Abstract In 1957 through 1962 six deep holes were drilled by means of specially developed electrically powered hotpoints, 4 cm diameter aluminum pipes were placed in them, and annual inclinometer surveys were made to investigate the deformation field and flow law of the ice at depth. Although a strongly maritime climate with moderate temperatures implies that lower Blue Glacier should be temperate, freezing at depths as great as 200 m, sometimes even in summer, seriously hindered inclinometer surveys. This freezing cannot be due solely to chilling by winter cold and to leakage into initially dry pipes, but may also be due to wintertime changes of water Table in the glacier and to contamination of the ice by antifreeze. Another possibility, residual subfreezing zones carried down from the ice fall, seems unlikely. Because the relatively inextensible pipe slips lengthwise in the deforming hole, observations of pipe motion at best give only the two components of ice velocity perpendicular to the hole. Thus, a single hole gives two independent equations connecting the nine unknown derivatives of the velocity components; two holes give four equations: and three or more give at most six. Incompressibility of the ice, when applicable gives another. The remaining unknowns must be either neglected or estimated from assumptions about the flow field. At the Blue Glacier holes the longitudinal strain-rate is less than about 0.01 per year, becoming more extensional down-glacier and more compressional at depth, because the holes were moving through a reach in which the surface steepens and the bed becomes more steep-sided and flat-bottomed. Although the effective strain-rates are only about 0.01 to 0.1 per year, so that errors are relatively large, they are in reasonable agreement with flow laws deduced from laboratory experiments by Glen, from tunnel contraction by Nye, and from deformation of Athabasca Glacier bore holes by Paterson and Savage, except that in the range of strain-rates covered the viscosities found for Blue Glacier are about half those derived from the other studies.
W. S. B. Paterson. The physics of glaciers. Oxford, etc., Pergamon Press, 1969. viii, 250 p., illus. (The Commonwealth and International Library. Geophysics Division.) 35s. (cloth), 25s. (paper). - Volume 9 Issue 57
Blackhawk Mountain in southern California rises above southeastern Lucerne Valley at the eastern end of the rugged 4,000-foot escarpment that separates the San Bernardino Mountains on the south from the Mojave Desert on the north. Its summit is a resistant block of marble thrust northward over easily eroded uncemented sandstone and weathered gneiss. Spread out on the alluvial apron at the foot of the mountain is the prehistoric Blackhawk landslide, a lobe of nearly monolithologic marble breccia from 30 to 100 feet thick, 2 miles wide, and 5 miles long. The Blackhawk landslide and an adjacent older landslide, the Silver...
The descending plate and overriding block in a subduction zone are analogous to the guide surface and slide block in a slipper bearing, and subducted sediment is analogous to the lubricant. Subduction is more complex and varied, however, because the overriding block is not rigid, the sediment is buoyant, underplating can occur, and sediment supply can vary widely. A model based on the bearing analogy but taking these differences into account makes detailed quantitative predictions for actual sites, which are illustrated by calculations for five diverse examples: Mariana, 16°N; Mexico, 17°N; Lesser Antilles, 13°N (Barbados); Alaska, 153°W (Kodiak); and Japan, 40°N. It requires as input the geometry of the overriding block and the top of the descending plate, the distribution of density and permeability of the overriding block, the speed of subduction, the density and rheological properties of the subducted sediment, and the rate of sediment input. Its predictions include the profile of thickness of the layer of subducted sediment (all sites; maximum of 360 m at Mariana, 5300 m at Japan), the velocities of flow in the layer (all sites), the shear stresses exerted on the walls (all sites; low beneath accretionary prisms, up to 6 MPa beneath Japan), the rate of offscraping (none at Mariana and late Tertiary Mexico; 85% of input at Lesser Antilles; includes melange at Japan), the distribution and rates of underplating (none at Mariana, extensive at Japan), the zones of possible subduction erosion (extensive at Mariana; local at the others), the amount of sediment subducted to the volcanic arc (all sites; 2% of input at Lesser Antilles, 100% at Mariana), the qualitative pattern of flow at the inlet (five basic patterns; all sites), the upward flow of melange in many instances (none at Mariana; extensive at Japan), and, under relatively rare conditions, the formation of large‐scale melange diapirs (only at Lesser Antilles beneath Barbados Island).
Soviet observations of anomalously low values of the ratio of the compressional wave velocity to the shear wave velocity (V(p)/ V(s)) in a restricted volume around the locus of a future earthquake are duplicated by models based on the dilatancy hypothesis. In nature the cracks that cause the dilation may be oriented, leading to anisotropic seismic wave propagation in the anomalous region. The models show that vertical cracks are most effective in producing the observed effects, but that a slightly higher density of randomly oriented cracks will yield similar effects. The premonitory observations at Blue Mountain Lake, New York, are also duplicated by the models. These models demonstrate that V(p)/V(s) measured at the surface is not that of the anomalous zone, but is related to it by a transfer function, involving the shape and velocity gradient of the zone boundary.
Abstract The performance of a thermal ice-drill having a smooth, solid, impervious frontal surface, termed a “solid-nose hotpoint”, is determined by the velocities, pressures, and temperatures in the thin layer of warm melt water between the hotpoint and the ice. The efficiency, the speed of penetration, the temperature of the frontal surface, and the distribution of pressure on it can be calculated from the equations of non-turbulent fluid flow. For hotpoints whose frontal surfaces are isothermal and axially symmetric, these quantities are functions of the total input of power Q of the weight W on the hotpoint, of the radius a and “shape factor” S of the frontal surface, and of the pertinent physical properties of water and ice. The calculation shows that with increasing “performance number” the efficiency E decreases and the surface temperature θ 0 increases. Thus, for example, E = 1·00 and θ 0 = 0°C. when N = 0.0 E = 0·76 and θ 0 = 48°C when N = 1.4; and E = 0·60 and θ 0 = 103°C. when N = 3.0. The coefficient Λ is a constant equal to . The shape factor S is a dimensionless number between 0 and 1 that varies according to the shape of the frontal surface, greater values of S being associated with blunter profiles (thus S = 1.0 for a plane frontal surface perpendicular to the axis). For coring hotpoints the same numerical results are obtained, but the performance number is given by where 2 ϖ i a is the inside diameter of the hotpoint.
Abstract Nye’s theory of glacier sliding, when modified to incorporate Gilpin’s model of the liquid layer adjacent to foreign solids in ice, predicts non-zero sliding speeds at subfreezing temperatures. Although the predicted speeds are too small to affect glacier motion or even to be observed readily, the total distance of sliding of large glaciers should be adequate to produce bedrock striations. Dissolved solutes in the liquid layer increase the sliding speeds slightly. At temperatures below about – 1° C, 90% of the drag comes from the part of the bed-roughness spectrum at wavelengths between 0.2 and 20 mm regardless of solute concentration. If no more basal ice melts than refreezes (as in a cold glacier), the average liquid-layer thickness and, concomitantly, the sliding speed for given drag and roughness are governed by the ambient temperature. With net melting (as in a temperate glacier), on the other hand, they are governed by the rate of escape of the excess water and no conflict arises between the thickness requirement for run-off water flow and that for regelation water flow. Thus, the proper distinction is not between temperate and cold, but between net melting and no net melting. The theory applies to both cases.
The statistical nature and remarkable generality of Horton's law of stream numbers suggest the speculation that the law of stream numbers arises from the statistics of a large number of randomly merging stream channels in somewhat the same fashion that the law of perfect gases arises from the statistics of a large number of randomly colliding gas molecules. The fact that networks with the same number of first-order Strahler streams are comparable in topological complexity suggests equating "randomly merging stream channels" with a topologically random population of channel networks, defined as a population within which all topologically distinct networks with given number of first-order streams are equally likely. In a topologically random population the most probable networks approximately obey Horton's law but exhibit certain systematic deviations. For networks with given number of first-order streams, the most probable network order is that which makes the geometric mean bifurcation ratio closest to 4. For networks with both order and number of first-order streams specified, the most probable networks have the property that the bifurcation ratio of the second-order streams is always close to 4 and, hence, that the bifurcation ratios respectively decrease, remain unchanged, or increase with order and the corresponding curves on the Horton diagram are respectively concave upward, straight, or concave downward according as the geometric mean bifurcation ratio is less than, equal to, or greater than 4. Statistical comparison of these properties with 172 published sets of stream numbers strongly supports the conclusion that, as speculated, populations of natural channel networks developed in the absence of geologic controls are topologically random and, hence, that the law of stream numbers is indeed largely a consequence of random development of channel networks according to the laws of chance.
Equations are derived for the speed and direction of migration of air-, vapor-, or brine-filled triaxial ellipsoidal cavities of any orientation, and expected velocities are computed for the spherical, cylindrical, and discoidal cases that have been investigated experimentally. In the case of air bubbles agreement is only fair for approximately spherical bubbles trapped during freezing and is somewhat better for drilled cylindrical holes open to the atmosphere. The lack of agreement and the considerable scatter in the data are probably due to uncontrolled variations in pressure and shape and to the slow accumulation of frost. In the case of discoidal vapor figures the agreement is much poorer and the scatter is much greater, probably because of large uncontrolled variations in shape, air content, and temperature of the figures. Calculation of the effect of small size, for which viscous flow of the vapor is important, shows it to be negligible for the figures used in the experiments. For spherical brine pockets at temperatures a few degrees or more below freezing agreement is fairly good, considering the uncertainties in the diffusion coefficient, but at the ice point the predicted speed is about 5 times that observed, probably because the brine concentration in the pockets at this temperature was not in fact zero as required by the theory.
