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Development, Principles, and Applications of Automated Ice Fabric Analyzers

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Development, Principles, and Applications of Automated Ice Fabric Analyzers 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.
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