A Method of Determining the Strain-Rate Tensor at the Surface of a Glacier

Abstract

ABSTRACT. The rate of strain tensor at a p oint on the surface of a glacier may be determined by setting up a number of stakes in a pattern and measuring the rate of change of the distances between them. A suitable pattern consists of four stakes at the corners of a square with one stake at the centre. Five such patterns were used on Austerdalsbreen, Norway, in August 1956. The problem is to d educe the best values of the 3 independent components of the strain-rate tensor from the 8 measured quantities, and, for this purpose, a least-squares method, invented by Bond for the analogous problem in crystal physics, is used. The principal strain-rates are found to within about ±o ' 005 yr. -, and their directions relative to the stake system to within about ±0 · 5°. The directions and magnitudes of the principal stresses are then deduced from Glen's flow law and a suitable general theory. The directions of the principal strain-rates are in good agreement with the directions of the crevasses, but the experiment is inconclusive on the question of the magnitude of thl! stress n eeded to form a crevasse.ZUSAMMENFASSUNG. Der Tensor der Deformationsgeschwindigkeit an einem Punkt auf der Gletscheroberflache kann bestimmt werden, indem man St6cke in regelmassiger Anordnung auf dem Gletscher befestigt und die Anderung der Distanzen zwischen ihnen misst. Eine geeignete Anordnung besteht au! 4 Stacken an den Ecken eines Quadrats mit einem Stock in der Mitte. Funf solche Anordnungen wurden im August 1956 auf dem Austerdalsbre in Norwegen aufgestellt. Das Problem besteht nun darin au! 8 Messwerten die besten Werte fUr die 3 unabhangigen Komponenten des DeformationsgeschwindigkeitsTensors abzuleiten. Fur diesen Zweck wurde eine Methode der kleinsten Quadrate verwendet, die von Bond fUr ein analoges Problem in der Kristallphysik erfunden wurde. Die Hauptgeschwindigkeiten wurden innerhalb einer Fehlcrgrenze von ±0,005 Jahre-' bestimmt und ihre Richtungen in Bezug auf das Stocksystem innerhalb ± 0,5 0 . Die Richtungen und Grossen der H a uptspannungen wurden dann aus Glen's Fliessgesetz und einer entsprechenden allgemeinen Theorie abgeleitet. Die Hauptdeformationsrichtungen stimmen mit den Richtungen der GletscherspaIten gut uberei n , aber das Experiment lasst die Frage der zur Spaltenbildung notigen Zugspannung offen.

A preliminary investigation of the influence of basal and surface topography on supraglacial lake distribution near Jakobshavn Isbrae, western Greenland

“…There is a need to better understand the relationship between surface (S) and basal (B) topographic roughness spectra. There have been several investigations examining basal‐to‐surface roughness transfer functions (Nye, 1959; Budd, 1970; Hutter et al , 1981; Whillans and Johnsen, 1983; Gudmudsson, 2003), mathematically expressed as S(λ) = T(λ)B(λ), where transfer of basal spectral components (B) to surface spectral components (S) are controlled by the transfer function (T) (Budd, 1968, 1969). The functional form of T(λ) can be strongly dependent on ice thickness ( h ).…”

Supraglacial lake spatial structure in western Greenland during the 2007 ablation season

“…Earlier studies examined the relationship between basal structure and surface topography, suggesting that transfer of basal undulations to surface topographic structure peaks at a wavelength three times the ice sheet thickness, with a decline at longer wavelengths [ Nye , 1959; Budd , 1970; Budd and Carter , 1971; Whillans and Johnson , 1983]. This estimate was refined by Reeh [1982] and Jóhannesson [1992] who state that basal wavelengths less than the ice thickness are not translated into the surface topographic structure.…”

Kinematics of Spruce Creek rock glacier, Colorado, USA

“…At all but one location, five boulders were chosen that most closely approximated the geometry specified by Nye (1959). As there was no suitable boulder in the center of diamond G, only the four corner points were marked.…”

“…These methods were not available at the time of initiation of this study, and while future studies of low-strain-rate rock glaciers will undoubtedly make use of these methods, they do not yet offer data of the time depth of the current steeltape study. Nye (1959) proposed using steel-tape measurements to evaluate strain on ice glaciers and we used a modified version of his method. Nye's method involved placing five stakes in the ice, four in a square, or 'strain-diamond', pattern with the diagonals of the diamond parallel and perpendicular to ice-flow direction.…”