The deformation and compaction of partial molten zones

Summary. The segregation of melt from a partially molten source region requires a corresponding deformation of the unmelted residue ('matrix'). The role of matrix deformation during melt segregation is examined using simple one-dimensional models, for which the deformation consists only of bulk compression or 'compaction'. In model I, a volume fraction φ₀ of ascending mantle material undergoes pressure-release melting at a depth z = 0 (localized melting). Compaction of the matrix occurs in a boundary layer whose thickness (reduced compaction length δ_R) is proportional to the square root of the matrix viscosity. In the Earth's mantle, δ_R∼ 10–100 m, indicating that compaction cannot be important over large distances. Model II examines the case in which melting occurs over a depth range of order h (distributed melting). In the limit h ≪δ_R, the solution is the same as for the case of localized melting, except in a 'melting layer' of thickness ∼ h near z = 0. In the more realistic limit h ≫δ_R, compaction makes a negligible contribution to the balance of forces associated with melt segregation. This result is also valid for the more general case of two-dimensional flow. Compaction is therefore likely to be of negligible importance in the Earth's mantle, with the consequence that melt segregation can be accurately described by Darcy's law.     

A MULTIBLOCK PARTIAL LEAST SQUARES ALGORITHM FOR INVESTIGATING COMPLEX CHEMICAL SYSTEMS

The details of a general multiblock partial least squares(PLS)algorithm based on one originallypresented by Wold et al.have been developed and are completely presented.The algorithm can handlemost types of relationships between the blocks and constitutes a significant advancement in the modelingof complex chemical systems.The algorithm has been programmed in FORTRAN and has been testedon two simulated multiblock problems,a three-block and a five-block problem.The algorithm combinesthe score vectors for all blocks predicting a particular block into a new block.This new block is used topredict the predicted block in a manner analogous to the two-block PLS.In a similar manner if one blockpredicts more than one other block,the score vectors of all predicted blocks are combined to form a newblock,which is then predicted by the predictor block as in the two-block PLS.Blocks that both predictand are predicted are treated in such a way that both of these roles can be taken into account whencalculating interblock relationships.The results of numerical simulations indicate that the computerprogram is operating properly and that the multiblock PLS produces meaningful and consistent results.     

Diapirism in the earth's mantle: Experiments on the motion of a hot sphere in a fluid with temperature-dependent viscosity

The ascent of magma diapirs through the earth's mantle is modelled experimentally by the motion of a hot metal sphere through a fluid whose viscosity varies strongly with temperature. The dimensionless drag on the sphere (drag number D) and the heat transfer from it (Nusselt number Nu) are found as functions of the dimensionless velocity of the sphere (Peclet number Pe) and the viscosity contrast μ_∞/μ₀ = 10^γ, where μ_∞ and μ₀ are the viscosities of the fluid far from the sphere and at its surface. The drag D = D(Pe, γ) has two limits. For large Pe and small γ (“Stokes” limit), the drag approaches the Stokes' Law result. For small Pe and large γ (“lubrication” limit), the drag is orders of magnitude less than that predicted by Stokes' Law. Nu is a function of Pe alone. For reasonable values of the diapir radius and the viscosity contrast, the dimensionless scale height Pe/3 Nu may exceed a critical value, resulting in progressive melting during ascent. This suggests that diapirs may ascend great distances through the mantle while remaining largely molten. Lamont-Doherty Geological Observatory Contribution No. 3414.     

Accuracy characteristics of the electronics of waverider buoys used in the ARSLOE

During the Atlantic Remote Sensing Land Ocean Experiment (ARSLOE), October-November, 1980, a large number of meteorological and oceanographic instruments, especially wave-measurement instruments, were deployed in the ocean near the Army Corps of Engineers Pier, Duck, NC. About nine Waverider buoys were deployed in an approximately rectangular pattern, about 30 km wide by 40 km seaward. The Waveriders were an accepted reference for study of other wave-measurement instrument systems. Almost all of the Waverider buoys were calibrated on the rotating-arm facility of the NOAA, Engineering Support Office. Pre- and post-deployment calibrations formed the basis for tables and equations for correction of the Waverider measurements. The calibrations discussed here established that the Waveriders were measuring lower than specification, averaging about 5 percent low (10 percent for variance spectra coefficients.) Corrections for effects of fluctuations in water temperature on Waverider sensitivity were required and are provided. The manufacturer's modification to prevent future drift in sensitivity is also described.