Hindered settling of sand grains

The sedimentation rate of sand grains in the hindered settling regime has been considered to assess particle shape effects. The behaviour of various particulate systems involving sand has been compared with the widely used Richardson–Zaki expression. The general form of the expression is found to hold, in as much as remaining as a suitable means to describe the hindered settling of irregular particles. The sedimentation exponent n in the Richardson–Zaki expression is found to be significantly larger for natural sand grains than for regular particles. The hindered settling effect is therefore greater, leading to lower concentration gradients than expected. The effect becomes more pronounced with increasing particle irregularity. At concentrations around 0·4, the hindered settling velocity of fine and medium natural sands reduces to about 70% of the value predicted using existing empirical expressions for n. Using appropriate expressions for the fluidization velocity and the clear water settling velocity, a simple method is discussed to evaluate the sedimentation exponent and to determine the hindered settling effect for sands of various shapes.     

Reaction Between Ultramafic Rock and Fractionating Basaltic Magma I. Phase Relations, the Origin of Calc-alkaline Magma Series, and the Formation of Discordant Dunite

This paper presents results of modelling reaction between peridotiteand fractionating tholeiitic basalt in simple and complex silicatesystems. Reactions are outlined in appropriate binary and ternarysilicate systems. In these simple systems, the result of reactionsbetween ‘basalt’ and ‘peridotite’ maybe treated as a combination of Fe-Mg exchange and mass transferreactions at constant Fe/Mg. Fe-Mg exchange in ternary and higher-ordersystems is nearly isenthalpic, and involves a slight decreasein magma mass at constant temperature. Mass transfer reactions,typically involving dissolution of orthopyroxene and consequentcrystallization of olivine, are also nearly isenthalpic in ternaryand higher-order silicate systems, and produce a slight increasein the magma mass at constant temperature. The combined reactionsare essentially isenthalpic and produce a slight increase inmagma mass under conditions of constant temperature or constantenthalpy. Initial liquids saturated in plagioclase+olivine will becomesaturated only in olivine as a result of near-constant-temperaturereaction with peridotite, and crystal products of such reactionswill be dunite. Liquids saturated in clinopyroxene+olivine willremain on the cpx-ol cotectic during reaction with peridotite,but will crystallize much more olivine than clinopyroxene asa result of reaction, i.e., crystal products will be clinopyroxene-bearingdunite and wehrlite rather than olivine clinopyroxenite, whichwould be produced by cotectic crystallization. The Mg/Fe ratioof crystal products is ‘buffered’ by reaction withmagnesian peridotite, and dunites so produced will have high,nearly constant Mg/Fe. Production of voluminous magnesian dunitein this manner does not require crystal fractionation of a highlymagnesian olivine tholeiite or picrite liquid. Combined reaction with ultramafic wall rock and crystal fractionationdue to falling temperature produces a calc-alkaline liquid lineof descent from tholeiitic parental liquids under conditionsof temperature, pressure, and initial liquid composition whichwould produce tholeiitic derivative liquids in a closed system.Specifically, closed-system differentiates show iron enrichmentat near-constant silica concentration with decreasing temperature,whereas the same initial liquid reacting with peridotite producessilica-enriched derivatives at virtually constant Mg/Fe. Reaction between fractionating basalt and mafic to ultramaficrock is likely to be important in subduction-related magmaticarcs, where tholeiitic primary liquids pass slowly upward throughhigh-temperature wall rock in the lower crust and upper mantle.Although other explanations can account for chemical variationin individual calc-alkaline series, none can account as wellfor the characteristics shared by all calc-alkaline series.This process, if it is volumetrically important on Earth, hasimportant implications for (Phanerozoic) crustal evolution:sub-arc mantle should be enriched in iron, and depleted in silicaand alumina, relative to sub-oceanic mantle, acting as a sourcefor sialic crust It is probable that inter-occanic magmaticarcs have basement similar to alpine peridotite, in which sub-oceanicmantle has been modified by interaction with slowly ascendingbasaltic liquids at nearly constant temperature. Discordantdunite bodies in alpine pendotite may record extraction of sialiccrust from the Earth's upper mantle. ^*Present address: Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543     

INVERSION OF POST-STACK SEISMIC DATA USING SIMULATED ANNEALING1

Model-based inversion of seismic reflection data is a global optimization problem when prior information is sparse. We investigate the use of an efficient, global, stochastic optimization method, that of simulated annealing, for determining the two-way traveltimes and the reflection coefficients. We exploit the advantage of an ensemble approach to the inversion of full-scale target zones on 2D seismic sections. In our ensemble approach, several copies of the model-algorithm system are run in parallel. In this way, estimation of true ensemble statistics for the process is made possible, and improved annealing schedules can be produced. It is shown that the method can produce reliable results efficiently in the 2D case, even when prior information is sparse.