BUBBLY-ICE DENSIFICATION IN ICE SHEETS - I - THEORY

Dry snow an the surface of polar ice ice sheets is first densified and metamorphosed to produce firn. Bubbly ice is the nest stage of the tr ansformation process which takes place below the depth of pore closure . This stage extends to the transition zone where, due to high pressur es and low temperatures, air trapped in bubbles and ice begins to form the mixed air clathrate hydrates, while the gas phase progressively d isappears. Here we develop a model of bubbly-ice rheology and ice-shee t dynamics taking into account glacier-ice compressibility. The intera ction between hydrostatic compression of air bubbles, deviatoric (unia xial) compressive deformation of the ice matrix and global deformation s of the glacier body is considered. The ice-matrix pressure and the a bsolute-load pressure are distinguished. Similarity theory and scale a nalysis are used to examine the resultant mathematical model of bubbly -ice densification. The initial rate of bubble compression in ice shee ts appears to be relatively high, so that the pressure (density) relax ation process takes place only 150-200 m in depth (below pore close-of f) to reach its asymptotic phase, wherein the minimal drop between bub ble and ice pressures is governed by the rate of loading (ice accumula tion). This makes it possible to consider densification under stationa ry (present-day) conditions of ice formation as a special case of prim ary interest. The computational tests performed with the model indicat e that both ice-porosity and bubble-pressure profiles in ice sheets ar e sensitive to variations of the rheological parameters of pure ice. H owever, only the bubble-pressure profile distinguishes between the rhe ological properties at low and high stresses. The porosity profile at the asymptotic phase is mostly determined by the air content in the ic e. In the companion paper (Lipenkov and others, 1997), we apply the mo del to experimental data from polar ice cores and deduce, through an i nverse procedure, the rheological properties of pure ice as well as th e mean air content in Holocene and glacial ice sediments at Vostok Sta tion (Antarctica).