Thermal Convection in Ice Sheets: We Look But Do Not See

Thermal convection in the Antarctic and Greenland ice sheets has been dismissed on the grounds that radio-echo stratigraphy is undisturbed for long distances. However, the undisturbed stratigraphy lies, for the most part, above the density inversion in polar ice sheets and therefore does not disprove convection. An echo-free zone is widespread below the density inversion, yet nobody has cited this as a strong indication that convection is indeed present at d�pth. A generalized Rayleigh criterion for thermal convection in e1astic-viscoplastic polycrystalline solids heated from below is developed and applied to ice-sheet convection. An infinite Rayleigh number at the onset of primary creep decreases with time and becomes constant when secondary creep dominates, suggesting that any thermal buoyancy stress can initiate convection but convection cannot be sustained below a buoyancy stress of about 3 kPa. An analysis of the temperature profile down the Byrd Station core hole suggests that about 1000 m of ice below the density inversion will sustain convection. Creep along the Byrd Station strain network, radar sounding in East Antarctica, and seismic sounding in West Antarctica are examined for evidence of convective creep superimposed on advective creep. It is concluded that the evidence for convection is there, if we look for it with the intention offinding it.

Magma-Driven Multiple Dike Propagation and Fracture Toughness of Crustal Rocks

Dike swarms consisting of tens to thousands of subparallel dikes are commonly observed at Earth's surface, raising the possibility of simultaneous propagation of two or more dikes at various stages of a swarm's development. The behavior of multiple propagating dikes differs from that of a single dike owing to the interacting stress fields associated with each dike. We analyze an array of parallel, periodically spaced dikes that grow simultaneously from an overpressured source into a semi-infinite, linear elastic host rock. To simplify the analysis, we assume steady state (constant velocity) magma flow and dike propagation. We use a perturbation method to analyze the coupled, nonlinear problem of multiple dike propagation and magma transport. The stress intensity factor at the dike tips and the opening displacements of the dike surfaces are calculated. The numerical results show that dike spacing has a profound effect on the behavior of dike propagation. The stress intensity factors at the tips of parallel dikes decrease with a decrease in dike spacing and are significantly smaller than that for a single dike with the same length. The reduced stress intensity factor indicates that, compared to a single dike, propagation of parallel dikes is more likely to be arrested under otherwise the same conditions. It also implies that fracture toughness of the host rock in a high confining pressure environment may not be as high as inferred from the propagation of a single dike. Our numerical results suggest fracture toughness values on the order of 100 MPa root m. The opening displacements for parallel dikes are smaller than that for a single dike, which results in higher magma pressure gradients in parallel dikes and lower flux of magma transport.