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Determining glacier flow direction from till fabrics
Determining glacier flow direction from till fabrics Neal R. Iverson PII: DOI: Reference:
S0169-555X(17)30429-4 doi:10.1016/j.geomorph.2017.10.005 GEOMOR 6191
To appear in:
Geomorphology
Received date: Revised date: Accepted date:
17 July 2017 5 October 2017 5 October 2017
Please cite this article as: Iverson, Neal R., Determining glacier flow direction from till fabrics, Geomorphology (2017), doi:10.1016/j.geomorph.2017.10.005
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Determining glacier flow direction from till fabrics
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Neal R. Iverson*, Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa, USA.
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*Tel: +1 515 294 8048; [email protected]
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ACCEPTED MANUSCRIPT Abstract Field and experimental data indicate that fabrics of sheared basal tills, based on particle
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orientations and on anisotropy of magnetic susceptibility, are inclined relative to the macroscopic
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plane of shear. As a result, if this plane is tilted with a transverse component, one of the longest-
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standing axioms of glacial geology—that particles in basal till are preferentially oriented parallel to the direction of shear—is not strictly true. The resultant correction to the shearing direction
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increases with the transverse and longitudinal components of shear-plane inclination and with the
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magnitude of the fabric inclination relative to the shear plane. Azimuthal corrections calculated herein range from being negligible to a few tens of degrees for reasonable ranges of shear-plane
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tilt. The past success of fabric azimuths as indicators of flow direction, despite the absence of
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this correction, likely reflects the clustering of shear planes about the horizontal in basal tills. However, on the flanks of accreting subglacial bedforms, shear-plane attitudes may well conform
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to the local bedform slope. As illustrated with hypothetical fabrics of drumlins and flutes, azimuthal corrections can in that case be sufficiently large and systematic to seriously affect interpretations of bedform genesis. Keywords: glacier; till fabric; drumlin; flute 1.0 Introduction Fabrics derived from the preferred orientations of particles in till have long played a central role in efforts to infer till genesis and the origins of glacial landforms. No aspect of till fabric interpretation is more venerable than the maxim that particle long axes develop preferred orientations parallel to the local direction of glacier flow (e.g., Miller, 1884; Bell, 1888; Richter, 1936; Holmes, 1941). However, this maxim is correct only if macroscopic planes of shear are
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ACCEPTED MANUSCRIPT horizontal. Herein, I calculate corrections to the shearing direction for reasonable ranges of shear-plane tilt. For some situations the correction is not important. However, as will be
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discussed, in studies of subglacial bedforms, the correction can significantly alter interpretations
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of landform genesis.
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2. Background
Although secondary particle fabric modes oriented perpendicular to flow have commonly been
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observed (e.g., Holmes, 1941; Evenson, 1971; Carr and Rose, 2003), overwhelming
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observational evidence indicates that the dominant fabric mode tends to lie parallel to independent indicators of flow direction (e.g., Benn and Evans, 2010). Fabrics that develop in
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tills deposited at glacier beds tend to be especially strong (i.e., highly clustered orientation
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distributions), owing to shear strain in some combination of the ice and till bed that results from
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basal slip. Importantly, field-based interpretations of the origins of subglacial landforms— particularly, streamlined landforms such as drumlins and flutes—commonly depend on vectors of local shear provided by till fabrics (e.g., Evenson, 1971; Boulton, 1976; Krüger and Thomsen, 1984; Stanford and Mickelson, 1985; Rose, 1989; Gordon et al., 1992; Benn, 1994; Hart, 1997; Glasser and Hambrey, 2001; Johnson et al., 2010; McCracken et al., 2016). In the 1950s a second aspect of till fabric began to be commonly described: the tendency for particles to plunge upglacier in basal tills. In describing the fabric of a basal till in Ontario, Dreimanis and Reavely (1953) alluded to the tendency for upglacier plunges. Harrison (1957), Wright (1957), and Gravenor and Meneley (1958) found that most particles, including sand-sized grains in the latter two studies, plunged upglacier, commonly more than 20º, in basal tills of the Laurentide ice sheet. Many other studies subsequently demonstrated the tendency for particles to plunge upglacier (e.g., Andrews and King, 1968; Boulton, 1970; Evenson, 1971; Linebeck, 3
ACCEPTED MANUSCRIPT 1971; Mickelson, 1973; Drake, 1974; Mills, 1977), leading Drake (1977) to comment that such ‘imbrication’ is ‘traditionally’ accepted as an indicator of the direction from which the ice
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flowed.
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Most subsequent field measurements indeed indicate that long axes of particles generally
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cluster around orientations that plunge upglacier. These measurements include field studies that use the anisotropy of magnetic susceptibility (AMS) of intact till specimens to infer the preferred
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orientations of magnetic grains. For such grains, the orientation of maximum anisotropy, k1, is
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coincident with the orientation of clustering of grain long axes (e.g., Fuller, 1962), provided that magnetic particles have so-called shape anisotropy (Tarling and Hrouda, 1993). Field studies of
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AMS-based fabrics from basal tills indicate that k1 fabrics tend to plunge upglacier (Stupavsky et
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al., 1974; Stewart et al., 1988; Shumway and Iverson, 2009; Thomason and Iverson, 2009; Gentoso et al., 2011; Vreeland et al., 2015; Hopkins et al., 2016a,b; McCracken et al., 2016).
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This observation is significant because AMS fabric measurements have less random error than traditional particle fabric measurements and none of the particle-sampling subjectivity that can lead to systematic error (Iverson et al., 2008). These observations also demonstrate that, even for the silt-sized grains that commonly control the magnetic signal (e.g., Hooyer et al., 2008), upglacier plunge is dominant. Although early observations of plunging fabrics prompted the hypothesis that compressive longitudinal strain superimposed on simple shear caused upward flow (e.g., Harrison, 1957; Wright, 1957), laboratory experiments in which tills have been subjected to only simple shear and studies of similarly inclined fabrics in fault gouge indicate that no compressive strain is necessary. The upward plunge of particles is a natural consequence of horizontally directed simple shear. Ring-shear experiments on five basal tills indicate that once a sufficient shear 4
ACCEPTED MANUSCRIPT strain (~10) is achieved, fabrics based either directly or indirectly (i.e., AMS) on particle long axes strongly cluster, align parallel to shear, and plunge upglacier 5-30º with respect to the shear
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plane (Fig. 1) (Hooyer and Iverson, 2000; Thomason and Iverson, 2006; Hooyer et al., 2008;
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Iverson et al., 2008; Shumway and Iverson, 2009; Vreeland et al., 2015; McCracken et al., 2016). The tills studied have a wide range of textures, with particle sizes used to compute
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fabrics that include fine gravel, sand, and silt (i.e., AMS). These experimental results agree with
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the aforementioned field observations and also with field studies of grain orientations in fault gouge that have, like many tills, matrix material consisting of silt and clay. Cladouhos (1999a)
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found that larger ‘survivor’ grains in such gouge tend to plunge upflow, on average, 25º relative to the macroscopic plane of shear, as provided by the orientations of adjacent wall rocks. Such
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grains help form the inclined P-foliation commonly described in fault gouges by structural geologists (Logan et al., 1979; Rutter et al., 1986). Similarly inclined surfaces have been
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described in basal till, in association with upglacier plunging particles (Boulton, 1970). The inclination of particles relative to the macroscopic plane of shear likely results from displacements along Riedel shears that are inclined systematically to the shear plane (Cladouhos, 1999b; Thomason and Iverson, 2006). This explanation, which requires shear of till beneath the glacier sole, is sufficient to explain most upglacier plunging fabrics of basal tills because, even if most sediment transport has not been by bed shear, it nevertheless accompanies the final lodgment of debris from ice (Boulton et al., 1974; Tulaczyk, 1999; Larsen et al., 2004; Piotrowski et al., 2004). An exception, when bed shear does not accompany deposition, are basal meltout tills that inherit particle fabrics during deposition from stagnant basal ice (e.g., Ham and Mickelson, 1994). Interestingly, however, particle (e.g., Lawson, 1979) and AMS-based fabrics (Fleming et al., 2013) measured in ice exhibit the same tendency for upglacier plunging particles,
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ACCEPTED MANUSCRIPT so the result would seemingly be the same as that for deposition during basal slip: fabrics have preferred orientations that plunge upglacier.
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The inclination of till fabrics within the basal shear zones of glaciers has an important
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implication: if there is any lateral component of shear-plane dip, the azimuth of shear is different
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from that of the particle fabric (Fig. 2). The resultant azimuthal correction increases with the
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lateral and longitudinal components of the shear-plane inclination, as described hereinafter. 3. Analysis and results
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If shear planes within till are horizontal, then the V1 eigenvector computed from the clustering of particle long axes (Mark, 1973) indeed plunges in a direction opposite of the local
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azimuth of shear and hence indicates the local direction of basal slip (Fig. 1). The more general
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case, however, is that shear planes are not horizontal. The commonly patchy nature of shear
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deformation in a till bed (e.g., Fischer and Clarke, 1997; Piotrowski et al., 2004) can cause inclined shear planes, as indicated by AMS fabric studies of flat-lying tills that allow shear-plane attitudes to be determined from orientations of the three principal susceptibilities (Figs. 1B, C) (e.g., Shumway and Iverson, 2009). More predictably, bedforms that develop subglacially may promote deformation along shear planes with attitudes that conform to the local bedform slope. In either case, fabric and shearing azimuths will not be parallel, owing to the angle between the shear plane and fabric orientation, defined within the inclined plane of the velocity gradient (Fig. 2). For the special case of a perfectly horizontal shear plane, is the fabric plunge (Figs. 1A, B). To correct the fabric azimuth as a function of the shear-plane attitude, consider a shear plane inclined at angles and measured in planes transverse (yz) and parallel (xz) to the flow direction respectively (Fig. 2). These angles, rather than a single strike and dip, are considered to 6
ACCEPTED MANUSCRIPT isolate the different effects of shear-plane inclination relative to the flow direction. Long axes of particles that have become preferentially aligned during simple shear cluster around the V1
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eigenvector f (Fig. 2). If coordinates xʹ, yʹ, and zʹ are defined referenced to the attitude of the
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cos f 0 sin
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shear plane (Fig. 2), then
(1)
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Note that yʹ = 0, so that the fabric azimuth in this coordinate system is zero and that is a
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negative angle, given that the right-handed coordinates and angles are measured counterclockwise.
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A convenient way to determine the azimuth and plunge of the shearing orientation from f is
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to rotate the shear plane to horizontal through the positive angles and in the yz and xz planes
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(Fig. 2). A complication, however, is that the rotation through will change the angle . Thus, ~
the rotation about the x axis must be adjusted to a value that provides the value of
commensurate with a horizontal shear plane. The rotation matrices (Tuma, 1979, p. 61) are, ~
thus, Rx( ) and Ry():
0 1 ~ Rx ( ) 0 cos ~ 0 sin
sin ~ cos
(2)
cos R y ( ) 0 sin
0 sin 1 0 0 cos
(3)
~
0
~
where the subscripts denote counterclockwise (i.e., right-hand rule) rotations about the respective axes. Multiplying the right-hand sides of Eqs. (1) and (2) and the result by the right-hand side of 7
ACCEPTED MANUSCRIPT Equation (3) results in a new vector s referenced to x, y, and z and parallel to the shearing direction (Fig. 2):
(4)
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cos cos sin cos ~ sin ~ s sin sin ~ sin cos cos cos sin
~
~
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Trigonometric relationships in the yz and xz planes provide the value of in terms of and : tan cos
tan 1
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(5)
The vector s can also be expressed in terms of its azimuth and plunge defined relative to the
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x, y, and z axes:
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cos cos s cos sin sin
(6)
Substituting Eq. (5) into Eq. (4) and equating the right-hand sides of Eqs. (4) and (6) along y and z respectively yield
tan sin sin tan 1 cos cos
sin 1
(7)
tan cos
sin 1 sin cos cos sin cos tan 1
(8)
Substitution of the right-hand side of Eq. (8) into Eq. (7) allows to be determined as a function of the shear plane attitude (and and the angle This azimuth points opposite that of the true shearing direction and is equal to the desired azimuthal correction Fig. 2).
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ACCEPTED MANUSCRIPT Over some ranges of reasonable parameter space the correction is large (e.g., > 5°) (Fig. 3). As noted, experimentally determined values of are 5-30° for various tills (Hooyer and Iverson,
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2000; Thomason and Iverson, 2006; Hooyer et al., 2008; Iverson et al., 2008; Shumway and
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Iverson, 2009), and field studies of gouge (Cladouhos, 1999a) and basal till (Harrison, 1957; Wright, 1957; Gravenor and Meneley, 1958) can indicate values >20°; values of 15° and 30° are
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considered in Fig. 3. Values of are sensitive to the transverse component of shear-plane
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inclination and are 0-16° for = 0-30° and = 0. Sensitivity to increases if shear planes also
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are inclined longitudinally; for = 0-30°, values of are up to 70% larger. Steeply inclined shear planes (= 30-50°) have corrections of 11-51°.
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4. Implications
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The inclination of particle fabrics relative to the macroscopic plane of shear and the
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associated correction required to determine flow direction from fabric azimuth highlights the need to measure shear-plane orientations independently. In principle, observations of basal-till micromorphology could allow shear-plane orientations to be measured. For example, a sufficient number of orthogonal thin sections of till that display Riedel shears (e.g., Tchalenko, 1970) could allow the macroscopic sense and plane of shear to be determined. Alternatively, focusing on the orientations of the A-B planes of particles (Benn, 1995; Evans and Hiemstra, 2005; Li et al., 2006; Evans et al., 2007) could help resolve shear-plane orientations. A laboratory-tested and less labor-intensive alternative is to use AMS-based fabrics to determine shear-plane orientation. As noted, shear of basal tills in experiments indicates that shear-plane attitudes are fully described by clustered orientations of maximum susceptibility k1 that lie at an angle to the shear plane and of intermediate susceptibility k2 that lie in the shear plane and perpendicular to
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ACCEPTED MANUSCRIPT the flow direction (Fig. 1B). Thus, AMS fabrics provide shear-plane attitudes so that fabric azimuths can be readily corrected to obtain shearing azimuths (Shumway and Iverson, 2009;
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Vreeland et al., 2015; McCracken et al., 2016). Importantly, however, applying the correction using AMS or any other method that yields shear-plane attitude requires also knowing the angle
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. This angle is best determined by shearing the till of interest in experiments in which the macroscopic plane of shear is horizontal and by measuring the fabric plunge (e.g., Shumway and
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Iverson, 2009; Vreeland et al., 2015).
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On the other hand, many decades of experience with clast fabrics indicate that they consistently provide a good indication of flow direction without any correction. This success
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likely reflects that strain in basal tills tends to be dominated by simple shear and directed along
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shear planes that cluster about the horizontal. Even where AMS fabrics indicate that many shear planes in flat-lying tills are inclined, the mean trend of such fabrics—if many fabrics are
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measured across sufficiently large distances—tends to be parallel to the flow direction, (e.g., Shumway and Iverson, 2009). Thus, for flat-lying basal tills where the goal is to infer regional flow direction, not correcting fabric data for the shear-plane attitude likely carries only a mild penalty: increased variability among the trends of multiple fabrics. The penalty can be substantially larger, however, in studies of some subglacial bedforms. In the case of those that may evolve through accretion of till on the bed, a reasonable expectation is that bed shear occurs along planes with attitudes that are related to the local slope of the bedform. In that case neglecting azimuthal corrections can lead to incorrect interpretations. Hypothetical fabrics of drumlins and flutes help illustrate this point. In the drumlins of Fig. 4, correcting the fabric azimuth eliminates evidence of till deposition during drumlin growth. The upglacier quadrant of the drumlin defined as ‘steep’ in the figure 10
ACCEPTED MANUSCRIPT reflects the largest relief-to-width ratios reported for large populations of drumlins in Britain (Spagnola et al., 2012) and North America (Mills, 1980), and the upglacier quadrant of the
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drumlin defined as ‘common, reflects ratios close to the middle of those populations. For these
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cases and the two values of considered in Fig. 3, azimuths were corrected by assuming that
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shear planes had attitudes tangent to the local drumlin slope. Fabric azimuths were chosen (associated apparent flow direction shown with green vectors) to illustrate flow divergence
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around the heads of drumlins. Such divergence is usually taken as evidence of till accretion during drumlin formation (e.g., Walker, 1973; Krüger and Thomsen, 1984; Hart, 1997;
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McCracken et al., 2016), whereas lack of flow divergence leaves open the possibility that till layers were deposited prior to drumlinization, with drumlin relief caused by erosion. Corrected
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flow directions (red vectors) are uniformly parallel to the drumlin long axes. Thus, accounting for inclined shear planes in this case erases apparent evidence that till deposition accompanied
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drumlin growth.
A similar potential problem arises in considering till fabrics of flutes—one of the principal criteria used to infer flute genesis. Sections of flutes defined as ‘steep’ and ‘common’ are depicted in Fig. 5, with lateral slope choices based on the distribution of the height-to-width ratios of the population of flutes described by Gordon et al. (1992). Consider hypothetical particle fabrics measured along the flanks of such flutes that indicate apparent ice flow parallel to their long axes (Fig. 5, green vectors), with seemingly no inward ice flow. Such flow azimuths would seem to refute a leading model of flute formation proposed by Benn (1994) (see also Boulton, 1976). In this model, cavity formation is invoked in the lee of an obstruction (e.g., a lodged boulder), and weak till of the bed shears inward and upward into the cavity. Flutes extend downglacier as the cavity and deposition within it propagate downstream. Shear planes are 11
ACCEPTED MANUSCRIPT expected to be inclined upglacier, consistent with upwardly directed shear, and inclined laterally at an angle comparable to the local transverse slope of the flute. Making these assumptions (blue
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arrows are normal to assumed shear planes) and correcting fabric azimuths on that basis yield inward flow azimuths that converge on the long axes of the flutes (red vectors). The corrected
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data, therefore, provide support for the inward flow of Benn’s model that is lacking if the data
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are not corrected.
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How should the azimuthal dependence on shear-plane attitude be handled in the common
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situation when particle fabrics are measured, but shear-plane orientations are unknown? In the case of a flat-lying basal till, the dependence simply needs to be acknowledged as a potential
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source of variability among fabric azimuths—one that can be considered in addition to
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variability that results from measurement error and human subjectivity (e.g., Drake, 1977; Benn and Ringrose, 2001). In the case of subglacial bedforms, a reasonable approach would be to
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consider uncorrected fabric azimuths and those corrected by assuming that shear planes were parallel to the local slope of the bedform (e.g., Fig. 4). This approach, although not really bracketing the real uncertainty, would at least highlight a greater fraction of it and could thus inhibit overzealous interpretations. Alternatively, shear-plane attitudes consistent with a particular model of bedform genesis could be used to correct fabric data (e.g., Fig. 5) and thereby encourage targeted and more accurate hypothesis testing. Many field studies of sheared till will have no experimental control on the value of . A possible approach to measuring this angle would be to determine shear-plane orientations from field data independently, using orientations of Reidel shears, and to then use fabric orientations to determine the value of . Alternatively, if cannot be estimated from field data, efforts to infer local flow direction form fabrics should acknowledge the potential variability of by 12
ACCEPTED MANUSCRIPT considering values bracketed by experimental studies (5-30°) and tailoring interpretations accordingly. Unfortunately, ring-shear experiments, to date, have been conducted on too few tills
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and with insufficient redundancy to provide more specific guidance. Additional experiments
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could yield useful dependencies of on till texture or on the sizes of fabric-forming particles.
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5. Conclusions
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Particle and AMS fabrics of tills developed in shear at glacier beds indicate the direction of glacier flow only for the special case in which the macroscopic plane of shear is horizontal.
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Otherwise, if there is any transverse component of shear-plane inclination, the upglacier inclination of particle fabrics relative to the shear plane requires that the fabric azimuth be
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corrected. For reasonable ranges of shear-plane attitude, corrections can range from being
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negligibly small to a few tens of degrees and are significantly larger if shear planes are inclined
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laterally and longitudinally. Shear-plane orientations determined from AMS-based fabrics allow the correction to be made if the value of is known from experiments in which the relevant till has been sheared. In a flat-lying till, with shear planes that likely cluster about the horizontal, the dependence of fabric azimuth on shear-plane attitude will add azimuthal variability among fabrics but should not influence regional fabric trends. In contrast, flow directions inferred from fabrics measured along the slopes of subglacial bedforms, such as drumlins and flutes, can be subject to systematic corrections that seriously alter interpretations. In the absence of independently determined shear-plane attitudes, corrections can be imposed using the local slopes of bedforms or models as predictors of shear-plane attitude. If the value of is not known, then interpretations of local flow directions from till fabrics should consider the full experimental range of measured in tills and relax interpretations on that basis.
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ACCEPTED MANUSCRIPT Acknowledgements J.K. Iverson and three anonymous reviewers provided helpful suggestions. This work was
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supported, in part, by the U.S. National Science Foundation (grant EAR-1225812).
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Krüger, J., Thomsen, H.H., 1984. Morphology, stratigraphy, and genesis of small drumlins in front of the glacier Mýrdalsjökull, south Iceland. J. Glaciol. 30, 94–105. Larsen, N.K., Piotrowski, J.A., Kronborg, C., 2004. A mulitproxy study of a basal till: a timetransgressive accretion and deformation hypothesis. J. Quat. Sci. 19(1), 9-21. Lawson, D.E., 1979. A comparison of the pebble orientation in ice and deposits of the Matanuska Glacier, Alaska. J. Geol. 87, 629-645. Li, D., Yi, C., Ma, B., Wang, P., Ma, C. and Cheng, G., 2006. Fabric analysis of till clasts in the upper Urumqi River, Tian Shan, China. Quat. Int. 154-155, 19-25. Linebeck, J.A., 1971. Pebble orientation and ice movement in south-central Illinois. In: Goldthwait, R.P. (Ed.), Till, a Symposium. Ohio State University Press, Columbus, Ohio, 328-334.
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ACCEPTED MANUSCRIPT Logan, J.M., Friedman, M. Higgs, N. Dengo, C. Shimamoto, T., 1979. Experimental studies of simulated gouge and their application to studies of natural fault zones. In: Proceedings of
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Conference VIII on Analysis of Actual Fault Zones on Bedrock. U.S. Geological Survey
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Open-File Report 79-1239.
Mark, D.M., 1973. Analysis of axial orientation data, including till fabrics. Geol. Soc. Amer.
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Bull. 84, 1369-1374.
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McCracken, R.G., Iverson, N.R., Benediktsson, Í.Ö., Schomacker, A., Zoet, L.K., Johnson, M.D., Hooyer, T.S., and Ingolfsson, Ó., 2016. Origin of the active drumlin field at
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Múlajökull, Iceland: New insights from till shear and consolidation patterns, Quat. Sci. Rev. 148, 243-260.
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Mickelson, D.M., 1973. Nature and rate of basal till deposition in a stagnating ice mass, Burroughs Glacier, Alaska. Arc. Alp. Res. 5, 17-27.
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Miller, H., 1884. On boulder-glaciation. Pr. Roy. Phys. Soc. Edinburgh 8, 156-189. Mills, H.H., 1977. Basal till fabrics of modern Alpine glaciers. Geol. Soc. Am. Bull. 88, 824828.
Mills, H.H., 1980. An analysis of drumlin form in the northeastern and north-central United States: summary. Geol. Soc. Am. Bull. 91, 2214-2289. Piotrowski, J.A., Larsen, N.J., Junge, F.W., 2004. Reflections on soft subglacial beds as a mosaic of deforming and stable spots. Quat. Sci. Rev. 23, 993-1000. Richter, K., 1936. Gefügestudian im Engebrae, Fondalsbrae, und ihre Vorlandsedimenten. Zeitschrift f. Gletscherkunde 24, 22-30. Rose, J., 1989. Glacier stress patterns and sediment transfer associated with the formation of superimposed flutes. Sed. Geol. 62, 151-176.
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ACCEPTED MANUSCRIPT Rutter, E.H., Maddock, R.H., Hall, S.H., and White, S.H., 1986. Comparative microstructures of natural and experimentally produced clay bearing fault gouges: Pure App. Geophys. 124, 3-
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39.
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Shumway, J.R., Iverson, N.R., 2009. Magnetic fabrics of the Douglas Till of the Superior lobe: exploring bed-deformation kinematics. Quat. Sci. Rev. 28, 107-119.
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Spagnola, M., Clark, C.D., Hughes, A.L.C., 2012. Drumlin relief. Geomorph. 153-154, 179-191.
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Stanford, S.D., Mickelson, D.M., 1985. Till fabric and deformational structures in drumlins near Waukesha, Wisconsin, U.S.A. J. Glaciol. 31, 220-228.
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Stewart, R.A., Bryant, D., Sweat, M.J., 1988. Nature and origin of corrugated ground moraine of the Des Moines Lobe, Story County, Iowa. Geomorph. 1, 111-130.
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Stupavsky, M., Symons, D.T.A., Gravenor, C.P., 1974. Paleomagnetism of the Port Stanley till, Ontario. Geol. Soc. Am. Bull. 85, 141-144.
London.
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Tarling, D.H., Hrouda, F., 1993. The Magnetic Anisotropy of Rocks. Chapman and Hall,
Tchalenko, J.S., 1970. Similarities between shear zones of different magnitudes. Geol. Soc. Am. Bull. 81, 1625-1640.
Thomason, J.F., Iverson, N.R., 2006. Microfabric and microshear evolution in deformed till. Quat. Sci. Rev. 25, 1027-1038. Thomason, J.F., Iverson, N.R., 2009. Deformation of the Batestown Till of the Lake Michigan Lobe. J. Glaciol. 55, 131-146. Tulaczyk, S. 1999. Ice sliding over weak, fine-grained tills: dependence of ice-till interactions on till granulometry. In: Mickelson, D.M., Attig, J.V. (Eds.), Glacial Processes: Past and Modern. Geological Society of America Spec. Pap. 337, Boulder, CO, 159-177.
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ACCEPTED MANUSCRIPT Tuma, J.J., 1979. Engineering Mathematics Handbook, second ed., McGraw-Hill, New York. Vreeland, N.P., Iverson, N.R., Graesch, M., Hooyer, T.S., 2015. Magnetic fabrics of drumlins of
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the Green Bay Lobe, southeastern Wisconsin, Quat. Sci. Rev. 112, 33-44.
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Walker, M.J.C., 1973. The nature and origin of a series of elongated ridges in the Morley Flats area of the Bow Valley, Alberta. Can. J. Earth Sci. 10, 1340–1346.
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Wright, H.E., 1957. Stone orientation in Wadena drumlin field, Minnesota. Geogr. Ann. 39, 19–
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31.
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Fig. 1. Upglacier plunges of the particle long axes and AMS principal susceptibility k1 measured in basal tills sheared experimentally. (A) Plunges of V1 eigenvectors, each computed from the
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long-axis orientations of 127-156 sand grains measured in the Douglas till of the Lake Superior
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Lobe of the Laurentide ice sheet, sheared to various strains . Vector length is scaled to the value
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of the strength of clustering, S1. Owing to shearing directed horizontally, the steady-state plunge achieved at high strains is equal to the angle (see text). In this case, = 14° (modified from
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Thomason and Iverson, 2006). (B) Orientations of principal magnetic susceptibilities (k1, k2, and k3) that develop in simple shear at a sufficiently high strain, with the angle equal to the plunge
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of k1 (owing to the horizontal shear plane). (C) Lower-hemisphere stereoplot showing a
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representative AMS fabric reflecting simple shear (Douglas till, = 39), based on 25 intact till
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specimens (k1-open squares, k2-solid triangles, k3-solid circles). The V1 eigenvector based on k1 orientations indicates = 26°. Although results from only the Douglas till are presented here, upglacier plunges of V1 eigenvectors based on particles and on k1 orientations have been measured in multiple tills sheared experimentally with similar results (see text). Fig. 2. The correction in azimuth that results from a shear plane inclined at a transverse angle
and a longitudinal angle n this example, the attitude of the shear plane reflects the local slope of the bed. The angle is measured in the tilted plane of the velocity gradient associated with shear. Fig. 3. The correction in azimuth as a function of the transverse angle and longitudinal angle that describe the inclination of the shear plane, for the cases of (A) = 15° and (B) = 30°. 21
ACCEPTED MANUSCRIPT Fig. 4. Local ice flow directions across an upglacier quadrant of hypothetical ‘steep’ and ‘common’ drumlins (see text) based on uncorrected fabric azimuths (green vectors) and flow
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directions that have been corrected (red vectors) assuming shear planes were tangent to drumlin
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surfaces, for = 15° and = 30°. The steep drumlin has mean transverse and longitudinal slopes
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of 17° and 7° respectively, and the common drumlin has mean transverse and longitudinal slopes of 5° and 2° respectively (colored lines are contours). Drumlin surfaces are modeled as the
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products of two orthogonal cosine functions, with the base of each drumlin set at the inflection
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point of the functions.
Fig. 5. Local ice flow directions on sections of ‘steep’ and ‘common’ flutes (see text) based on
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uncorrected fabric azimuths (green vectors) and flow directions that have been corrected (red
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vectors) assuming shear planes with attitudes consistent with the model of Benn (1994). Blue vectors are normal to the shear planes used to correct the flow azimuth, which were assumed to
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be laterally inclined at an angle equal to the transverse slope of the flute and inclined upglacier at an angle = 30°. White arrows depict vectors of till shear like those envisioned by Benn (1994). Cosine functions describe the transverse surface profiles of the flutes.
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ACCEPTED MANUSCRIPT Highlights of “Determining glacier flow direction from till fabrics: adjusting a paradigm”
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Particle fabrics of sheared tills are inclined relative to the plane of shear.
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Inclined shear planes require that fabric azimuths be corrected.
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Corrections to obtain local ice flow direction can be tens of degrees.
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Corrections to fabrics of drumlins and flutes can alter genetic interpretations.
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S0169-555X(17)30429-4 doi:10.1016/j.geomorph.2017.10.005 GEOMOR 6191
To appear in:
Geomorphology
Received date: Revised date: Accepted date:
17 July 2017 5 October 2017 5 October 2017
Please cite this article as: Iverson, Neal R., Determining glacier flow direction from till fabrics, Geomorphology (2017), doi:10.1016/j.geomorph.2017.10.005
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Determining glacier flow direction from till fabrics
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Neal R. Iverson*, Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa, USA.
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*Tel: +1 515 294 8048; [email protected]
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ACCEPTED MANUSCRIPT Abstract Field and experimental data indicate that fabrics of sheared basal tills, based on particle
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orientations and on anisotropy of magnetic susceptibility, are inclined relative to the macroscopic
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plane of shear. As a result, if this plane is tilted with a transverse component, one of the longest-
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standing axioms of glacial geology—that particles in basal till are preferentially oriented parallel to the direction of shear—is not strictly true. The resultant correction to the shearing direction
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increases with the transverse and longitudinal components of shear-plane inclination and with the
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magnitude of the fabric inclination relative to the shear plane. Azimuthal corrections calculated herein range from being negligible to a few tens of degrees for reasonable ranges of shear-plane
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tilt. The past success of fabric azimuths as indicators of flow direction, despite the absence of
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this correction, likely reflects the clustering of shear planes about the horizontal in basal tills. However, on the flanks of accreting subglacial bedforms, shear-plane attitudes may well conform
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to the local bedform slope. As illustrated with hypothetical fabrics of drumlins and flutes, azimuthal corrections can in that case be sufficiently large and systematic to seriously affect interpretations of bedform genesis. Keywords: glacier; till fabric; drumlin; flute 1.0 Introduction Fabrics derived from the preferred orientations of particles in till have long played a central role in efforts to infer till genesis and the origins of glacial landforms. No aspect of till fabric interpretation is more venerable than the maxim that particle long axes develop preferred orientations parallel to the local direction of glacier flow (e.g., Miller, 1884; Bell, 1888; Richter, 1936; Holmes, 1941). However, this maxim is correct only if macroscopic planes of shear are
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ACCEPTED MANUSCRIPT horizontal. Herein, I calculate corrections to the shearing direction for reasonable ranges of shear-plane tilt. For some situations the correction is not important. However, as will be
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discussed, in studies of subglacial bedforms, the correction can significantly alter interpretations
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of landform genesis.
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2. Background
Although secondary particle fabric modes oriented perpendicular to flow have commonly been
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observed (e.g., Holmes, 1941; Evenson, 1971; Carr and Rose, 2003), overwhelming
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observational evidence indicates that the dominant fabric mode tends to lie parallel to independent indicators of flow direction (e.g., Benn and Evans, 2010). Fabrics that develop in
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tills deposited at glacier beds tend to be especially strong (i.e., highly clustered orientation
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distributions), owing to shear strain in some combination of the ice and till bed that results from
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basal slip. Importantly, field-based interpretations of the origins of subglacial landforms— particularly, streamlined landforms such as drumlins and flutes—commonly depend on vectors of local shear provided by till fabrics (e.g., Evenson, 1971; Boulton, 1976; Krüger and Thomsen, 1984; Stanford and Mickelson, 1985; Rose, 1989; Gordon et al., 1992; Benn, 1994; Hart, 1997; Glasser and Hambrey, 2001; Johnson et al., 2010; McCracken et al., 2016). In the 1950s a second aspect of till fabric began to be commonly described: the tendency for particles to plunge upglacier in basal tills. In describing the fabric of a basal till in Ontario, Dreimanis and Reavely (1953) alluded to the tendency for upglacier plunges. Harrison (1957), Wright (1957), and Gravenor and Meneley (1958) found that most particles, including sand-sized grains in the latter two studies, plunged upglacier, commonly more than 20º, in basal tills of the Laurentide ice sheet. Many other studies subsequently demonstrated the tendency for particles to plunge upglacier (e.g., Andrews and King, 1968; Boulton, 1970; Evenson, 1971; Linebeck, 3
ACCEPTED MANUSCRIPT 1971; Mickelson, 1973; Drake, 1974; Mills, 1977), leading Drake (1977) to comment that such ‘imbrication’ is ‘traditionally’ accepted as an indicator of the direction from which the ice
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flowed.
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Most subsequent field measurements indeed indicate that long axes of particles generally
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cluster around orientations that plunge upglacier. These measurements include field studies that use the anisotropy of magnetic susceptibility (AMS) of intact till specimens to infer the preferred
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orientations of magnetic grains. For such grains, the orientation of maximum anisotropy, k1, is
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coincident with the orientation of clustering of grain long axes (e.g., Fuller, 1962), provided that magnetic particles have so-called shape anisotropy (Tarling and Hrouda, 1993). Field studies of
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AMS-based fabrics from basal tills indicate that k1 fabrics tend to plunge upglacier (Stupavsky et
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al., 1974; Stewart et al., 1988; Shumway and Iverson, 2009; Thomason and Iverson, 2009; Gentoso et al., 2011; Vreeland et al., 2015; Hopkins et al., 2016a,b; McCracken et al., 2016).
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This observation is significant because AMS fabric measurements have less random error than traditional particle fabric measurements and none of the particle-sampling subjectivity that can lead to systematic error (Iverson et al., 2008). These observations also demonstrate that, even for the silt-sized grains that commonly control the magnetic signal (e.g., Hooyer et al., 2008), upglacier plunge is dominant. Although early observations of plunging fabrics prompted the hypothesis that compressive longitudinal strain superimposed on simple shear caused upward flow (e.g., Harrison, 1957; Wright, 1957), laboratory experiments in which tills have been subjected to only simple shear and studies of similarly inclined fabrics in fault gouge indicate that no compressive strain is necessary. The upward plunge of particles is a natural consequence of horizontally directed simple shear. Ring-shear experiments on five basal tills indicate that once a sufficient shear 4
ACCEPTED MANUSCRIPT strain (~10) is achieved, fabrics based either directly or indirectly (i.e., AMS) on particle long axes strongly cluster, align parallel to shear, and plunge upglacier 5-30º with respect to the shear
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plane (Fig. 1) (Hooyer and Iverson, 2000; Thomason and Iverson, 2006; Hooyer et al., 2008;
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Iverson et al., 2008; Shumway and Iverson, 2009; Vreeland et al., 2015; McCracken et al., 2016). The tills studied have a wide range of textures, with particle sizes used to compute
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fabrics that include fine gravel, sand, and silt (i.e., AMS). These experimental results agree with
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the aforementioned field observations and also with field studies of grain orientations in fault gouge that have, like many tills, matrix material consisting of silt and clay. Cladouhos (1999a)
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found that larger ‘survivor’ grains in such gouge tend to plunge upflow, on average, 25º relative to the macroscopic plane of shear, as provided by the orientations of adjacent wall rocks. Such
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grains help form the inclined P-foliation commonly described in fault gouges by structural geologists (Logan et al., 1979; Rutter et al., 1986). Similarly inclined surfaces have been
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described in basal till, in association with upglacier plunging particles (Boulton, 1970). The inclination of particles relative to the macroscopic plane of shear likely results from displacements along Riedel shears that are inclined systematically to the shear plane (Cladouhos, 1999b; Thomason and Iverson, 2006). This explanation, which requires shear of till beneath the glacier sole, is sufficient to explain most upglacier plunging fabrics of basal tills because, even if most sediment transport has not been by bed shear, it nevertheless accompanies the final lodgment of debris from ice (Boulton et al., 1974; Tulaczyk, 1999; Larsen et al., 2004; Piotrowski et al., 2004). An exception, when bed shear does not accompany deposition, are basal meltout tills that inherit particle fabrics during deposition from stagnant basal ice (e.g., Ham and Mickelson, 1994). Interestingly, however, particle (e.g., Lawson, 1979) and AMS-based fabrics (Fleming et al., 2013) measured in ice exhibit the same tendency for upglacier plunging particles,
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ACCEPTED MANUSCRIPT so the result would seemingly be the same as that for deposition during basal slip: fabrics have preferred orientations that plunge upglacier.
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The inclination of till fabrics within the basal shear zones of glaciers has an important
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implication: if there is any lateral component of shear-plane dip, the azimuth of shear is different
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from that of the particle fabric (Fig. 2). The resultant azimuthal correction increases with the
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lateral and longitudinal components of the shear-plane inclination, as described hereinafter. 3. Analysis and results
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If shear planes within till are horizontal, then the V1 eigenvector computed from the clustering of particle long axes (Mark, 1973) indeed plunges in a direction opposite of the local
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azimuth of shear and hence indicates the local direction of basal slip (Fig. 1). The more general
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case, however, is that shear planes are not horizontal. The commonly patchy nature of shear
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deformation in a till bed (e.g., Fischer and Clarke, 1997; Piotrowski et al., 2004) can cause inclined shear planes, as indicated by AMS fabric studies of flat-lying tills that allow shear-plane attitudes to be determined from orientations of the three principal susceptibilities (Figs. 1B, C) (e.g., Shumway and Iverson, 2009). More predictably, bedforms that develop subglacially may promote deformation along shear planes with attitudes that conform to the local bedform slope. In either case, fabric and shearing azimuths will not be parallel, owing to the angle between the shear plane and fabric orientation, defined within the inclined plane of the velocity gradient (Fig. 2). For the special case of a perfectly horizontal shear plane, is the fabric plunge (Figs. 1A, B). To correct the fabric azimuth as a function of the shear-plane attitude, consider a shear plane inclined at angles and measured in planes transverse (yz) and parallel (xz) to the flow direction respectively (Fig. 2). These angles, rather than a single strike and dip, are considered to 6
ACCEPTED MANUSCRIPT isolate the different effects of shear-plane inclination relative to the flow direction. Long axes of particles that have become preferentially aligned during simple shear cluster around the V1
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eigenvector f (Fig. 2). If coordinates xʹ, yʹ, and zʹ are defined referenced to the attitude of the
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cos f 0 sin
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shear plane (Fig. 2), then
(1)
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Note that yʹ = 0, so that the fabric azimuth in this coordinate system is zero and that is a
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negative angle, given that the right-handed coordinates and angles are measured counterclockwise.
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A convenient way to determine the azimuth and plunge of the shearing orientation from f is
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to rotate the shear plane to horizontal through the positive angles and in the yz and xz planes
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(Fig. 2). A complication, however, is that the rotation through will change the angle . Thus, ~
the rotation about the x axis must be adjusted to a value that provides the value of
commensurate with a horizontal shear plane. The rotation matrices (Tuma, 1979, p. 61) are, ~
thus, Rx( ) and Ry():
0 1 ~ Rx ( ) 0 cos ~ 0 sin
sin ~ cos
(2)
cos R y ( ) 0 sin
0 sin 1 0 0 cos
(3)
~
0
~
where the subscripts denote counterclockwise (i.e., right-hand rule) rotations about the respective axes. Multiplying the right-hand sides of Eqs. (1) and (2) and the result by the right-hand side of 7
ACCEPTED MANUSCRIPT Equation (3) results in a new vector s referenced to x, y, and z and parallel to the shearing direction (Fig. 2):
(4)
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cos cos sin cos ~ sin ~ s sin sin ~ sin cos cos cos sin
~
~
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Trigonometric relationships in the yz and xz planes provide the value of in terms of and : tan cos
tan 1
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(5)
The vector s can also be expressed in terms of its azimuth and plunge defined relative to the
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x, y, and z axes:
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cos cos s cos sin sin
(6)
Substituting Eq. (5) into Eq. (4) and equating the right-hand sides of Eqs. (4) and (6) along y and z respectively yield
tan sin sin tan 1 cos cos
sin 1
(7)
tan cos
sin 1 sin cos cos sin cos tan 1
(8)
Substitution of the right-hand side of Eq. (8) into Eq. (7) allows to be determined as a function of the shear plane attitude (and and the angle This azimuth points opposite that of the true shearing direction and is equal to the desired azimuthal correction Fig. 2).
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ACCEPTED MANUSCRIPT Over some ranges of reasonable parameter space the correction is large (e.g., > 5°) (Fig. 3). As noted, experimentally determined values of are 5-30° for various tills (Hooyer and Iverson,
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2000; Thomason and Iverson, 2006; Hooyer et al., 2008; Iverson et al., 2008; Shumway and
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Iverson, 2009), and field studies of gouge (Cladouhos, 1999a) and basal till (Harrison, 1957; Wright, 1957; Gravenor and Meneley, 1958) can indicate values >20°; values of 15° and 30° are
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considered in Fig. 3. Values of are sensitive to the transverse component of shear-plane
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inclination and are 0-16° for = 0-30° and = 0. Sensitivity to increases if shear planes also
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are inclined longitudinally; for = 0-30°, values of are up to 70% larger. Steeply inclined shear planes (= 30-50°) have corrections of 11-51°.
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4. Implications
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The inclination of particle fabrics relative to the macroscopic plane of shear and the
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associated correction required to determine flow direction from fabric azimuth highlights the need to measure shear-plane orientations independently. In principle, observations of basal-till micromorphology could allow shear-plane orientations to be measured. For example, a sufficient number of orthogonal thin sections of till that display Riedel shears (e.g., Tchalenko, 1970) could allow the macroscopic sense and plane of shear to be determined. Alternatively, focusing on the orientations of the A-B planes of particles (Benn, 1995; Evans and Hiemstra, 2005; Li et al., 2006; Evans et al., 2007) could help resolve shear-plane orientations. A laboratory-tested and less labor-intensive alternative is to use AMS-based fabrics to determine shear-plane orientation. As noted, shear of basal tills in experiments indicates that shear-plane attitudes are fully described by clustered orientations of maximum susceptibility k1 that lie at an angle to the shear plane and of intermediate susceptibility k2 that lie in the shear plane and perpendicular to
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ACCEPTED MANUSCRIPT the flow direction (Fig. 1B). Thus, AMS fabrics provide shear-plane attitudes so that fabric azimuths can be readily corrected to obtain shearing azimuths (Shumway and Iverson, 2009;
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Vreeland et al., 2015; McCracken et al., 2016). Importantly, however, applying the correction using AMS or any other method that yields shear-plane attitude requires also knowing the angle
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. This angle is best determined by shearing the till of interest in experiments in which the macroscopic plane of shear is horizontal and by measuring the fabric plunge (e.g., Shumway and
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Iverson, 2009; Vreeland et al., 2015).
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On the other hand, many decades of experience with clast fabrics indicate that they consistently provide a good indication of flow direction without any correction. This success
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likely reflects that strain in basal tills tends to be dominated by simple shear and directed along
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shear planes that cluster about the horizontal. Even where AMS fabrics indicate that many shear planes in flat-lying tills are inclined, the mean trend of such fabrics—if many fabrics are
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measured across sufficiently large distances—tends to be parallel to the flow direction, (e.g., Shumway and Iverson, 2009). Thus, for flat-lying basal tills where the goal is to infer regional flow direction, not correcting fabric data for the shear-plane attitude likely carries only a mild penalty: increased variability among the trends of multiple fabrics. The penalty can be substantially larger, however, in studies of some subglacial bedforms. In the case of those that may evolve through accretion of till on the bed, a reasonable expectation is that bed shear occurs along planes with attitudes that are related to the local slope of the bedform. In that case neglecting azimuthal corrections can lead to incorrect interpretations. Hypothetical fabrics of drumlins and flutes help illustrate this point. In the drumlins of Fig. 4, correcting the fabric azimuth eliminates evidence of till deposition during drumlin growth. The upglacier quadrant of the drumlin defined as ‘steep’ in the figure 10
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drumlin defined as ‘common, reflects ratios close to the middle of those populations. For these
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cases and the two values of considered in Fig. 3, azimuths were corrected by assuming that
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shear planes had attitudes tangent to the local drumlin slope. Fabric azimuths were chosen (associated apparent flow direction shown with green vectors) to illustrate flow divergence
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around the heads of drumlins. Such divergence is usually taken as evidence of till accretion during drumlin formation (e.g., Walker, 1973; Krüger and Thomsen, 1984; Hart, 1997;
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McCracken et al., 2016), whereas lack of flow divergence leaves open the possibility that till layers were deposited prior to drumlinization, with drumlin relief caused by erosion. Corrected
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flow directions (red vectors) are uniformly parallel to the drumlin long axes. Thus, accounting for inclined shear planes in this case erases apparent evidence that till deposition accompanied
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drumlin growth.
A similar potential problem arises in considering till fabrics of flutes—one of the principal criteria used to infer flute genesis. Sections of flutes defined as ‘steep’ and ‘common’ are depicted in Fig. 5, with lateral slope choices based on the distribution of the height-to-width ratios of the population of flutes described by Gordon et al. (1992). Consider hypothetical particle fabrics measured along the flanks of such flutes that indicate apparent ice flow parallel to their long axes (Fig. 5, green vectors), with seemingly no inward ice flow. Such flow azimuths would seem to refute a leading model of flute formation proposed by Benn (1994) (see also Boulton, 1976). In this model, cavity formation is invoked in the lee of an obstruction (e.g., a lodged boulder), and weak till of the bed shears inward and upward into the cavity. Flutes extend downglacier as the cavity and deposition within it propagate downstream. Shear planes are 11
ACCEPTED MANUSCRIPT expected to be inclined upglacier, consistent with upwardly directed shear, and inclined laterally at an angle comparable to the local transverse slope of the flute. Making these assumptions (blue
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arrows are normal to assumed shear planes) and correcting fabric azimuths on that basis yield inward flow azimuths that converge on the long axes of the flutes (red vectors). The corrected
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data, therefore, provide support for the inward flow of Benn’s model that is lacking if the data
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are not corrected.
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How should the azimuthal dependence on shear-plane attitude be handled in the common
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situation when particle fabrics are measured, but shear-plane orientations are unknown? In the case of a flat-lying basal till, the dependence simply needs to be acknowledged as a potential
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source of variability among fabric azimuths—one that can be considered in addition to
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variability that results from measurement error and human subjectivity (e.g., Drake, 1977; Benn and Ringrose, 2001). In the case of subglacial bedforms, a reasonable approach would be to
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consider uncorrected fabric azimuths and those corrected by assuming that shear planes were parallel to the local slope of the bedform (e.g., Fig. 4). This approach, although not really bracketing the real uncertainty, would at least highlight a greater fraction of it and could thus inhibit overzealous interpretations. Alternatively, shear-plane attitudes consistent with a particular model of bedform genesis could be used to correct fabric data (e.g., Fig. 5) and thereby encourage targeted and more accurate hypothesis testing. Many field studies of sheared till will have no experimental control on the value of . A possible approach to measuring this angle would be to determine shear-plane orientations from field data independently, using orientations of Reidel shears, and to then use fabric orientations to determine the value of . Alternatively, if cannot be estimated from field data, efforts to infer local flow direction form fabrics should acknowledge the potential variability of by 12
ACCEPTED MANUSCRIPT considering values bracketed by experimental studies (5-30°) and tailoring interpretations accordingly. Unfortunately, ring-shear experiments, to date, have been conducted on too few tills
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and with insufficient redundancy to provide more specific guidance. Additional experiments
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could yield useful dependencies of on till texture or on the sizes of fabric-forming particles.
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5. Conclusions
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Particle and AMS fabrics of tills developed in shear at glacier beds indicate the direction of glacier flow only for the special case in which the macroscopic plane of shear is horizontal.
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Otherwise, if there is any transverse component of shear-plane inclination, the upglacier inclination of particle fabrics relative to the shear plane requires that the fabric azimuth be
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corrected. For reasonable ranges of shear-plane attitude, corrections can range from being
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negligibly small to a few tens of degrees and are significantly larger if shear planes are inclined
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laterally and longitudinally. Shear-plane orientations determined from AMS-based fabrics allow the correction to be made if the value of is known from experiments in which the relevant till has been sheared. In a flat-lying till, with shear planes that likely cluster about the horizontal, the dependence of fabric azimuth on shear-plane attitude will add azimuthal variability among fabrics but should not influence regional fabric trends. In contrast, flow directions inferred from fabrics measured along the slopes of subglacial bedforms, such as drumlins and flutes, can be subject to systematic corrections that seriously alter interpretations. In the absence of independently determined shear-plane attitudes, corrections can be imposed using the local slopes of bedforms or models as predictors of shear-plane attitude. If the value of is not known, then interpretations of local flow directions from till fabrics should consider the full experimental range of measured in tills and relax interpretations on that basis.
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ACCEPTED MANUSCRIPT Acknowledgements J.K. Iverson and three anonymous reviewers provided helpful suggestions. This work was
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supported, in part, by the U.S. National Science Foundation (grant EAR-1225812).
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Fig. 1. Upglacier plunges of the particle long axes and AMS principal susceptibility k1 measured in basal tills sheared experimentally. (A) Plunges of V1 eigenvectors, each computed from the
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long-axis orientations of 127-156 sand grains measured in the Douglas till of the Lake Superior
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Lobe of the Laurentide ice sheet, sheared to various strains . Vector length is scaled to the value
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of the strength of clustering, S1. Owing to shearing directed horizontally, the steady-state plunge achieved at high strains is equal to the angle (see text). In this case, = 14° (modified from
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Thomason and Iverson, 2006). (B) Orientations of principal magnetic susceptibilities (k1, k2, and k3) that develop in simple shear at a sufficiently high strain, with the angle equal to the plunge
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of k1 (owing to the horizontal shear plane). (C) Lower-hemisphere stereoplot showing a
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representative AMS fabric reflecting simple shear (Douglas till, = 39), based on 25 intact till
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specimens (k1-open squares, k2-solid triangles, k3-solid circles). The V1 eigenvector based on k1 orientations indicates = 26°. Although results from only the Douglas till are presented here, upglacier plunges of V1 eigenvectors based on particles and on k1 orientations have been measured in multiple tills sheared experimentally with similar results (see text). Fig. 2. The correction in azimuth that results from a shear plane inclined at a transverse angle
and a longitudinal angle n this example, the attitude of the shear plane reflects the local slope of the bed. The angle is measured in the tilted plane of the velocity gradient associated with shear. Fig. 3. The correction in azimuth as a function of the transverse angle and longitudinal angle that describe the inclination of the shear plane, for the cases of (A) = 15° and (B) = 30°. 21
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directions that have been corrected (red vectors) assuming shear planes were tangent to drumlin
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surfaces, for = 15° and = 30°. The steep drumlin has mean transverse and longitudinal slopes
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of 17° and 7° respectively, and the common drumlin has mean transverse and longitudinal slopes of 5° and 2° respectively (colored lines are contours). Drumlin surfaces are modeled as the
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products of two orthogonal cosine functions, with the base of each drumlin set at the inflection
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Fig. 5. Local ice flow directions on sections of ‘steep’ and ‘common’ flutes (see text) based on
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uncorrected fabric azimuths (green vectors) and flow directions that have been corrected (red
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vectors) assuming shear planes with attitudes consistent with the model of Benn (1994). Blue vectors are normal to the shear planes used to correct the flow azimuth, which were assumed to
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be laterally inclined at an angle equal to the transverse slope of the flute and inclined upglacier at an angle = 30°. White arrows depict vectors of till shear like those envisioned by Benn (1994). Cosine functions describe the transverse surface profiles of the flutes.
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ACCEPTED MANUSCRIPT Highlights of “Determining glacier flow direction from till fabrics: adjusting a paradigm”
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Particle fabrics of sheared tills are inclined relative to the plane of shear.
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Inclined shear planes require that fabric azimuths be corrected.
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Corrections to obtain local ice flow direction can be tens of degrees.
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Corrections to fabrics of drumlins and flutes can alter genetic interpretations.
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