Introduction
Exponential functions of the form, dV p/dz = (dV p/dz)0 e −γz , where (dV p/dz)0 and γ are constants, have been used successfully to approximate segments of curves of compressional wave velocity gradient dV p/dz versus depth z on the ice sheets of Greenland (Reference Brockamp and PistorBrockamp and Pistor, [1968]) and of Antarctica (Reference Kohncn and BentleyKohnen and Bentley, 1973). Kohnen and Bentley correlate the depths at which the constants change at old and new “Byrd” stations with significant depths in the densification process of the firn. They suggest that sequences of exponential approximations might be used generally to relate seismic velocity gradients to glaciological parameters and to densification mechanisms. Accordingly, a general study of short refraction data from over-snow traverses throughout Antarctica has been undertaken to seek relationships between P-wave velocity gradients and accumulation, temperature, and the structure and metamorphism of polar snow cover.
Fig. 1. Part 1
Fig. 1. Part 2.
Fig. 1. Part 3
Fig. 1 Part 4. Fig. 1 Compressional wave vewcity gradient versus depth at seismic stations along the Little America-Byrd Traverse, 1956-57, Sentinel Traverse, 1957-58, Horiick Traverse, 1958-59, Queen Maud Land Traverse 1, ¡964-65, and Queen Maud Land Traverse 2, 1965—66,
Results
Graphs of dV p/dz versus z have been constructed on semilogarithmic paper for short refraction velocity-depth data from fifty locations in Antarctica (Fig. I). The following oversnow traverses are represented: Little America-Byrd Traverse, 1956-57; Sentinel Traverse, 1957-58; Horlick Traverse, 1958-59; Queen Maud Land Traverse I, 1964-65; and Queen Maud Land Traverse 2, 1965-66. Individual stations are listed in Table I together with pertinent glaciological data and with geophysical data to be explained below. The maximum depth Z max sampled by each short refraction profile is a function of the length of the profile and varies from 50 m to 65 m along the West Antarctic traverses and from 80 m to 155 m along the East Antarctic traverses.
The plots may be divided fundamentally into two classes: type (a), fitted well by one straight line over the depth interval, ≈10 m-≈50 m, and hence similar to the new “Byrd” station graph of Reference Kohncn and BentleyKohnen and Bentley (1973, fig. 2); and, type (b), fitted well by not one but two straight lines over this interval. An additional straight-line segment appears at the lower ends of a few of the graphs. Depths of intersections of straight lines fitted to the graphs are listed in Table I under letter headings which match the lettering of Figure I. At seven stations no depths of intersection have been picked since the data there are not fitted well by straight lines. The mean depths to В and С are źB = 8.4±2.3 m and źc= 27.7±4.4 m respectively. No mean depth to D is given since it would be strongly biased by the limited sampling depth, which clearly cuts off almost all values greater than about 50 m.
Fig. 2. Mean compressional wave velocity gradient versus depth at seismic stations in Antarctica. • mean annual accumulation < 16okgm−2 year−1' (19 stations, b= 274±96kg m−2 year-1). О annual accumulation < 160 kg m−2 year−1 (16 stations, b=96±49 Kg M−2 year−1
Table.I. Geophysical and claciological data for selected seismic stations in antarctica
Both the velocity gradient and the occurrence of intersection С depend upon the mean annual accumulation, b. The dependence is illustrated in Figure 2. Depth-velocity gradient data from those stations for which measurements of accumulation are available have been arbitrarily divided into two approximately equal groups by separation according to whether b>160 kg m−2 year−1 (19 stations, b=274±96kg m−2 year−1) or b <160kg m−2 year−l (16 stations, b= 96±49 kg m−1 year−1). Mean values and standard deviations of the velocity gradients of the two groups are plotted in Figure 2. It is apparent (1) that values of P-wave velocity gradient itself are low at stations where accumulation is high, and (2) that the change in slope at intersection С increases with increased accumulation. The mean values of the group for which b < 160 kg m−2 year−1 have been divided at źB and źc (8.4 and 27.7 m), and straight lines have been fitted to the resulting linear segments by the technique of least squares. The other group has been divided only at źB as С is not obviously present, although a change in slope is suggested. The constants (dVp/dz)0 and slopes γ of the least-squares lines are given in Table II.
Table II. Parameters of least-squares lines through data
A bilinear regression was performed on the data in Table I to test the dependence of depths to B (ZB) and C (zc) on mean annual accumulation and mean annual temperature T. The regression equations are:
and
The partial and multiple correlation coefficients for Equations (1) and (2) are given in Table III.
Table III. Partial and multiple correlation coefficients
Discussion
An interval of constant slope on plots of ln (dVp/dz) versus z probably reflects the predominance of a particular metamorphic process in the corresponding depth interval, breaks occurring at depths where the predominant metamorphic mechanism changes. Upon comparing their seismic results at old and new “Byrd” stations with direct observations on ice cores made by Reference Gow and HalhertonGow (1965, 1970), Reference Kohncn and BentleyKohnen and Bentley (1973) correlate the breaks В and D with, respectively, the “critical depth” of Reference Anderson, Benson and KingeryAnderson and Benson (1963) and the depth where firn becomes impermeable. The “critical depth” is the limit (“close random packing”) beyond which grain packing is no longer an effective densification mechanism, and occurs when density equals about 0.55 Mg m−3 (Reference Anderson, Benson and KingeryAnderson and Benson, 1963, p. 400). The present results appear to conform with that correlation for B.
D is present on only ten graphs, presumably owing to insufficient profile length. Profile lengths at West Antarctic stations are not long enough conclusively to define D breaks below 50 m. At three inland sites in Antarctica, exclusive of the high East Antarctic plateau, where drilling has been done to sufficient depth, the firn-ice transition is observed or estimated to lie at 64 m (old “Byrd”; Reference Gow and HalhertonGow, 1965,) 56 m (new “Byrd”, Reference GowGow, 1970), and 58 m (“Southice”, Reference GowGow, 1968). Thus, only unusually shallow D breaks would be expected to appear in the graphs of Figure 1, as is indeed the case. Whether those D breaks that do appear represent truly shallow firn-ice boundaries or inaccuracy in the seismic method of determination is impossible to say for certain. The close correlation cited by Reference Kohncn and BentleyKohnen and Bentley (1973) suggests, however, that the former may well be the case. The depths to D at the three sites on the Queen Maud Land Traverses (55 m–64 m) are much shallower than estimated for the firn-ice boundary at the South Pole (110 m; Reference GowGow, 1968) and “Plateau” station (160 m; Reference GowGow, 1971). However, temperatures at the traverse sites are substantially warmer than at “Plateau” (—57°C), and accumulation rates are substantially less than at the South Pole (70 kg m−2 year−1; Reference GowGow, 1968), Further direct comparisons between seismic and drilling results are clearly needed.
The results of the current study indicate that С is a real and widespread seismic phenomenon in Antarctica. The glaciological significance of the appearance of С is that it suggests that two distinct mechanisms successively dominate the metamorphic process between the depth of closest-packing of snow grains and the firn-ice boundary. An interesting parallelism exists between the appearance of С and unconfined compressive creep tests performed by Reference Ramseier and PavlakRamseier and Pavlak (1964) and Reference Mellor, Smith and OuraMellor and Smith (1967). Upon comparing the depthdensity curve presented by Reference GowGow (1968) for the 309 m drill hole at old “Byrd” station with depths to С listed in Table I, we estimate that С occurs in the density range, 0.62–0.68 Mg m−3. The approximate density range between В and С (0.55–0.65 Mg m−3) corresponds to the density range (0.53–0.64 Mg m−3) in which Reference Mellor, Smith and OuraMellor and Smith (1967) found that compressive viscosity was nearly independent of density during unconfined compressive creep tests on snow samples. Reference Ramseier and PavlakRamseier and Pavlak (1964) presented a similar curve of compressive viscosity versus density for snow from the South Pole which shows breaks at 0.47 and 0.625 Mg m−3. This correlation between seismic results and creep tests supports the interpretation of the seismic horizon as a real glaciological phenomenon; it should be tested by obtaining cores from locations where С is known to occur.
Acknowledgements
This work was supported by NSF grants GV-27044 and GV-32873.
