Abstract
The propagation of elastic waves in polycrystals is revisited, with an emphasis on configurations relevant to the study of ice. Randomly oriented hexagonal single crystals are considered with specific, non-uniform, probability distributions for their major axis. Three typical textures or fabrics (i.e. preferred grain orientations) are studied in detail: one cluster fabric and two girdle fabrics, as found in ice recovered from deep ice cores. After computing the averaged elasticity tensor for the considered textures, wave propagation is studied using a wave equation with elastic constants c=〈c〉+δc that are equal to an average plus deviations, presumed small, from that average. This allows for the use of the Voigt average in the wave equation, and velocities are obtained solving the appropriate Christoffel equation. The velocity for vertical propagation, as appropriate to interpret sonic logging measurements, is analysed in more details. Our formulae are shown to be accurate at the 0.5% level and they provide a rationale for previous empirical fits to wave propagation velocities with a quantitative agreement at the 0.07–0.7% level. We conclude that, within the formalism presented here, it is appropriate to use, with confidence, velocity measurements to characterize ice fabrics.
Highlights
The propagation of sound in polycrystals has long been the subject of studies
The prediction is accurate up to the second order in the local deviation of the elasticity parameters from their average values. This is justified for weak anisotropic single crystals or for fabrics with concentrated c-axes, that is, in general a system with a low variability in the elasticity tensor of the grains
Motivated by measurements in deep ice cores, we have inspected this small variability case in more detail, revealing an accuracy better than 0.5%
Summary
The propagation of sound in polycrystals has long been the subject of studies (for a review, see [1]). Among the many possible fabrics, girdle fabrics (defined below) are characteristic of ice encountered in convergent flow regions, where the vertical axis corresponds to the compression due to gravity and with a tensional axis due to a given ice flow direction [19] This is the case for ice along a ridge, a few hundred metres from a geographical dome; here, the dissymmetry in the surface slopes along and perpendicular to the ridge can induce a horizontal tension component in the strain field [20]. There is a need to provide accurate models for these media to answer the question of whether or not sonic logging is able to discriminate the different fabrics and, within a given fabric, to determine the degree of anisotropy This is the goal of this paper, where the propagation of elastic waves in polycrystals with cluster and girdle fabrics is studied. Where (A, C, L, N, F) are the elastic parameters of the elasticity tensor (see equation (3.3))
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