MICROSCOPY RESEARCH AND TECHNIQUE 62:2–18 (2003)

Development, Principles, and Applications of Automated Ice Fabric Analyzers

1 1 2 3 L.A. WILEN, * C.L. DIPRINZIO, R.B. ALLEY, AND N. AZUMA 1Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701 2EMS Environment Institute and Department of Geosciences, The Pennsylvania State University, University Park, Pennsylvania 16802 3Nagaoka University of Technology, Nagaoka, Niigata 940-2137, Japan

KEY WORDS ice fabric; ice texture; c-axes; nearest-neighbor correlation; polygonization; Schmidt plot; Rigsby stage; fabric analysis ABSTRACT We review the recent development of automated techniques to determine the fabric and texture of polycrystalline ice. The motivation for the study of ice fabric is first outlined. After a brief introduction to the relevant optical concepts, the classic manual technique for fabric measurement is described, along with early attempts at partial automation. Then, the general principles behind fully automated techniques are discussed. We describe in some detail the simi- larities and differences of the three modern instruments recently developed for ice fabric studies. Next, we discuss briefly X-ray, radar, and acoustic techniques for ice fabric characterization. We also discuss the principles behind automated optical techniques to measure fabric in quartz rock samples. Finally, examples of new applications that have been facilitated by the development of the ice fabric instruments are presented. Microsc. Res. Tech. 62:2–18, 2003. © 2003 Wiley-Liss, Inc.

INTRODUCTION TO ICE FABRIC Shoji and Higashi, 1978). As ice flows, the crystal tex- AND TEXTURE ture and fabric evolve in a way that depends on the The fabric of ice refers to the distribution of crystal deformation rate and symmetry as well as temperature axes of an assemblage of ice crystals. Ice has a hexag- (Alley, 1988; Azuma and Higashi, 1985; Budd and onal crystal structure consisting of stacks of basal Jacka, 1989; Lipenkov et al., 1989). For example, if ice planes of molecules arranged in hexagons. The crystal having an initially random fabric undergoes vertical orientation is specified by the direction of a c-axis (per- uniaxial compression, c-axes will rotate on average to- pendicular to the basal planes) and 6-fold degenerate ward the compressional axis (Azuma and Higashi, a-axis (in the basal plane). Ice is optically (and acous- 1985), leading to a fabric concentrated about the verti- tically) uniaxial, so optical and acoustic techniques can cal (Gow and Williamson, 1976; Gow et al., 1997; Thor- only determine the direction of the c-axis. Hence, for steinsson et al., 1997). At the same time, the ice grains most purposes, the fabric refers to the direction of the will be squeezed in the vertical direction and elongated c-axes of an assemblage. The c-axis for one grain is in a direction normal to vertical. (see Fig. 1). For other specified by a polar and azimuthal angle or, equiva- types of deformation, such as uniaxial extension or lently, a point on a hemisphere of unit radius. The pure shear, different patterns of fabric and grain fabric is typically represented on a Schmidt plot, which shapes will develop. The texture and fabric of ice, maps each crystal c-axis direction from a point on the therefore, contain a fingerprint of the history of the ice hemisphere to a circle, using an equal area projection. flow. This information is useful in a number of con- The distribution of crystal axes is also often character- texts. The study of ice fabrics to understand glacier ized using other average measures that indicate how flow dynamics was pioneered by Rigsby in his measure- random or concentrated the fabric is, or how the axes ments on Emmons Glacier, Mount Rainier, Washing- are distributed about the vertical axis. ton (Rigsby, 1951) (also see Bader, 1951). The history of The texture of ice refers to the shape, size, and ar- ice flow is particularly important for the paleoclimatic rangement of an assemblage of ice crystals (or grains). interpretation of ice cores. Ice texture has been characterized in many different An ice core records the earth’s past climate in the ways according to the preference of the various au- form of various physical, chemical, isotopic, and bio- thors. However, in general, it is common to see the logical indicators embedded in the ice (Alley and average crystal size for a sample and, more recently, the average elongation, or distribution of elongations of the grains in an assemblage. We will revisit this point *Correspondence to: L.A. Wilen, Department of Physics and Astronomy, Ohio below in our discussion of newer applications of auto- University, Athens, Ohio 45701. E-mail: [email protected] mated techniques. Received 21 January 2003; accepted in revised form 15 April 2003 Grant sponsor: U.S. National Science Foundation Division of Atmospheric MOTIVATION FOR STUDYING ICE Sciences/Earth System History and Office of Polar Programs; Grant numbers: FABRIC AND TEXTURE ATM#9905738, and OPP#0135989, and OPP#9814774, and OPP#0087160; Grant sponsor: Comer Foundation Over long time scales, ice in nature deforms as a DOI 10.1002/jemt.10380 power-law material (Alley, 1992; Duval et al., 1983; Published online in Wiley InterScience (www.interscience.wiley.com).

© 2003 WILEY-LISS, INC. AUTOMATED ICE FABRIC ANALYZERS 3

Fig. 1. a: Schmidt plots at two depths from the Greenland Ice Sheet Project 2 (GISP2) ice core showing the rotation of c-axes to the vertical under uniaxial compression. b: Photograph of a vertical thin section from GISP2 at 1,681 m showing horizontal elongation of grains.

Bender, 1998). These include oxygen isotope ratios these indicators is retrieved can be dated using a that measure temperature, gas bubbles that archive number of methods, the most straightforward being atmospheric composition, dust and salt that indicate to count annual layers down the core. These layers wind strength, Be-10 that reflects the amount of are visible due to the seasonal variability in bubble solar radiation, and more. The depth at which each of formation and/or dust in the ice, and also are detect- 4 L.A. WILEN ET AL. able using isotopic, chemical, or electrical techniques OPTICS REVIEW AND NOTATION that sense seasonal variations in many characteris- In order to describe the physical principles of the tics. At depths where annual layers are no longer techniques (both new and old) devised to analyze ice resolvable, one must sometimes rely on ice flow mod- fabrics, it is useful to review a few basic concepts in- els. Ice core sites are often picked to be at a dome in volving crystals and visible light. (Readers familiar the surface topography, where ice is presumably with standard ideas of crystal optics may want to skip flowing straight downward. In steady state, the ac- this section). We assume here that the reader is famil- cumulation of snow over the dome is balanced by a iar with the ideas of birefringence and polarization. In continual squeezing of the ice downward and out- what follows, we always assume that the light is prop- ward to the periphery. The accuracy of the estimated agating along the positive z-direction. We will some- depth-age relationship relies critically on a stable set times use compass directions where North (N) is along of ice flow conditions persisting over tens of thou- the positive y-axis and East (E) is along the positive sands of years. However, the measurements that x-axis. characterize the ice flow at the site are typically Light of an arbitrary polarization is represented by a based on the current-day flow patterns as character- 2-element vector whose complex elements specify the ized by surveys over the course of several years. The amplitude of the electric field in two orthogonal direc- fabric of the core can be used to confirm that the tions. For example, light propagating in the z direction symmetry of the flow has not changed drastically and polarized along x is represented by (1 0), light over the time period that contributed significantly to polarized along y is represented by (0 1) and right the formation of that fabric, usually many millenia. circularly polarized light is represented by (1 i). Light In some cases, examination of ice fabric and other linearly polarized (in the x,y plane) along a direction characteristics has helped to determine that flow specified by an azimuthal angle ␾ may be specified by near the bottom of the ice sheet has indeed been the vector (cos ␸ sin ␸). A linear polarizer is repre- disrupted, corrupting the paleoclimatic record (Alley sented by a matrix that selects out light of a particular et al., 1997). polarization. For example, a polarizer oriented along The process of ice flow is further complicated by 10 the x-direction is represented by ͩ ͪ. A polarizer the fact that the flow law for ice (i.e., strain rate vs. 00 stress) itself depends on the fabric and texture of ice oriented along an arbitrary direction specified (Alley, 1992; Azuma and Goto Azuma, 1996; Azuma, by the azimuthal angle ␾ is represented by 1994, 1995; Russell-Head and Budd, 1979). For ex- ͩ cos2␸ sin ␸ cos ␸ͪ ample, the deformation of ice occurs principally by sin ␸ cos ␸ sin2␸ . A slab of optically uniaxial glide along the basal plane. For ice having a random material, such as ice, may be represented by a complex fabric, there are many crystals that have some com- matrix. For example, consider a crystal of ice whose ponent of the applied stress resolved along the basal optic axis (the c-axis for ice) lies along the x-axis. Light plane. However, as discussed above, under compres- polarized along x will undergo a phase shift as it prop- ␲ ␭ sion, c-axes of ice crystals rotate toward the compres- agates through the material given by eine(2 d/ ) where d sional axis. As the crystals rotate, the applied stress is the thickness of the ice, ␭ is the wavelength of the becomes increasingly perpendicular to the basal light, and ne is the extraordinary index of refraction. planes, and the ice becomes harder to compress. This Similarly, light polarized along y will undergo a phase ino(2␲d/␭) is just one example, but in general, there is a very shift e ,where no is the ordinary index of refrac- complicated feedback between flow and fabric (e.g., tion. (The ordinary and extraordinary indices of refrac- Castelnau et al., 1996, 1998; Thorsteinsson, 2002; tion for ice are 1.3090 and 1.3104 at a wavelength of van der Veen and Whillans, 1994). The development 590 nm, respectively). Hence the matrix for this ele- ͑ ␲ ␭͒ of a correct flow law for ice must properly model the ͩ eine 2 d/ 0 ͪ ment is given by ͑ ␲ ␭͒ . If the optic axis development of the fabric and the feedback of the 0 eino 2 d/ fabric on the flow. Fabric measurements provide im- is not aligned along the x-axis, but rather is in the x-z portant ground truth in testing such models. plane at an angle ␪ from the z-axis, then ne must be ␪ ϭ ͌ 2 2␪ϩ 2 2␪ An additional complicating factor in the development replaced with ne( ) (neno/ ne cos nosin )in of fabric is the production of new grains in the ice the above equation. The result of polarized light prop- (Alley, 1992; Kamb, 1972). Active grain formation usu- agating through various elements is obtained by ma- ally occurs either by polygonization, the splitting of trix multiplication. The intensity of light after passing larger grains into smaller, or by recrystallization, the through all of the elements is found by taking the nucleation of new grains at highly strained regions in square of the magnitude of the vector obtained from the the polycrystal. These processes cause a change in the matrix operation. ice fabric and hence feedback on the flow. Especially in Let us now examine a few simple results for some the case of recrystallization, these processes also can combinations of optical elements. First consider light erase the effects that older deformation had on the polarized in an arbitrary polarization incident upon a fabric, limiting how far back the history of the flow- second polarizer (i.e., an analyzer) aligned along the y field symmetry can be recreated. With increased sta- direction. The amplitude of the transmitted light is 00 tistics on the fabric of ice resulting from automated ͑ ␸ ␸͒ͩ ͪ ϭ ͑ ␸͒ techniques, it becomes easier to discern the level of given by cos sin 01 0 sin and taking activity of these various processes using methods we the square of the amplitude yields the common result will discuss below in New Applications. for the intensity, sin2 ␾. AUTOMATED ICE FABRIC ANALYZERS 5 Suppose light polarized along x is incident on a uni- When the optic axis of the ice is aligned with either of axial crystal (such as ice) of thickness d whose optic the crossed polarizers, the ice has no effect on the axis is specified by the usual polar angles ␪ and ␾. The polarization, and a first order red interference color is light is then analyzed with a polarizer aligned with the observed. When the ice crystal has its optic axis in the y-axis. The result is given by: NW-SE direction, the combined effect of the crystal and retarder is to act as a retarder with greater birefrin- ␲ ͑␪͒͑ ␭͒ cos ␸ sin ␸ ei2 ne d/ 0 gence than the original retarder, and the result is an ͑10͒ͩ ͪͩ ␲ ͑ ␭͒ ͪ interference color whose complement is of longer wave- Ϫsin ␸ cos ␸ 0 i2 no d/ e length. ␸Ϫ ␸ Conversely, when the crystal has its optic axis in the cos sin 00 ␲͓ ͑␪͒ϩ ͔͑ ␭͒ ϫ ͩ ͪͩ ͪ ϭ i ne no d/ sin ␸ cos ␸ 01 ie NE-SW direction, the combined effect is to act as a retarder with less birefringence than the original re- ␲d tarder, and the result is an interference color whose ϫ ͩ ␸ ͓ ͑␪͒ Ϫ ͔ ͪ 0, sin 2 sinͭ ␭ ne no ͮ (1) complement is of shorter wavelength. If the extinction curve is observed through an appro- priate color filter, the period will no longer be 90°, but Eq. 1 is the key to understanding essentially all of the rather 180°. Hence, the effect of the retarder is to break optical techniques used to analyze ice fabrics. the 90° degeneracy of the system and allow the deter- There are three important points that should be not- mination of the unique plane containing the c-axis. ed: (For fuller details, the reader is again referred to a text on optics or optical mineralogy; Born and Wolf, 1964; 1. If the sample is rotated about the z axis, when the Shelley, 1975.) optic axis of the ice crystal is in the plane specified The ideas discussed in this section were geared by either of the polarizers (the x-z or y-z plane), no toward an explanation of the orthoscopic (parallel light gets though the system; this is called the light) techniques used to analyze fairly large crystals “angle of extinction.” For the above example, this of ice found in typical thin sections from ice cores or occurs when ␾ϭ0°, 90°, 180°, or 270°. We will laboratory ice. The usual conoscopic methods for ori- refer to the ambiguity regarding the plane of the enting and analyzing mineral crystals using a polar- c-axis as the “90 degeneracy.” (It should be noted izing microscope involving isogyres and flash figures that instead of rotating the crystal, one may can be found in any standard text on optical miner- equivalently consider a fixed crystal and rotating alogy. crossed polarizers.) We now turn to a discussion of the techniques used to 2. If one considers the transmitted light intensity as a analyze ice fabrics. Some of the features of these vari- function of ␾ (or “extinction curve”), it is oscillatory ous techniques are summarized in Table 1. with a period of 90°. For a given ice thickness and wavelength, the contrast (or amplitude of the oscil- RIGSBY STAGE TECHNIQUE latory curve) depends on the polar c-axis angle ␪. The classic manual technique for analysis of ice fab- When ␪ϭ0°, there is no contrast to the curve (the ric are based on the traditional “Rigsby stage” (Rigsby, crystal is dark). For increasing ␪, the contrast in- 1951). The technique was later standardized and de- creases, although the exact dependence is a function scribed by Langway (1958). The ideas were adapted of the sample thickness and light wavelength. For from techniques in optical mineralogy (Berek, 1923; thin enough samples, the intensity will increase Emmons, 1943). The Rigsby stage is a 4-axis universal monotonically with ␪. stage including both an inner vertical and an outer 3. Suppose the optic axis of a crystal lies in the x-y vertical axis. The basic arrangement is shown in Fig- plane. If monochromatic light is incident upon the ure 2. Note the directions specified by points on a ͉ Ϫ ͉ ␭ ϭ crystal and ( ne no d/ ) 1, then this grain will compass. Vertical is defined as out of the page. Beneath appear dark. If this condition is satisfied for green the stage is a polarizer oriented along E-W, and above light, then for incident white light, the complement the stage is a second polarizer oriented N-S. A source of of green (i.e., red) will be observed. This is referred white light shines upward from below the lower polar- to as a first order red interference color. (Higher izer. The procedure for finding the orientation of the ͉ Ϫ ͉ ␭ ϭ orders are obtained for ( ne no d/ ) m, where optic axis of a grain involves a series of manipulations m Ͼ 1). that bring the c- axis to lie either in the E-W direction, or to a vertical position (i.e., perpendicular to both Before discussing the different automated tech- polarizer orientations). A final operation determines niques, it is useful to work out one additional example. which of these conditions applies. It is not difficult to Consider the same system as above, but with an extra understand how this is done. First, the sample alone is uniaxal crystal (a “retarder”) placed in front of the rotated about an “inner” vertical axis until the grain analyzer polarizing filter with its optic axis at a 45° becomes extinct. This implies the c-axis of the grain is angle (NW-SE) to the polarizer orientation. Let us sup- in either the N-S/vertical plane or the E-W/vertical pose that the thickness and birefringence of the re- plane. The two possibilities are distinguished by a ro- tarder are such that when no ice sample is present, a tation about the A4 axis. If the c-axis is in the N-S/ first order red interference color is produced. Also, as- vertical plane, then the grain will remain extinct; if Ͼ sume that ne no for the retarder. For simplicity, not, the grain will come out of extinction. If the grain is suppose the optic axis of the ice is in the equatorial in the N-S/vertical plane, then the sample is rotated by plane. Now, consider the behavior as the ice is rotated. 90° to bring it into the E-W/vertical plane. The c-axis is 6 L.A. WILEN ET AL.

TABLE 1. Comparison of various fabric analysis techniques Observational Method parameters Information obtained Sampling volume Note Rigsby stage Stage settings for various C-axis of each grain Individual grains in thin section Manual ice fabric grain extinctions (section typically 100 mm technique diameter ϫ 0.4 mm thick) Automated Sets of images of thin C-axis of each grain. Location of Thin section (typically 100 mm optical ice section viewed at grain boundaries yielding grain diameter ϫ 0.4 mm thick) fabric various angles through locations, shapes and sizes. instruments crossed polarizers X-ray Diffraction spots C-axis and a-axis of each grain Individual grains in thin section diffraction Radar Reflection intensities, Weighted average of c-axis Grains along radar path, 50–200 MHz reflection times for orientations in sample volume; typically hundreds of meters frequency range various transmitter/ location of abrupt changes in receiver configurations fabric Sonic Speed of sound (from Weighted average of c-axis Grains near surface along ϳ1–2 30 KHz frequency borehole time of flight) of orientations in sample volume meter length of borehole range logging acoustic p-wave in ice along axis of borehole Sonic Speed of sound of shear Weighted averages of c-axis Typically 100 mm long samples 2 MHz frequency and longitudinal waves orientations in sample volume range propagated through core in various directions Seismic Speed of sound of shear Weighted averages of c-axis Grains along sound path, 10 Hz frequency and longitudinal waves orientations in sample volume; typically hundreds of meters range location of abrupt changes in fabric Automated Sets of images of thin C-axis of each grain. Location of Thin section (typically 20 ␮m optical section viewed at grain boundaries yielding grain thick). Field of view is quartz various angles through locations, shapes and sizes. ϳ 0.3 mm. fabric crossed polarizers, a instruments retarder, and color filters

the “outer” axis A5, which rotates the whole universal stage (and the ice sample) with respect to the polariz- ers. If the c-axis is in the polar position, the grain will not come out of extinction. If the c-axis is in the equa- torial position, it will come out of extinction. There are some other subtleties that occur when a grain is ini- tially already aligned close to the polar or equatorial positions, but we will not go into these here. Once the angles defining the c-axis direction for all the grains have been tabulated, corrections for refraction must be applied (Kamb, 1962; Wilen, 2000). An important point is that, as all the above manip- ulations are performed, the observer must keep his or Fig. 2. Axes of the universal stage. Reproduced from the Journal her eye directly above the grain being observed. When of Glaciology, Wilen, Vol. 46, 2000, with permission of the Interna- analyzing ice, the analysis must be in a cold room or tional Glaciological Society. out in the field. The process is fairly time consuming and tedious, not extremely accurate, and prone to er- rors. The accuracy of the technique was stated by Lang- now in the E-W/vertical plane and tipped toward either way to be approximately 5°. Nevertheless, heroic ef- E or W by some angle. Now suppose that the tipping forts using the manual technique have shown that angle were known and a rotation about A2 were per- fabric analysis is important and can yield much infor- formed to align the c-axis with either the vertical (the mation about physical processes occurring in the ice “polar” direction) or the E -W (“equatorial”) direction. A sheet as discussed above. subsequent rotation about the A4 axis would leave the grain in extinction. The procedure for finding the un- IMPROVEMENTS TO THE known tipping angle is accomplished by reversing the MANUAL TECHNIQUE above two steps. A rotation about A4 (of some arbitrary A reasonable fraction of the time involved in per- amount) brings the grain out of extinction; then a ro- forming fabric analysis with a Rigsby stage goes into tation about A2 brings the grain back into extinction. recording the final positions of the stages and the re- The angle of rotation of A2 is then the angle between sult of the operation to distinguish polar or equatorial the c-axis and vertical, or the c-axis and the E-W di- alignments. A partially automated technique records rection. Which of these two conditions applies can be the final positions of the stages using digital encoders determined (after setting A4 back to zero) by rotating and sends the results to a computer. The result of the AUTOMATED ICE FABRIC ANALYZERS 7 test to determine polar or equatorial alignments is also sin ␪ cos ␸ 1/2 sent. This is not an insignificant improvement, given cˆ ϭ ͩ sin ␪ sin ␸ ͪ ϭ ͩ 1/2 ͪ (2) that one is working in the cold (and dark, except for the cos ␪ ͱ2/2 light from the stage), and reading scales and writing numbers legibly into a notebook can be a painstaking task. Such improvements were discussed by Lange Looking at the grain from the rotated view is equiva- (1988) and Morgan et al. (1984). They found that the lent to rotating the section by 45° about the y-axis. The time for analyzing grains could be reduced by about a new direction of the c-axis is then given by: factor of four, depending on the observer. cos 45 0 sin 45 1/2 .853 FULLY AUTOMATED OPTICAL ICE cˆЈ ϭ ͩ 010ͪͩ 1/2 ͪ ϭ ͩ .5 ͪ FABRIC ANALYSIS TECHNIQUES Ϫsin 45 0 cos 45 ͱ2/2 .147 Fully automated optical instruments for ice fabric ␪Ј ␸Ј analysis have been developed by three separate groups sin cos ϭ ͩ sin ␪Ј sin ␸Ј ͪ (3) over the last 3–4 years. These instruments were devel- oped in Australia by D. Russell-Head and C. Wilson cos ␪Ј (Russell-Head and Wilson, 2001), in Japan by N. Azuma and Y. Wang (Wang and Azuma, 1999), and in In this rotated view, the azimuthal angle for the the United States by D. Hansen and L. Wilen (Hansen c-axis is found from the inverse tangent of the y-com- and Wilen, 2002; Wilen, 2000). The basic principle be- ponent over the x-component of cˆЈ which gives 30.4°. hind all of the instruments is similar, so we discuss the This extinction angle constrains the c-axis to lie on one similarities first, and later elaborate on the differences. of the two dashed lines shown in the Schmidt plot (Fig. We also discuss briefly an additional automated optical 3c). These lines were obtained by applying the inverse apparatus that yields qualitative fabric information. 45° rotation matrix to the two planes (lines on a Schmidt plot) obtained from the 45° view extinction Common Principles angle. Note the four intersections of the different lines, Let us imagine that we place an ice thin section one of which is the true c-axis direction. A third image between crossed polarizers, and record a series of im- series, with a 45° view through the section from the ages as the polarizers are rotated over at least a 90° opposite side (Fig. 4c) yields the two dotted lines (Fig. range. For each grain in the section, an angle of extinc- 3d) on the Schmidt plot that unambiguously determine tion can be determined from the series of images. the c-axis direction. (White light is used for these measurements. Then, no Including the effect of refraction is not difficult and grains appear dark for the reason discussed in point 3, essentially requires one to correct the angle for the different views using Snell’s law (Wang and Azuma, Optics Review and Notation). The angle of extinction 1999; Wilen, 2000). determines two possible planes in which the c-axis of a All of the automated ice fabric analyzers work on the grain must lie. (As discussed earlier, we refer to this above principles, with some variations. The differences ambiguity as the 90° degeneracy.) Now, the same pro- lie mainly in the particular views taken of the section cedure is carried out with a different view through the and the way in which these views are obtained. In the thin section. This again determines two planes in case of the Australian machine, an extra optical ele- which the c-axis must lie. The intersection of the planes ment is employed that removes the 90° degeneracy and yields four possible directions (or distinct points on a allows the c-axis to be determined with fewer views Schmidt plot) for the c-axis of the grain. To pick be- through the section. There are also some differences in tween these possibilities, a third sequence is required. the details of data analysis. In the following, we discuss For some very special c-axis orientations, one or more some specifics of the three different instruments. additional series of images (giving extinction angles) may be required to uniquely determine the c-axis di- U.S. Instrument rection. The U.S. instrument, shown in Figure 5, employs a This procedure is best illustrated with a specific ex- fiber optic white light source, one fixed B&W video ample. Let us suppose that the c-axis of a grain is given camera and four rotations stages. Two of the rotation ␪ϭ ␾ϭ by the polar and azimuthal angles: 45°, 45°. stages contain the polarizers, and the other two (table For simplicity, we neglect refraction here. (We are not and sample stages) are used to rotate the thin section neglecting the effect of birefringence, only the change to specified orientations. For each orientation of the in direction of a light ray as it refracts into a sample.) section, a sequence of 20 images is acquired as the The c-axis is shown on the Schmidt plot in Figure 3a. A polarizers rotate by 5°-increments. Each image is an series of images is taken looking normal to the section average of ten video frames. The image resolution is (Fig. 4a), and the extinction angle is found to be 45°. 576 by 576 pixels. The field of view is 100 by 100mm. This constrains the c-axis to lie along one of the two The image sequences are acquired for 9 different an- solid lines shown on the Schmidt plot in Figure 3b. An gular settings of the table/sample given by: 0/0, 45/0, additional series of images looking through the thin 45/45, 45/90, 45/135, 45/180, 45/225, 45/270, and 45/ section at a 45° angle (Fig. 4b) yields a value of 30.4° for 315. All of the imaging and rotation of stages is done by the extinction angle. This result is easily obtained us- computer and takes 16 minutes. The nine image se- ing rotation matrices as follows. Denote the c-axis by quences (60 Mb) are stored on mass storage media and the unit vector: analyzed whenever convenient. To do this, the grains 8 L.A. WILEN ET AL.

Fig. 3. a: Schmidt plot showing grain with c-axis specified by ␪ϭ extinction angle measured from the 45° rotated view. d: Schmidt plot 45°, ␾ϭ45°. b: Schmidt plot showing c-axis directions consistent with showing additional c-axis directions consistent with the extinction the 45° extinction angle measured from the normal view. c: Schmidt angle measured from the 45° rotated view from opposite side. plot showing additional c-axis directions consistent with the 30.4°

(or grain regions) to be analyzed are specified. A simple ing the unique c-axis orientation from the extinction mapping algorithm allows each grain region to be angles is as follows. To every c-axis direction (or point tracked through all the sequences. For each grain, a fit on a Schmidt plot), there corresponds a unique set of to the extinction curve yields an extinction angle for extinction angles for the nine sequences. These are ␣i every sequence. These are denoted by exp where i found as in the example by rotating the c-axis in the indexes the sequence number. The technique for find- appropriate way (for each of the 9 sequences), and then AUTOMATED ICE FABRIC ANALYZERS 9

Fig. 6. Schematic diagram of the Japanese ice fabric instrument. Fig. 4. Diagram of the three views of the thin section used in the Reproduced from Annals of Glaciology, Wang and Azuma, Vol. example in Fully Automated Optical Ice Fabric Analysis Techniques. 29,1999, with permission of the International Glaciological Society. Photo courtesy of Y. Wang.

outlines by hand. Either way, the grain boundary outlines may also be used to find textural character- istics of grains. Japanese Instrument The Japanese instrument is shown in Figure 6. The setup consists of a mobile color camera, rotatable po- larizers, and rotatable sample stage and a white light source. To obtain different views through the section, the camera is moved laterally on a translation stage and also rotated to point back to the sample. The view- ing angle is 20°. The thin section is rotated using a Fig. 5. Schematic diagram of the U.S. ice fabric instrument. Re- stepping motor and gears. The orientations are analo- produced from the Journal of Glaciology, Hansen and Wilen, Vol. 48, gous to the ones listed above for the U.S. device, but 2002, with permission of the International Glaciological Society. with 45 replaced by 20 (i.e., 0/0, 20/0, 20/45, etc.). There are small corrections to the polarization (for the 20° view settings) because the optical path is not perfectly calculating the azimuthal angle of the rotated c-axis. normal to the polarizers. With this system, the grain ␣i ␪ ␸ Denote these theoretical extinction angles as th( c, c) regions are chosen first, by taking a preliminary se- ␪ ␾ where c and c specify the c-axis direction and i quence of images with the camera in the vertical (0° indexes the sequence number. Define the function viewing angle) position and rotating the polarizers 2 ␪ ␸ ϭ ¥ 2 ␣i Ϫ␣i ␪ ␸ 2 R ( c, c) i sin 2[ exp th( c, c)]. R is close to (also by stepper-motors and gears) by 5°-increments zero whenever the theoretical and experimental extinc- over a range of 90°. From these images, automatic tion angles are in close agreement. The factor of 2 in image processing is used to find grain outlines of the the argument of the sine accounts for the 90° degener- individual crystals and pick 3 ϫ 3 pixel regions in the ␣i acy (adding multiples of 90° to exp does not change the center of each grain. Once these are chosen, the polar- 2 2 ␪ value of R ). A minimization of R with respect to c and izers are rotated through 90° in 2°-increments, and the ␾ c determines the unique c-axis direction. average gray values of the grain regions are stored in The grains that are to be analyzed can be specified in data files. (These data files require very little memory a number of different ways. compared to the large image files stored in the U.S. technique.) This process is then repeated with the cam- 1. The grains may be chosen manually from the 0/0 era moved to the 20° view, and with the ice sample in sequence of images by clicking on a region in each each of the 8 positions. A mapping algorithm allows the grain. grain regions to be tracked through all 8 settings. The 2. A grid may be defined and each region on the grid field of view for this instrument is 46 ϫ 35 mm and the analyzed. Grid points that fall on grain boundaries image size is 640 ϫ 480, yielding a resolution of or other anomalous regions prove impossible to an- .072 pixel/mm. alyze and are discarded automatically. From the stored intensity values, the intensity ver- 3. Image analysis may be performed to find grain sus polarizer angle curve is fit to give the 9 extinction boundaries, and the grain boundary outlines may be angles for each grain. In contrast to the U.S. technique, used to automatically pick regions in the center of the determination of the c-axis direction for each grain grains. This works well on very clean sections, but in is done in a way that is conceptually somewhat closer general, one may need to correct some fraction of the to the discussion in Optics Review and Notation. From 10 L.A. WILEN ET AL. could be obtained continuously down the length of a core. A section of the core was machined down along its length to leave a thin (0.1–6 mm width, 6–16 mm length) rectangular piece sticking out from the side. This protrusion was essentially a continuous thin sec- tion running down the core. A polarized laser beam was aimed through the thin section and analyzed with a second polarizer and light detector as the core was translated along a track. Measurements were taken with the light propagating through the ice at various angles. Different curves for the light intensity vs. angle were obtained for different grains. Each curve had a peak in intensity, and the position and height of the peak provided qualitative information about the c-axis Fig. 7. Schematic diagram of the Australian ice fabric instrument. Reproduced from the Annals of Glaciology, Wilson et al., Vol. 37, 2003, direction. The linear size of grains could also be mea- with permission of the International Glaciological Society. sured by sensing abrupt changes in the light intensity as the core was translated at a known speed (see also Zagorodnov et al., 1991). two sequences, the intersection of planes mathemati- ALTERNATIVE NONOPTICAL METHODS cally determines four possible c-axis directions. To FOR ICE FABRIC ANALYSIS choose between these, a set of criteria was developed X-Ray Analysis that looks at inequalities between the extinction angles The basic ideas for using X-ray diffraction to deter- for the various sequences and deduces which of the four mine the crystallographic orientation of crystals can be choices is correct. found in most standard texts on condensed matter From the grain outlines determined from the prelim- physics (see Ashcroft and Mermin, 1976) In the Laue inary sequence, textural parameters such as grain size method, a broad band (i.e., not monochromatic) source and shape can be determined, as well as the spatial of X-rays is directed to a sample producing a Bragg relationship between grains. diffraction pattern that can be used to fix the orienta- tion of the crystal. The advantage of using X-rays for Australian Instrument ice is that both the c-axis and a-axis directions can be In the Australian instrument (Fig. 7), different views determined. through the section are accomplished by using five Mori et al. (1985) adapted and optimized this tech- separate color cameras looking at the sample from nique to ice and developed an instrument for automatic different positions. The sample is illuminated with an ice fabric determination. They employed an algorithm LED light source. One camera looks at the thin section for analyzing the diffraction pattern that significantly straight on, and the other four are positioned off to reduced the time needed to determine the crystal axes. opposing sides at a fixed angle to the vertical. With this The basic idea was to identify groups of spots in the system, the sample itself does not need to be rotated. pattern that were all related to a common “zone axis” The image resolution is 1,000 ϫ 1,000 pixels. The ice is that corresponded to a low index direction in the crys- translated to access all of the grains in a large thin tal. Each zone axis was associated with the correct section. A sequence of images with the polarizers ro- index by comparing measured angles between pairs of tating is acquired with all of the cameras simulta- zone axes with theoretically expected values for differ- neously. From the images, extinction angles are deter- ent pairs of low index directions. Once two (linearly mined for each of the camera angles for all of the grains independent) low index directions were specified, the in view. The use of a retarder allows one to find the crystal orientation was determined. unique plane of the c-axis for each view. Once the The apparatus is shown in Figure 8. A video image of unique plane containing the c-axis is determined for the sample through crossed polarizers was used to find each of the views, the plane intersections are used to the coordinates of the grains, which were then auto- find the c-axis direction. Because the 90° degeneracy is matically positioned (one at a time) into the X-ray removed using this technique, fewer views suffice to beam using a translation stage. The diffraction spots determine the c-axis direction. In common with the on the direct image were weak, so a video signal of the other instruments, the images of the section can also be direct image was integrated for several seconds in a used to identify grain boundaries to find textural pa- digital image processor. The coordinates of the spots rameters such as grain size and shape, and also to were fed into a computer and the crystal orientations specify the spatial relationship between grains. A determined as described above. The crystal orienta- unique feature of this instrument is that grains can be tions could then be plotted up on fabric diagrams. Us- identified by calculating the c-axis direction of each ing the known positions of the grains, the misorienta- pixel in the image and color-coding the direction to tion between adjacent grains could also be determined. produce an AVA (analysis of the distribution of the The total time to analyze 100 grains was approxi- axes, “Achsenverteilungsanalysis”) diagram. mately 3 hours. Additional Automated Techniques Radar Techniques Zagorodnov et al. (1994) discussed a technique Recent measurements by Fujita et al. (1993) showed whereby some information about the fabric and texture that the birefringence of ice extends down to radio AUTOMATED ICE FABRIC ANALYZERS 11 crystal of birefringent material, whose birefringence depends on the fabric (Hargreaves, 1978; Polder and van Santen, 1946). The optic axis of the material is given by the average direction of the c-axes over all the crystals in the sample (in this case the ice sheet). The birefringence is given by the amount to which the c- axes are concentrated in the average direction. So, for example, if the c-axes of a sample were arranged in a cone (similar to that discussed for the acoustic tech- niques, below), whose axis of symmetry pointed in some direction, the optic axis would coincide with that symmetry direction. The birefringence would lie some- where between the single crystal value and zero, de- pending on the cone angle. For a cone angle of 90° (i.e., random fabric), the polycrystal would behave as an isotropic material with no birefringence. With this model, polarized radar measurements of the ice sheet can be treated using the formulism devel- oped in section III. For example, if the transmitter and receiver are crossed and rotated together, the mea- sured intensity yields an extinction curve. The mini- mum in intensity (i.e., extinction angle) will occur when the optic axis lies in the polarization direction of one of the antennae. The contrast of the extinction curve along with the ice sheet thickness (calculated Fig. 8. X-ray apparatus for automated fabric measurement. Re- from the round trip echo time) can determine the cosine produced from the Annals of Glaciology, Mori et al., Vol. 6, 1985, with of the phase difference between the ordinary and ex- permission of the International Glaciological Society. traordinary wave. (Recall that for a thin single crystal, the contrast could be related to the polar angle of the c-axis; here, the birefringence of the polycrystal is not known a priori and the ice is thick (i.e., ͉n Ϫ n ͉d/␭Ͼ frequencies. They determined the difference in dielec- e o 1), hence the polar angle of the optic axis cannot be tric constant for electromagnetic waves propagating determined unambiguously. However, the cosine of the parallel and perpendicular to the c-axis in an ice single crystal to be 0.037 Ϯ 0.007 at 9.7 GHz, and suggested phase difference still contains useful information about that this result remains valid into the MHz frequency the fabric.) range. [The average dielectric constant in the fre- Liu et al. (1994) employed 50-MHz polarized radar to quency range 106–1013 Hz is about 3.15 at Ϫ20°C and show that an abrupt change in the fabric symmetry depends weakly on temperature. See Fujita et al. axis occurs at Upstream B along a line perpendicular to (2000).] Later, using a very precise microwave resona- the ice stream flow. Fujita and Mae (1993) showed that tor technique, Matsuoka et al. (1997) determined the 179-MHz polarized radar measurements were consis- dielectric anisotropy to be 0.0339 Ϯ .0007 at 30– tent with the symmetry of the fabric (as measured by 40 GHz. They also performed measurements at 1 MHz standard optical techniques) at Mizuho Station, Ant- and found a similar value. arctica. Polarized radar measurements take advantage of the It should be noted that radar (polarized or unpolar- birefringence to measure the fabric of ice. In a typical ized) can also be used to detect locations of abrupt experiment, polarized waves (typically between 50– changes in the fabric of the ice. At such locations, the 300 MHz) are transmitted downward into the ice sheet change in fabric is accompanied by a change in the and reflect from the bedrock at the bottom of the ice or effective dielectric constant, leading to wave reflec- from layers (discontinuities in dielectric properties) in- tions. The round-trip time for echoes yields the depths side the ice itself. The upward reflection intensity and at which abrupt fabric variations occur. Care must be total transit time are measured with a polarized re- taken in the interpretation of such measurements be- ceiver. The polarization direction of the transmitter cause abrupt changes in the dielectric properties can and receiver antennae can be varied to any desired also arise from changes in ice density or electrical con- direction. For example, in analogy with the optical ductivity, resulting in non-fabric related reflections techniques, the two antennae may be crossed and ro- (Fujita et al., 1993, 1999; Seigert and Fujita, 2001). tated together. Other variations are also commonly However, reflections due to electrical conductivity can used, such as keeping the two aligned (co-polarized) be reduced by using higher frequencies (Fujita and and rotating them together, or keeping one fixed and Mae, 1993; Fujita et al., 2000). For example, at fre- rotating the second. quencies in the range 150–300 MHz, conductivity- The wavelength of the radio waves is much larger based reflections are greatly reduced. Below about than the crystal sizes in the ice sheet, but is much 1,000 m, the density of the ice is very constant and, smaller than the ice sheet thickness. Using mixture hence, in principle, radar measurements can detect theory, it has been shown that, under these conditions, fabric changes in deeper ice with high reliability (Fu- a polycrystal can be treated effectively like a single jita, personal communication). 12 L.A. WILEN ET AL. It should be emphasized that, in contrast to ice cores, ric can be used to calculate the wave speeds, but there radar is a potentially viable method to probe ice fabrics is no unique way to invert the acoustic measurements over very wide regions in the ice sheet. By using proper to calculate the fabric. However, in many cases the platforms like airplanes or over-snow vehicles, it may fabric is known to have a high symmetry a priori (from be possible to construct a 3-D image of the fabric evo- other measurements). For example, the fabric at lution in the ice sheet (Fujita et al., 2003). GISP2 and GRIP is azimuthally symmetric about the axis of the core. A key desired measure of the fabric is Acoustic Methods the degree to which c-axes have rotated toward the Ice crystals are anisotropic with regard to acoustic as vertical. Hence, a one- (or possibly, few-) parameter well as electromagnetic waves. Both sonic and seismic model of the ice fabric is often used to interpret the techniques have been used to characterize ice fabric. sonic velocity results. For example, it is typically as- Both refer to acoustic waves propagating through the sumed that the ice fabric can be represented by a solid ice. Sonic techniques typically probe the ice at length cone (circle on the Schmidt plot) where the density of scales on the order of centimeters to meters using high c-axes within the cone is constant and where no c-axes frequency (30 Khz–3 MHz) acoustic compressional and fall outside the cone. The cone angle represents the shear waves. Seismic techniques probe the ice at length degree to which c-axes have rotated toward the verti- scales on the order of kilometers using low (3–20 Hz) cal. With this one-parameter model, a single measure- frequency excitations (Bentley, 1972). We discuss the ment of the sonic velocity can determine the cone angle. two methods briefly. In practice, more than one measurement is used to Sonic Techniques. The speed of sound depends on subtract out the effect of other physical properties of the orientation of an ice crystal. For example, for com- the ice (such as temperature and density) that also pressional waves in a single crystal, the speed varies affect the sound velocity. So, for example, the P-wave from about 3,800–4,000 m/s, depending on crystal ori- velocity is usually measured along the core axis and entation. The measurement of sound velocity in a poly- perpendicular to it. The difference in the two velocities crystal can yield an average orientation for the assem- can then be used to calculate the cone angle for the blage of crystals. A number of workers have used this solid cone model. technique to characterize the fabric of an ice core The setup employed by Anandakrishnan et al. (1994) (Anandakrishnan et al., 1994; Bennett, 1968; Herron et is shown in Figure 9. S-waves and P-waves are propa- al., 1985; Kohnen and Gow, 1979; Langway et al., gated through a slab of ice cut from an ice core. Each 1988). kind of wave probes a particular weighted average of Because the velocities measure only a weighted av- the orientation of the crystals throughout the volume erage of the crystal orientations, knowledge of the fab- in which the wave propagates. The weighting depends on the direction of propagation and the type of wave being propagated. Four types of measurements were performed. P-wave (compressional waves) velocities were measured propagating along the core axis and also perpendicular to the core axis. S-wave (shear wave) velocities were measured for waves of two or- thogonal polarizations propagating along the core axis. The P-wave measurements were used to derive the cone angle for the fabric as a function of depth. Going beyond the cone model somewhat, the shear waves propagating down the core axis in two orthogonal po- larizations were used to discern a small azimuthal asymmetry in the fabric. Sonic Borehole Logging. It is also possible to mea- Fig. 9. Sonic apparatus for fabric measurement (Anandakrishnan sure the speed of acoustic waves propagating in the et al., 1994). a: Arrangement for measurement of P-wave velocity along core axis. b: Arrangement for measurement of P-wave velocity walls of a borehole left behind by the ice core. The transverse to core axis. c: Transducer arrangement for S-wave gen- technology for such measurements is somewhat com- eration. Modified from Anandakrishnan et al. (1994). plicated, because the apparatus must be operated on a

Fig. 10. Borehole sonic logging device. Reproduced from J Geo- phys Res, Bentley, Vol. 77, 1972, with permission of the American Geophysical Union. Photo courtesy of C.R. Bentley and the Simplec Corporation. AUTOMATED ICE FABRIC ANALYZERS 13 long cable that is extended down many meters into the waves provide additional information. For example, in hole, but once developed, allows for a continuous mea- the Upstream B region on Whillans Ice Stream, West surement of ice fabric properties down the entire bore- Antarctica, ice was nearly isotropic in P-wave surveys hole length. This technique was pioneered by C. Bent- but exhibited strong shear-wave splitting in reflected ley (1972) at Byrd Station, Antarctica. More recently it shear waves, shear waves arising from P-to-S conver- has been used by K. Taylor at Dye-3 (Taylor, 1982; sions of basal reflections, and natural-source (micro- Thorsteinsson et al., 1999) and G. Lamorey at Siple earthquake) waves, indicating c-axis clustering toward Dome, GISP2 and GRIP (Lamorey, 2002). A typical a near-vertical transverse plane (Bentley et al., 1987; setup for borehole logging is shown in Figure 10. A Blankenship et al., 1987; Blankenship, 1989). mechanism accurately measures the amount of cable Especially for simple seismic experiments, data may spooled out, and hence the depth of the instrument. be insufficient to allow a unique determination of the Sound waves are generated from a transducer located velocity-depth hence anisotropy-depth function, with near the top of the instrument. The sound refracts from trade-offs between the thickness of anisotropic ice and the liquid in the borehole into the ice, propagates down the strength of the anisotropy (e.g., Blankenship and the ice, and is received at two locations below with Bentley, 1987). Careful design of experiments, often separate receivers. The time difference for reception in with crossing survey lines sampling a restricted vol- the two receivers and the spacing of the receivers yields ume of an ice sheet, resolves angular issues. Use of the sound speed in the ice. Two receivers instead of one refracted waves with a range of offsets between source are used to eliminate any extra time delays caused by and receiver (hence a range of depths sampled in the the electronics and the time for the sound to propagate ice sheet) as well as reflected waves from the bed pro- through the liquid to the ice. As with the acoustic vides additional insight to the depth-variation of the technique discussed earlier, the results yield some av- anisotropy (Bentley, 1971). Calibration against ice-core erage measure of the fabric that must usually be inter- measurements (Blankenship and Bentley, 1987) sim- preted with a simple model that presumes some knowl- plifies this exercise greatly. edge of the fabric symmetry. The latter is often deter- If c-axis fabric changes abruptly with position (that mined from optical measurements on thin sections is, changes over a distance that is short compared to from the core. the seismic wavelength being used), a reflection will be An obvious advantage of the sonic borehole logging generated. The strength of the reflection provides in- method is that the fabric record acquired is continuous formation on the contrast in fabric across the interface, and also that it averages over a large volume (and and the phase reveals whether it is a fast-to-slow or hence, number) of crystals compared to the traditional slow-to-fast contrast (Bentley, 1971; Burkett, 2000). methods using thin sections. The latter feature is de- Care must be taken to exclude other possible sources of sirable because it reduces statistical noise, but can be a reflections such as internal moraine. Calibration of re- disadvantage if high spatial resolution is needed to flection strength can be difficult. Where multiple reflec- observe small-scale features in the fabric. An added tions (shot-bed-surface-bed-receiver) are visible, the advantage of borehole logging is that the technique near-perfect reflection from the surface allows (with does not require processing of the core itself and, hence, appropriate corrections for attenuation and geometri- there is no competition for core samples. The technique cal spreading) the basal reflection coefficient to be also could be used in access holes bored rapidly through learned by comparing the strengths of the two basal production of chips or meltwater without recovery of reflections to determine energy loss; comparison of di- core. rect internal-reflector and basal-reflector strengths Such methods have been successful in resolving the then calibrates the internal reflector (Burkett, 2000). abrupt change in ice properties that often marks the upper and sometimes the lower edge of ice deposited AUTOMATED OPTICAL FABRIC during the last ice age, and it is hoped that sonic TECHNIQUES IN OTHER logging may be able to quickly discern places where MINERAL SYSTEMS stratigraphic continuity in the ice is lost, resulting in a Two groups (Fueten and Goodchild, 2001; Heilbron- disruption of the climate record. ner and Pauli, 1993) have recently developed auto- Seismic Techniques. Seismic surveys offer a range mated microscopic techniques to measure the fabric of of techniques for determining crystallographic anisot- quartzites. Interestingly, these techniques rely on ropy of ice. Only some of these are highlighted here. quite different principles (compared to those for ice) Seismic techniques sample large sections of an ice that exploit interference colors and contrast in the ex- sheet rapidly, allowing characterization on the scale tinction curve. The details are a bit technical but the that controls ice-sheet flow. However, rapid spatial general idea is as follows. A thin section of the desired changes in character may be difficult to resolve owing sample is prepared to be of a specific and uniform ͉ Ϫ ͉ to the coarse sampling in comparison to thin-section or thickness. The thickness is chosen so that d ne no is borehole techniques. about 200 nm. Quartz has a birefringence of 0.009, so Because of the dependence of seismic velocity on this corresponds to a thickness of about 20 ␮m. Digital c-axis orientation, mean velocity determined over some images of the thin section (positioned normal to the interval provides a probe on the c-axis orientation in optic path) are acquired as crossed polarizers are ro- that interval for the direction and wave-type used. tated. As with the other techniques, the positions of the Reflection surveys (with reflections from the bed or extinction angles (or sometimes the intensity maxima from internal horizons) and refraction surveys may be occurring midway between the extinction angles) are used (e.g., Bentley, 1971; Kohnen and Bentley, 1973). used to determine two possible planes for the c-axis. To P-wave surveys are probably most common, but S- distinguish between these planes, a retarder is added 14 L.A. WILEN ET AL. to the arrangement. As discussed above (Optics Review grain boundaries, thereby lowering the overall system and Notation), the retarder breaks the 90° degeneracy energy. If this process continues, the subgrain bound- and causes the extinction curve to have a period of aries can eventually be considered to be low angle grain 180°. Hence, the unique plane containing the c-axis is boundaries between distinct grains. found. To find the polar angle, the contrast (maximum Since ice in an ice core gets older with depth, the gray value minus minimum gray value) of the extinc- expectation is that normal grain growth should cause tion curve is used. As noted above, for thin enough grains to increase in size continuously down the core. samples, the contrast of the curve is a calculable single- In many ice cores, however, it has been observed that valued function of the polar angle. If the c-axis is ver- the size of grains becomes constant below a particular tical, there is no contrast, and if it is horizontal, the depth. The prevailing explanation for this behavior is contrast is a maximum. Since the maximum transmit- that the onset of polygonization results in a continual ted light intensity may be sensitive to the sample thick- subdivision of larger grains, leading to a more or less ness and lighting conditions, it is usually calibrated constant grain size. using a grain in the sample known to have its c-axis To check this hypothesis, Alley et al. (1995) looked at horizontal. For a sample having a large number of the distribution of misorientations between neighbor- grains, this is often chosen simply to be the grain with ing grains in 5 samples from the Byrd Station ice core the highest maximum intensity (of all the grains) in its bracketing the depth at which downward increase in extinction curve. Once the polar angle is determined grain size ceased (Gow and Williamson, 1976). If poly- from the contrast of the extinction curve, the c-axis gonization were occurring, one would expect in deeper direction is fully determined up to an azimuthal rota- samples that the occurrence of low-angle grain bound- tion of 180°. This final ambiguity may be removed by aries would be higher for neighboring grain pairs com- taking images with the sample tilted slightly in two pared to random pairs. If recrystallization were occur- orthogonal directions. When this is done, the extinction ring (which could also result in smaller average angles for a grain shift slightly up or down in a pre- grains), then the occurrence of high-angle grain bound- dictable way depending on the grain’s absolute azi- aries would be higher for neighboring grains pairs com- muth. A number of other techniques, such as X-ray, pared to random pairs. The results of the study con- neutron, and electron diffraction, are also commonly cluded that polygonization was indeed active, and was used to analyze mineral fabrics (Ullemeyer et al., likely responsible for the constant grain size. The anal- 2000). These are outside the scope of the current re- ysis to determine the fabric and also the nearest neigh- view. bors of each grain was done manually, and took many hours. The study clearly indicated the need for similar NEW APPLICATIONS studies at other sites with preferably larger data sets. The development of automated ice fabric techniques Nearest neighbor correlation studies are an ideal is facilitating a number of new applications that were application for automated fabric analyzers. Once an either previously impossible, or could only be achieved outline of grain boundaries is produced from one or with prodigious effort. These applications exploit the more images of a thin section (discussed below), the knowledge of the c-axis direction for large numbers of identification of individual grains is easily automated. grains (compared to what can usually be obtained man- Grains in the thin section can then be numbered, ana- ually), the spatial relationship of the grains, and the lyzed to get the c-axes, and re-analyzed to determine texture (size and shape) of the grains. We will concen- the nearest neighbors of each grain. With these results trate here on a few examples of recent and ongoing tabulated, it takes only seconds to produce histograms studies that fall into the latter two categories. of grain misorientations. Using the automated fabric analyzer, Azuma et al. Nearest Neighbor Correlation Functions (2000) have recently applied nearest neighbor analysis A number of studies have discussed the idea that the to thin sections from the Dome Fuji ice core. They distribution of misorientations between neighboring calculated the misorientation between nearest neigh- grains in a sample may be different from the distribu- bor grains and plotted the results on a histogram show- tion of misorientations of random grain pairs (Alley et ing the percentage of grains in the sample vs. misori- al., 1995; Trimby et al., 1998; Wheeler et al., 2001). entation angle, over the range of depths from 0–2,500 (The misorientation between two ice grains is defined m (Fig. 11). A similar histogram was produced for simply as the angle between the two c-axis directions). random pairs of grains in the sample. In the range from There are many ways in which this situation can arise. 1,300–2,000 m, a preponderance of low-angle misori- We will concentrate on two specific ones, involving the entations between nearest neighbors was found, sug- formation of new grains that are thought to be relevant gesting that polygonization was active in this range. to deforming ice (Alley, 1992). As ice deforms, localized Wilson et al. (2003) applied an automatic fabric an- regions of high strain may develop. At these high strain alyzer to study the fabric of folded layers in shear regions, it may be energetically favorable for the nu- zones. Ice was deformed in the laboratory to produce cleation of grains in new orientations. This process, the desired deformation and nearest neighbor misori- known as recrystallization, results in new grains that entation analysis was applied to assess the nature and usually have high misorientations with their neigh- level of active grain formation. Histograms of misori- bors. A second grain formation process is known as entations of adjacent grain pairs and random grain polygonization. Polygonization is essentially the subdi- pairs were determined from the fabric of thin sections vision of a grain. It can occur when a grain is subjected cut from the sample at various stages of the deforma- to a bending stress. Dislocations will organize along tion process. These were used to argue that (1) neigh- walls between different parts of the grain to form sub- boring grains interacted to form special boundary re- AUTOMATED ICE FABRIC ANALYZERS 15

Fig. 12. Plot of the number in first bin of normalized misorienta- tion histogram versus depth.

and GRIP ice cores. Based on the Byrd results and other evidence, researchers have hypothesized that polygonization is responsible for the saturation in grain size. Twenty-five horizontal thin sections spanning a range of depths from 100 to 2,700 m were analyzed. The nearest neighbor correlations were analyzed using the method discussed by Alley et al. (1995) with one minor modification. First, the misorientations between all (as opposed to random) pairs of grains in the sample were calculated and a histogram (number of pairs hav- ing misorientations in range of angles composing bin) Fig. 11. Frequency distributions of (a) the angle between c-axes of was created. The bin sizes of this reference histogram adjacent grains (misorientation angle), and (b) the misorientation were adjusted until equal numbers of pairs fell into angle of two randomly chosen grains. Reproduced from Physics of Ice each bin. Next, the misorientations between all pairs of Core Records, Azuma et al., 2000, with permission of Hokkaido Uni- neighboring grains were calculated and a histogram versity Press. was created using the same bin sizes as the reference histogram. The numbers in each bin were also scaled by a uniform factor of Nbins/Npairs. In the absence of any lationships due to recrystallization and (2) the absence phenomena tending to correlate nearest neighbors, the of low-angle misorientation indicated minimal activity nearest neighbor histogram would have a value of one of polygonization. In a separate deformation experi- in each bin to within statistical error. In Figure 12, the ment, Wilson and Sim (2003b) studied the strain dis- result for the first bin is plotted as a function of depth. tribution and fabric related to varying layer orientation In the range from 0–1,500 m, a clear increase in low- in ice. The mechanical behavior of samples of anisotro- angle misorientations among nearest neighbors is dem- pic ice in various orientations under different types of onstrated, lending support to the polygonization hy- deformation was compared to the behavior of isotropic pothesis. A second study (not shown) using vertical ice under uniaxial compression. Here, the similarity sections was conducted and showed a similar increase between nearest neighbor and random pair histograms but with smaller slope, indicating that the polygoniza- was used to argue that grains were not influenced by tion of grains was occurring mostly in the horizontal their neighbors. plane. Wilen et al. (2002) have recently completed a de- tailed nearest neighbor analysis of thin sections from Automated Texture Applications the GISP2 ice core using the U.S. automated fabric The ability to analyze the texture of ice is closely analyzer and associated software. Grain sizes become connected to the determination of fabric. In order to roughly constant below about 700 m in both the GISP2 study the shapes and sizes of grains in a thin section, 16 L.A. WILEN ET AL.

Fig. 13. Plot of average grain length versus direction in sample from GISP2 at a depth of 1,681 m (vertical thin section).

Fig. 15. Frequency distribution of crystal aspect ratio and elonga- tion direction versus depth at Fuji Dome. Reproduced from Physics of Ice Core Records, Azuma et al., 2000, with permission of Hokkaido University Press.

Fig. 14. Plot of normalized deformation (A/B) for vertical thin sections from GISP2. 1993; Fitzpatrick, 2000; Goodchild and Fueten, 1998), so this step can be automated if one has a set of images where at least one image of the set shows contrast one must first have a method to find the pixel locations between any given pair of adjacent grains. The images composing each grain. From this information, the char- acquired by an automated fabric system (no matter acterization of the texture (and determination of neigh- what its principle of operation) must be such a set. By bor grains) is easily performed. There are simple par- design, if there is no contrast between two adjacent ticle analysis programs that will take an outline of regions in any image, these regions will be determined grain edges and return the pixel locations for each to have the same c-axis direction, and will not be dis- grain. So the first step in texture analysis is to obtain tinguished as separate grains. All of the automated an outline of all the grain boundaries in the sample. fabric systems have associated software that allows There are many algorithms that can be used to find grains to be identified from the images. edges along regions of contrast in intensity and/or color Wilen et al. (2002) recently investigated deformation at (Canny, 1986; Starkey and Samantaray, 1993; Eicken, GISP2 using the U.S. automated instrument. Grain out- AUTOMATED ICE FABRIC ANALYZERS 17 lines were generated by computer analysis of images and many helpful comments and suggestions from three then perfected manually. To find all of the grain bound- anonymous reviewers. aries, it was necessary to examine the thin section in the normal view and also one or more of the rotated views. To REFERENCES do this, a program was written that took the images from Alley RB. 1988. Fabrics in polar ice sheets: development and predic- a rotated view of the section (e.g., 45/0) and mapped them tion. Science 240:493–495. 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