Two thermal convection problems of geophysical interest are examined, theoretically. First, convection in the earth's mantle is treated on the basis of a one-dimensional 'strip model'. This model results from further simplification of the well known 'Rayleigh model'. For homogeneous, Newtonian fluids, the strip model yields results similar to those obtained by the Rayleigh method. The strip model is used to determine the critical Rayleigh number for convection in an internally heated two-phase fluid. The critical number depends on the parameters of the phase transition, the physical properties of the fluid, and the depth of the fluid layer. Depending on these factors, a univariant phase transformation may either enhance or hinder convective instability. For the olivine-spinel and spinel-oxides transitions in (MgFe)₂SiO₄ which are thought to take place in the upper mantle, it is shown that the critical Rayleigh number is altered only slightly from the critical number for convection in a fluid with one phase. This result holds both for convection in the entire mantle or convection restricted to the upper mantle. Hence the phase changes are of minor importance regarding the existence of mantle convection in general. A method for estimating the order of magnitude of the displacement of the phase surface as a function of Rayleigh number is outlined for a fluid with only one phase transition. The strip model is also used to treat convection in non-Newtonian fluids obeying a power law rheological equation. If the mantle is governed by a flow law of this type, it appears that convection can take place. Lastly, the procedure for applying the strip model to fluids with variable viscosity and thermal conductivity is outlined. The second convection problem concerns some aspects of convection of fluids in thin vertical fractures in the crust. A steady state model is developed to estimate the magnitude of the mass flow as a function of fracture thickness. It is shown that fractures of the order of a millimeter thick or greater can carry a measurable convective flow. A time dependent model is used to estimate the rate of decay of the mass flow with time. The results indicate that in fractures of the order of a centimeter thick, a measurable decrease of the mass flow takes place after a period of the order of a day. This rapid decay rate suggests that the principal effect of sea water convection in extensive fracture systems which are expected on mid-ocean ridge crests is to cool a volume of crustal rock in the vicinity of the fractures. Circulation of sea water in vertical fractures in the upper crust may provide an explanation of 1) the relatively low conductive heat flow measured at some locations on ocean ridge axes and 2) the very 'noisy' data obtained in the axial zone. / Graduation date: 1972

Thesis (M.S.)--University of Delaware, 2009. / Principal faculty advisor: Michael A. O'Neal, Dept. of Geography. Includes bibliographical references.

The best type of information about the Earth's interior is seismic. Seismic wave velocity depends on the value of the bulk modulus of the rock. The geophysicist Sir Harold Jeffreys derived a relation between temperature and bulk modulus for solids. From this, and the well known variation of velocity with bulk modulus for solids, we derived the variation of velocity for solids with temperature. We compared this relation to general data on rocks in order to test Jeffreys' predictions in our applications. Next, using the above relation as well as the well known relation between temperature and radius for an adiabatic Earth, we found the variation of bulk modulus with radius. This relation was then compared to actual values of the bulk modulus of the Earth in each major region.The variation of bulk modulus with radius should have been a close fit to the derived equation. This closeness of the fit would then be a measure of how close a region was too adiabatic conditions.The results of this study seem to indicate that the inner core and the outer core of the Earth seem to be near adiabatic conditions. / Department of Physics and Astronomy

Thesis (Ph.D.) -- McMaster University, 1998. / Includes bibliographical references (leaves 148-150). Also available via World Wide Web.

Thesis (M.Sc.). / Written for the Dept. of Atmospheric and Oceanic Sciences. Title from title page of PDF (viewed 2008/05/14). Includes bibliographical references.

Thesis--Cambridge. / Includes bibliography.

Thesis--Finland Institute of Technology. / Bibliography: p. [104]-105.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

A theoretical analysis was made of steady-state temperature and heat flow anomalies in the earth's crust caused by contrasts in heat production and thermal conductivity. Exact expressions were derived for the temperature and heat flow anomalies caused by polygonal prism heat sources in a half space overlain by a layer of contrasting conductivity. Expressions were also developed for the approximate thermal effects of polygonal prisms of contrasting conductivity. A comparison was made between the exact and approximate heat flow over an infinite semicircular cylinder of contrasting conductivity. The two heat flow fields agree to within 5% for conductivity radios (the ratio of the conductivity of the medium and the conductivity of the cylinder) which are between 0.25 and 1.5. Comparisons were also made between polygonal prism and finite difference models, three-dimensional and one-dimensional models, and half space and two-layered half space models. To illustrate the interpretation of heat flow anomalies a heat flow model was prepared for the Rolesville batholith and Castalia pluton, in Nash and Franklin Counties, North Carolina. It was shown that the observed variation in surface heat flow over these two granitic intrusions can be explained by variations in the thickness of the granite from 1 km to 30 km. / Master of Science

Equilibrium relations between garnet and orthopyroxene have been investigated by reversal experiments in the range of 20-45Kb and 975-1400°C in the FeO-MgO-Al₂O₃-SiO₂(FMAS) system. The Fe-Mg exchange reaction seems to have little or no compositional dependence at these conditions. The experimental results can be fitted adequately by the linear relation: ln K(D) = 2243/T°K - 0.9522 at 25Kb where K(D) = (X(Fe)/X(Mg))ᴳᵗ/(X(Fe)/X(Mg))ᴼᵖˣ. Combination of the available data for the mixing properties of garnet and V° for the Fe-Mg exchange reaction with the above experimental results yields the following geothermometric expression for the common natural assemblages that can be represented essentially within the system CaO-MnO-FeO-MgO-Al₂O₃-SiO₂. T°K = (1968 + 11P(Kb) + 1510(X(Ca)+X(Mn))ᴳᵗ)/(ln K(D) + 0.9522). The stability field of pyrope+quartz, defined by the reaction pryope+quartz=opx+sill, has been calculated as a function of P,T,X(Fe)ᴳᵗ in the FMAS system using the reversal experimental data of Perkins (1983) in the MAS system, and the present data on K(D)(Fe-Mg) between garnet and orthopyroxene. This reaction is very sensitive to pressure and compositional effects. Combination of P,T conditions for the garnet stability and that defined by (K(D)(Fe-Mg))ᴳᵗ⁻ᴼᵖˣ yields a simultaneous solution for both P and T of equilibration of garnet and orthopyroxene in the presence of Al₂SiO₅ and SiO₂. The effect of FeO on Al₂O₃ solubility in orthopyroxene in equilibrium with garnet has been determined experimentally at several pressures at 975 and 1200°C. These data have been modeled to develop a thermodynamic method for the calculation of Al₂O₃ in orthopyroxene as a function of P,T and composition. The Al₂O₃ isopleths have moderate P-T slopes, and provide virtually the only means of determining the pressure of mantle derived rocks.