinning within the neck zone stopped when the extension fractures formed and were filled by quartz.
Foliation Boudins in Diatexite Migmatites
Foliation boudins also occurred in the dia-texite migmatite domain, which is composed of quartzofeldspathic gneisses with penetrative foliation (Figs. 7E–7H). Boudinaged gneisses in these domains typically exhibit larger crystal sizes than what is observed in the non-boudinaged gneiss. Quartz-filled, X-type conjugate fractures often occur within the neck zones of these boudins and commonly display sigmoidal or forked geometries. This type of foliation boudin has been called a sigmoidalgash boudin or forkedgash boudin (Goscombe et al., 2004; Arslan, 2008).
In our study area, the stromatic leucosomes and pegmatites within different rock domains show a difference in both the strain and effective viscosity contrast, and therefore they developed into different types of boudins (Fig. 8).
In the study area, torn boudins are observed where thick pegmatites intrude the foliated diatexite migmatite host (Figs. 8A and 8B). The thickness of these boudinaged pegmatites is typically ~5–20 cm, and the torn boudins generally show a straight exterior edge and a convex inter-boudin surface. They also display a relatively narrow neck zone and a long distance between boudin blocks. The enveloping foliation is symmetrically drawn into the inter-boudin zone.
Pinch-and-swell structures (necked boudins): Pegmatites that intrude into the diatexite migmatite domain are generally developed into pinch- and- swell structures. Almost all of them show straight exterior edges and a narrow neck zone (Figs. 8C–8E). At the neck zones of some thick pegmatites, brittle shear fractures occur and are filled by quartz (Figs. 8C and 8D).
Some of the pegmatites intruding into the palaeosome domain experienced a ductile stretch and also developed into pinch- and- swell structures (Fig. 8F). The stromatic leucosomes in the melanosome domain commonly developed into pinch- and- swell structures with a high aspect ratio (Fig. 8G). These pinch- and- swell structures show a convex exterior edge and are still connected by a long and thin neck zone. The average length of neck zones is almost equal to the wavelength of the pinch- and- swell structure.
Tapering boudins: Some thin, intrusive pegmatites in melanosome developed into tapering boudins (Fig. 8H). Stromatic leucosomes in the highly strained melanosome domain have a thickness of ~1–10 cm and generally developed into pinch- and- swell structures and tapering boudins (Figs. 8I–8K). The thick stromatic leucosomes tend to develop into pinch- and- swell structures (Fig. 8I), and the thin ones tend to develop into tapering boudins (Figs. 7J and 7K). These tapering boudins have high aspect ratios, high layer-parallel extension, and boudin isolation. These characteristics suggest that at high strain, the boudin block was flattened concomitant with boudin separation (Goscombe et al., 2004). The tapering boudins are more common in the metatexite domain, which indicates a much higher layer-parallel extension and strain in the metatexite.
Multiple-Layer and Composite Boudins
Some schollen diatexite migmatites show that a blocked boudin shape forms a high order of boudins (Fig. 9A). The pegmatites in these schollen diatexite migmatite boudins were also stretched and developed into pinch- and- swell structures that comprise a sub-order of boudins. In the melanosome domain, both a sequence of pegmatitic and multilayered stromatic leucosomes developed into multilayered (Fig. 9B) or composite boudins (Figs. 9C–9E). The spacing of these multilayers is generally less than 5 cm, and the first-order shape of the composite boudins is that of separated block boudins. The lower-order boudins are generally torn and tapering boudins. For some pegmatite that developed into pinch- and- swell structures, the quartz within it developed into sub-order pinch- and- swell structures, and X-type conjugate fractures often occur in the quartz, which indicate that the quartz shows a higher effective viscosity than pegmatite (Fig. 9F).
In the Taili deformation zone, isolated residuum in the diatexite and melt patches in the melanosome locally developed into object boudins with low aspect ratio during progressive strain.
Residuum Object Boudins
Some patches of residuum from the melting stage were preserved in the diatexite migmatite. These masses show a lenticular shape with low aspect ratio, which indicates that the residuum was more competent than the diatexite migmatite and that the deformation took place at the melting stage. (Fig. 10A). The fact that fractures and quartz veins terminate on the contact boundary between the residuum and diatexite indicates that the residuum was incompetent compared to diatexite during the period in which the rocks were undergoing solidstate deformation (Fig. 10A).
Leucosome Object Boudins
A small number of pegmatites occur in the melanosome as isolated objects and show a porphyroclastic shape (Fig. 10B). The in situ melt patches and pools in these locations have not been extracted from the enveloping rocks, and they are preserved in the foliated melanosome as isolated object boudins with a tapering shape and an aspect ratio that is generally less than 1:3 (Fig. 10C). Some equiaxed felsic objects have a concave margin shape and show a fish-mouth boudin geometry (Fig. 10D). Other felsic objects display straight margins and have secondary quartz filling in an adjacent pressure shadow (Fig. 10E). The thin felsic bands exhibit geometries ranging from those of tapering boudins to object boudins, whereas some of the felsic objects fractured and developed into domino boudin blocks (Fig. 10F). Together, these observations indicate that during the solid-state deformation phase, these in situ leucosome objects were more competent than the melanosome host rock.
Asymmetric Shear-Band Boudins in Diatexite Migmatite
In the Taili deformation zone, shear-band boudins occur within both melanosome and diatexite. Most shearband boudins display an asymmetric shape and a small amount of back rotation relative to the left-lateral shearing (Fig. 11). In the diatexite migmatite domain, the shear-band boudins typically occur together with C′-type shear bands (Fig. 11D). The average angle between the shear plane and the C′-type shear bands is 27 ± 7°. The overall shear-band geometry denotes a bulk layer-parallel extension of the deformation zone as a whole (Passchier, 1991; Passchier and Trouw, 2005).
Some types of boudins experienced continued deformation, including progressive coaxial layer-parallel extension, sequential shearing, and layer-parallel shortening, but the mechanism and intensity of the continued deformation varies spatially.
At the southern margin of the syntectonic migmatite deformation zone, the stromatic leucosomes are parallel to the earlier foliation and developed into tapering boudins in the early layer-parallel extension and then folded under late layer-parallel shortening (Fig. 12A). The pegmatite dikes that intrude into the melanosome experienced later buckle folding under solid-state conditions (Figs. 12A and 12B). Individual boudins within the lamprophyre-separated boudin block train are stacked on top of one another in response to late, layer-parallel shortening (Fig. 12B).
At the center part of the deformation zone, some pegmatites that intrude into the melanosome developed into bone-type boudins due to progressive stretching, and thick layers boudinage more easily than thin layers (Fig. 12C). Quartz filled the inter-boudin zones and brittle fractures that formed under the earlier stretch, and then continued thinning occurred in the center of the boudin blocks. Quartzvein infill in the inter-boudin zone is more competent during the progressive boudinage.
Fractured Pinch-and-Swell Structures
In contrast to the earlier fracturing and late thinning of bone-type boudins, some thick pegmatites in the melanosome experienced early pinch- and- swell boudinage and late brittle fracturing (Figs. 8I and 12D). These pegmatites appear to be more ductile and developed into pinch- and- swell structures during the earlier layer-parallel extension. During progressive stretching, the pegmatites were more brittle and fractured at their neck zones. The fractured inter-boudin zones were incompletely filled by quartz. Meanwhile, the melanosome host remained ductile and flowed into the fractures (Fig. 12D).
Synthetic and Antithetic Shear-Fracture Boudins
MEASURING RESULTS OF BOUDIN GEOMETRY
In this study, 221 sets of geometrical parameters of single-layer boudins were measured either in the field or in photographs (Fig. 13). To compare the geometric properties and interpreted viscosity contrast of boudins in different migmatite domains, the data from single-layer boudins have been classified into four groups: (1) boudinage of medium crystalsized, stromatic leucosomes in melanosome (SLM); (2) boudinage of pegmatite dikes in melanosome (PM); (3) boudinage of pegmatite dikes in diatexite migmatite (PD); and (4) boudinage of pegmatite dikes in palaeosome (PP). All of the data measured are plotted in Figure 13.
The width of pegmatites ranges from 3 cm to 25 cm, and the width of stromatic leucosomes ranges from 0.2 cm to 10 cm. The thinning ratios of neck zones for pegmatites in melanosome, diatexite, and palaeosome are respectively between 0.57–1.0, 0–0.63, and 0.29–1.0. The aspect ratios of neck zones for pegmatites in melanosome, diatexite, and palaeosome are respectively between 0–4.8, 0.2–1.8, and 0.6–2.6. For the boudinaged stromatic leucosomes in melanosome, the thinning ratio and aspect ratio of neck zones are respectively between 0.2–1.0 and 0.87–8.48 (Fig. 13A). In the melanosome domain, the neck zones of stromatic leucosomes show a higher aspect ratio than those of pegmatites with the same thinning ratio. The thinning ratios of neck zones of pegmatites in diatexite migmatites are generally less than 0.64, whereas the thinning ratios in melanosome are generally more than 0.57 (Fig. 13A). The deviation angle, θ, for stromatic leucosomes in melanosome ranges from 1° to 17° (Fig. 13B). The θ for pegmatites in melanosome, diatexite, and palaeosome, respectively, ranges from 6° to 76°, from 0° to 20°, and 8° to 28° (Fig. 13B). The neck length (Ln) of SLM is much higher than that of PM and PD, and the length of SLM is much higher than that of PM, PD, and PP (Fig. 13C). However, both the average thinning ratio, Rn, and average deviation angle, θ, of SLM are less than that of PM (Fig. 13B). Both the average and maximum deviation angle, θ, of PM are much high than those of others. The thinning at the neck zone of pegmatites in the melanosome is much higher than that of diatexite (Fig. 13D).
Strain Partitioning during the Deformation of Migmatites
The composition of rocks in the migmatization deformation zone is highly heterogeneous, and the melt fraction, proportion of leucosome, and grain size all vary among the different lithologic domains (Fig. 14). The rheology and deformation behavior of rocks in the study area are primarily related to the mineral composition (Liang et al., 2015a, 2015b) and the grain sizes of quartz and feldspar (Li et al., 2017). Differences in competency have caused the bulk layerparallel extension deformation of the whole deformation zone to be partitioned into outcropscale zones that accommodated different amounts of strain. Evidence of this is captured in the wide variety of boudins in the Taili deformation zone.
Strain Partitioning between Melanosome and Leucosome
The pegmatites and leucosome layers under solid-state deformation conditions in the melanosome domain generally developed into separated, torn boudins and tapering boudins, whereas the pegmatites in the diatexite migmatite domain developed into pinch- and- swell structures with low thinning ratio neck zones (Figs. 8 and 13). The separated, torn boudins and tapering boudins are rarely found in the diatexite migmatite domain. Those boudins in the melanosome show a high separation distance and a much higher aspect ratio of the neck zone than those exhibited by pinch- and- swell structures in the diatexite migmatite domain. The elongation of pegmatites in metatexite is much higher than that in diatexite. The lower thinning ratios of neck zones of pegmatites in the diatexite domain than that of the metatexite domain may indicate that the pegmatites in diatexite migmatites generally experienced a lower stretch in the diatexite migmatite domain. Furthermore, the foliation in the metatexite is also more intensely developed than that in the diatexite. We interpret these observations as an indication that the bulk stretch in the metatexite domain is much higher than that in the diatexite domain.
Strain Partitioning during Boudinage
The different types of boudins reflect what we interpret as a significant difference in strain partitioning during deformation. The foliation boudins both in the melanosome and diatexite generally have a very narrow neck zone with slight thinning and limited extension that is typically accommodated by brittle fractures filled with quartz (Figs. 7C–7H). Prior to quartz precipitation, the strain within the neck zone was higher than the bulk strain of the foliated melanosome. However, when the fractures in the neck zone were sealed by quartz, the strain within the neck zone became much lower than the bulk strain.
For the pegmatites that deformed into torn boudins, the highest layer-parallel extensional strain is localized within the inter-boudin zone, and the host rocks are preserved flowing into this zone (Figs. 8A and 8B). If the inter-boudin zone is filled with quartz, which usually shows a larger grain size and is more competent (Fig. 8I), the localized strain within the neck zone may become lower than the bulk strain, hence resulting in the formation of bone-type boudins (Fig. 12C). Numerical modeling results (Samanta et al., 2017) also show that the viscosity of inter-boudin material has significant control on the shape of torn boudins, and bone-type boudins develop only when the inter-boudin is more competent than the boudin.
The stromatic leucosomes in melanosome generally developed into tapering boudins. Both the neck zones and boudin blocks of these tapering boudins have the highest aspect ratio of the boudins we analyzed. The higher aspect ratio of stromatic leucosomes indicates that their neck zones experienced a higher and more ductile extension than that of pegmatites. It furthermore indicates that the pegmatite is more competent than stromatic leucosome. Tapering boudins with high aspect ratios suggest that the boudin block is being flattened concomitant with boudin separation (Goscombe et al., 2004). Under the same stretching deformation time frame, these stromatic leucosomes experienced faster thinning than the thick, coarse-grained pegmatites, even though both the stromatic leucosomes and the pegmatites generally behaved as competent layers. Moreover, the strain difference on the contact boundary of tapering boudins composed of leucosome is much lower than that on the contact boundary of torn boudins composed of pegmatite.
Effective Viscosity Contrast of Migmatites
The measurements we collected indicate that the geometry of boudins in migmatites can be an effective estimator of the viscosity contrast of rocks undergoing migmatization. A wide variety of boudins and strain partitioning indicate that the migmatites in the migmatization deformation zone show a significant difference in relative effective viscosity under solid-state deformation conditions (Figs. 15A and 15B). The migamatites are significantly different in composition, grain size, and intensity of foliation development, which leads to competence (viscosity) contrast between different domains (e.g., Liang et al., 2015a; Li et al., 2017). The competence contrast was likely to have been controlled by the composition of the migmatites and consequently changed during the different migmatization stages.
Competency Contrast during Partial Melting
During melting, the strength of rock is significantly controlled by the melt fraction (Vigneresse and Tikoff, 1999; Rosenberg and Handy, 2005; Diener and Fagereng, 2014). In particular, the heterogeneous distribution of melt causes spatial and temporal variations in the competency contrasts between melanosome and leucosome layers (Cavalcante et al., 2016). In addition to the influence of melt distribution, the competence of migmatite is also controlled by the evolution and distribution of mineral composition during the partial melting stage. The mafic rocks are usually considered stronger than felsic rocks (Wilks and Carter, 1990). During partial melting, the melt moves along foliation planes, migrating into coeval shear zones during melting. Melt loss strengthens the remaining bulk rock aggregate (Diener and Fagereng, 2014; Cavalcante et al., 2016). As the melt is progressively extracted from the source, the residuum becomes more and more competent. Meanwhile, mafic dikes, like the lamprophyre seen in the Taili deformation zone, are more competent than the residuum because they have a more mafic mineral composition and a higher melting temperature.
Effective Viscosity Contrast during Solid-State Deformation
The boudinage of migmatites indicates that leucosome is more competent than the melanosome during the solid-state deformation stage that follows complete crystallization. This reversal of competence contrast between the leucosome and melanosome has also been interpreted by field researchers in the Jasidih-Deoghar area of East India (Ghosh and Sengupta, 1999) and the Espinho Branco region of northeastern Brazil (Cavalcante et al., 2016). Combined with this previous work, our observations suggest that migmatites can be subdivided into three rock domains with distinctly different effective viscosity: (1) a competent diatexite migmatite domain, (2) a moderately competent metatexite migmatite domain, and (3) an incompetent melanosome migmatite domain. In the metatexite migmatite domain, the progressive increase of the leucosome fraction will increase the effective viscosity and overall strength of the migmatite.
The boudinage of migmatites is significantly controlled by the competence contrast between the leucosome and melanosome. The neck zones of stromatic leucosomes show a higher aspect ratio, thinning ratio, and length than those of pegmatites (Figs. 13A and 13C), which indicates that the stromatic leucosomes have a relatively lower effective viscosity and more easily develop into tapering boudins (Figs. 8J and 8K), whereas the pegmatites are more competent and develop into torn boudins and pinch- and- swell structures (Figs. 8A–8C). The pegmatites in melanosome show a highest deviation angle and thinning at the neck zone (Figs. 13B and 13D) and a relatively straight inter-boudin face, which indicates that there is a highest viscosity contrast between pegmatite and melanosome.
Based on the type of boudins and our geometric analysis of more than 200 boudins (Fig. 13), we propose the following decreasing effective viscosity sequence for different parts of a migmatitic rock: (1) quartz veins—highest competence (e.g., Figs. 9F and 15D); (2) coarse-grained, thick pegmatite (e.g., Fig. 15C); (3) coarse-grained, diatexite migmatite (granitic gneiss; e.g., Fig. 9A); (4) medium-grained leucosome (e.g., Figs. 9C and 9D); and (5) fine-grained melanosome—lowest competence (e.g., Fig. 9E).
Solid rock rheology varies as a function of a number of constitutive and environmental variables, including mineralogy, fluid content and chemistry, mineral grain size, melt fraction, temperature, pressure, and differential stress conditions (Bürgmann and Dresen, 2008). As noted by Heilbronner and Bruhn (1998) and Bürgmann and Dresen (2008), grain size plays a particularly important role in the rheology of Earth materials. The different minerals influence each other, which controls nucleation and precipitation processes, mass transfer, grain boundary sliding, and grain rotation (Herwegh et al., 2011). Viscous deformation of rock has mainly been described in terms of two mechanisms: grain size–insensitive creep (dislocation creep), and grain size–sensitive creep (diffusion creep and/or grain boundary sliding; Svava Olsen and Kohlstedt, 1985; Poirier, 1985; Fukuda and Okudaira, 2013). These influences are evident in the observation that pegmatite is distinctly more competent than amphibolite (Ghosh and Sengupta, 1999), and that the emplacement of pegmatitic neosome will increase the relative effective viscosity of banded gneisses (Ghosh and Sengupta, 1999). Besides the difference in composition, the difference in the grain size is also the most important distinctive feature for the migmatites. The grain size of the leucosome is significantly greater than that of the protolith, and the grain size of melanosome is less than that of the protolith. As a result, whereas melt fraction controls the strength of rocks during the melting stage, and mineral composition controls the rheology during the solidstate deformation stage, the difference and spatial distribution of grain sizes may exert the greatest influence on rheology during the partial melting stage.
Evolution of Rock Rheology and Boudinage during Migamatization
A number of theoretical and experimental investigations (e.g., Arzi, 1978; Paquet et al., 1981; Rutter and Neumann, 1995; Rushmer, 1996; Bagdassarov and Dorfman, 1998a, 1998b; Mecklenburgh and Rutter, 2003; Rutter et al., 2006; Acosta-Vigil et al., 2006; Mader et al., 2013) have provided insight into the relationship among the strength, viscosity, and melt fraction of partially molten granite. The evolution of rock rheology during migmatization in the study area occurred in a manner that is consistent with these previous studies (e.g., Diener and Fagereng, 2014; Cavalcante et al., 2016). From the start of partial melting to solid-state deformation after complete crystallization, the strength and rheology of the rocks were changing during the entire migmatization process. We propose that this evolution of rock rheology and the corresponding style of boudinage can be subdivided into three stages: (1) melt-assisted deformation stage, (2) solid-state deformation after crystallization, and (3) sequential solid-state deformation (Fig. 16).
Melt-Assisted Deformation Stage
Experimental studies predict a drastic drop in strength at melt volume proportions as low as ~7 vol% (i.e., melt connectivity transition; Rosenberg and Handy, 2005). During earliest melting, the leucosomes exist as in situ, irregular, and discontinuous melt patches with feathered margins. Strain partitioning due to the contrasted rheology of the two phases induces melt segregation (Vigneresse and Tikoff, 1999). As the melt fraction progressively increases, the melt will move along the foliation planes and migrate into the dilatational shear zones. These melt patches connect to form stromata. The foliations and stromatic leucosomes bend into the weak shear zone to form foliation boudins. The connection of leucosome melt patches will decrease rock strength, while the extraction of melt will increase rock strength. The ultimate consequence of significant melt loss in a shearzone setting is to strengthen the bulk rock until a new episode of partial melting again weakens the rocks (Diener and Fagereng, 2014; Cavalcante et al., 2016).
When the melt volume proportion is more than 30 vol% (i.e., solid- to- liquid transition; Rosenberg and Handy 2005), the layer-parallel leucosome and extensional shear bands intersect to form net-structured migmatites in which the solid and interlocking crystalline skeleton has broken down (Arzi, 1978; Rosenberg and Handy, 2005). Once an interconnected melt network is established, deformation is partitioned between the solid and liquid components, resulting in segregation of the viscous phase in rheologically weak layers (Vanderhaeghe, 2009). As the melt fraction continues to increase, the net-structured migmatites will evolve into a schollen diatexite migmatite. Any mafic dikes that are present will deform into separated, torn boudins. The residuum preserved in the diatexite will develop block-boudin geometries. When the melt volume proportion is >50 vol%, the strength of the aggregate is dominated by the melt viscosity (Renner et al., 2000). A viscous, suspending silicate melt can be treated as a Newtonian liquid at a low strain rate and transition to non-Newtonian at conditions of high stress and strain rate (Cordonnier et al., 2012; Mader et al., 2013). During the melting stage, the deformation and boudinage of rocks is controlled by the melting temperature of the rock type and the melt fraction.
Solid-State Deformation Stage after Crystallization
In the metatexite domain, where the volume proportion of leucosome is less than 10 vol% because most of the melt will have been extracted out of the source, there is no distinct competent layer in the melanosome domain, and the competence of the bulk rock is nearly homogeneous. In our field area, the foliated melanosome containing few in situ leucosomes showed a relatively higher competence than the whole rock and developed into foliation boudins under foliation-parallel stretch. Extension fractures occurred in the neck zones of these boudins and were filled by quartz. In the metatexite domain, where the leucosome volume proportion is ~10–30 vol%, in situ melt patches or pools that have been preserved in melanosome developed into object boudins. Where the leucosome volume proportion is more than 30 vol%, the formation of numerous stromatic leucosomes and pegmatites leads to the wellknown, highly heterogeneous rheology of migmatites and is recorded by the formation of single-layer boudins. With a continued increase in the leucosome fraction, a pack of stromatic leucosomes and pegmatites with small spacing developed into multilayered or composite boudins as a whole.
In the diatexite migmatite domain, the rock is dominated by leucosomes, and the rheology of the bulk rock becomes nearly homogeneous. Foliation boudins dominate these gneisses, X-type conjugate fractures are common within the boudin neck zones, and many of these are filled by quartz to form sigmoidal-gash or forked-gash boudins. The type and geometry of boudins are strongly correlated with the volume proportions of leucosome in the migmatites (Table 2, Fig. 17). As the leuco-some fraction in migmatites increases, the strength of rock progressively increases, and the rheology evolves from homogeneous to heterogeneous, and then back to homogeneous again. The strain is initially uniform throughout the bulk rock, but as the rock becomes compositionally and rheologically segregated, strain begins to vary among the different rock components. Eventually, these different, partitioned strains revert to uniform. The grain size is highly sensitive to boudinage and strain localization in migmatites, which indicates that the boudinage of migmatites occurred during solid-state deformation conditions just after full crystallization.
Sequential Solid-State Deformation Stage
During post-boudinage deformation, decreasing temperature and pressure cause migmatites to become more competent. Brittle deformation can occur in the competent layers (Figs. 15C and 15D), and the quartz infill in the brittle fractures locally increases effective viscosity and affects the continued deformation of the boudins.
Implications for the Geodynamics of the Mid-Crust
The presence of substantial migmatite terrains indicates that during synorogenic, partial melting of continental crust, or during post-orogenic mafic underplating, 40 vol% or more of the lower crust may be partially molten (Mecklenburgh and Rutter, 2003). Melting in the crust causes a drastic weakening at depth on the scale of an orogeny (Vanderhaeghe and Teyssier, 2001; Mecklenburgh and Rutter, 2003; Rosenberg and Handy, 2005; Vanderhaeghe, 2009; Jamieson et al., 2011; Zheng et al., 2011), creates a viscous anisotropy (Qi et al., 2015), and perhaps facilitates effective mechanical decoupling of the crust and mantle (Rosenberg and Handy, 2005). Shearing in lithospheric faults may induce partial melting in the lower crust through shear heating of the upper mantle, and this is an important factor that controls the mechanical response of continental plates in collisional environments (Tommasi et al., 1994).
The presence of melt promotes rock weakening, whereas efficient melt extraction is likely to strengthen the bulk rock (Cavalcante et al., 2016). The competency contrasts between migmatite layers documented in this study illustrate the stages of rheological weakening/strengthening that are likely to occur during orogenic evolution (Cavalcante et al., 2016) and suggest that the flow behavior of the middle continental crust should not be considered as exclusively viscous (e.g., Mancktelow, 2006). Anatexis can create extensive petrological diversity from a uniform granodiorite protolith and cause crustal reworking (e.g., the Kinawa migmatite in a regional-scale shear zone, Campo Belo Meta morphic Complex, Brazil; Carvalho et al., 2016). Partial melting and migmatization may enhance the heterogeneous rheological properties of the mid-crust and may induce large-scale boudinage. During partial melting and migmatization, a protolith with a relatively homogeneous rheology can be transformed into different lithologic domains with dramatically different effective viscosities, a process that almost certainly promotes strain localization at midcrustal conditions.
Field and geometric analysis of more than 200 boudinage structures in the Taili syntectonic migmatite deformation zone enabled us to interpret relationships between rheology, competence contrast, and boudin shape during migmatization.
Foliation boudins occur in the foliated melanosome and diatexite migmatite domains. Object boudins, torn boudins, pinch- and- swell structures, and tapering boudins generally occur in the metatexite migmatite domain. The type and geometry of boudins is correlated to the fraction of leucosome in the migmatites.
The boudinage of migmatites is significantly controlled by the evolving contrast in competence between the leucosome and melanosome. The type and geometry of boudins suggest that the effective viscosity of migmatite can be ranked from high to low as: quartz vein (highest effective viscosity); thick, coarse-grained pegmatite; coarse-grained, diatexite migmatite (granitic gneiss); medium-grained leucosome; and fine-grained melanosome (lowest effective viscosity).
While experiencing partial melting and migmatization, a protolith with homogeneous rheology turned into two dominant lithologic domains: a competent diatexite migmatite domain and an incompetent melanosome migmatite domain. The melanosome domain shows a much higher strain than the diatexite domain during the same deformation event.
During the melting stage, the residuum and melanosome are more competent than the leucosome. The effective viscosity of these rocks is dependent on the mineral composition, with the most mafic rocks showing the highest effective viscosity. The deformation and boudinage of rocks is controlled by the melting temperature of rock type and the melt fraction. During solid-state deformation after crystallization, the competence contrast is reversed: the leucosome is much more competent than the melanosome. The effective viscosity of migmatites is also highly dependent on the mineral grain size. The fine-grained melanosome shows the lowest effective viscosity, while the coarse-grained veins of pegmatite show the highest effective viscosity.
During the melting stage, rock strength is drastically weakened by melt. The rock strength progressively decreases as the melt fraction increases, whereas during the solid-state deformation stage, the existence of leucosomes and intrusion of pegmatites strengthens the migmatites.
The authors thank Mark P. Fischer for revising the content and proofreading the text of drafts of this paper. The very constructive reviews of Fernando Ornelas Marques and anonymous reviewers helped to improve the manuscript significantly. This work was supported by the National Nature Science Foundation of China [grant nos. 41402173 and 41230206], Taishan Scholars (ts20190918). This work has been also supported by the China Scholarship Council, which facilitated Z. Li’s status as a visiting scholar at Northern Illinois University.