Numerical models of plate‐scale convection confined to the upper mantle predict large deviations from observed ocean bathymetry, gravity, and geoid, while whole mantle models yield first‐order agreement with these observations. The upper mantle models fail because there is insufficient radioactivity in the upper mantle to explain the surface heat flux, the upper mantle must therefore be heated mainly from below, the resulting hot boundary layer generates buoyant material, and when this buoyant material rises to the base of the lithosphère, it generates large positive anomalies in topography (2 km), the geoid (30 m), and gravity (50 mGal). The concept of the magnitude of a hotspot swell is introduced: it is the rate at which new topography is created, expressed as a volume per unit time, and is a measure of the buoyancy and heat fluxes in the underlying plume. By this measure the major Pacific hots pots dominate the Earth's total plume flux, but plumes account for less than 10% of the Earth's total heat flux. This is comparable to the amount of heat likely to be coming from the core and supports the idea that plumes originate at the core mantle boundary and not at the 670‐km transition. These results indicate that mantle convection is dominated by a plate‐scale flow which penetrates throughout the mantle, with a secondary mode involving plumes rising from a weak thermal boundary layer at the bottom of the mantle.

The determination of the elastic properties of composite materials (multiphase aggregates, polycrystals, and porous or cracked solids) from the elastic properties of the components may be approached in several ways. The problem may be treated statistically, via scattering theory, through variational principles, or by the assumption of specific geometries for the material under consideration. Each of these methods is reviewed in turn. The widely used Voigt‐Reuss‐Hill average can be a poor approximation for both two‐phase composites and polycrystals, and its replacement by the two Hashin‐Shtrikman bounds is recommended. For pore‐containing or crack‐containing media, specific geometry models must be considered if useful results are to be obtained. If aggregate theory is used to estimate the moduli of individual components of a composite whose bulk properties are known, the shear moduli of the component phases must be matched (within a factor of 2 or 3) for the method to be useful. Results for nonlinear composites (which allow calculation of the pressure variation of aggregate moduli) have been obtained for only a few special cases.

No abstract

No abstract

Thermal histories have been calculated for simple models of the earth which assume that heat is transported by convection throughout the interior. The application of independent constraints to these solutions limits the acceptable range of the ratio of present radiogenic heat production in the earth to the present surface heat flux. The models use an empirical relation between the rate of convective heat transport and the temperature difference across a convecting fluid. This is combined with an approximate proportionality between effective mantle viscosity and T -'n, where T is temperature and it is argued that n is about 30 throughout the mantle. The large value of n causes T to be strongly buffered against changes in the earth's energy budget and shortens by an order of magnitude the response time of surface heat flux to changes in energy budget as compared to less temperature-dependent heat transport mechanisms. Nevertheless, response times with n --30 are still as long as 1 or 2 b.y. Assuming that the present heat flux is entirely primordial (i.e., nonradiogenic) in a convective model leads back to unrealistically high temperatures about 1.7 b.y. ago. Inclusion of exponentially decaying (i.e., radiogenic) heat sources moves the high temperatures further into the past and leads to a transition from 'hot' to 'cool' calculated thermal histories for the case when the present rate of heat production is near 50% of the present rate of heat loss. Requiting the calculated histories to satisfy minimal geological constraints limits the present heat production/heat loss ratio to between about 0.3 and 0.85. Plausible stronger eonstraints narrow this range to between 0.45 and 0.65. These results are compatible with estimated radiogenic heat production rates in some meteorites and terrestrial rocks, with a whole-earth K/U ratio of 1-2 x 104 giving optimal agreement.The thermal history of the earth has been a subject of major controversy in geology for over a century. The first major issue was settled with the discovery of radioactivity, which provided a source for the presently observed surface heat flux which could maintain itself through the long ages demanded by geologists to explain their observations [Kelvin, 1899;Strutt, 1906;Stacey, 1977]. The second major issue, still not settled, concerns the means by which heat generated deep in the earth's interior is transported to the surface at the observed rate, and in the last two decades, conduction, convection, and radiation have all been vigorously advocated and disparaged. Since the prevailing view, until recently, has been that the earth's mantle is immobile, conduction and radiation have received more attention. A difficulty which has been encountered with both conduction and radiation is that much larger conductivities (or effective conductivities, in the case of radiative transport) are required at depth in the earth than are observed in rocks at the surface or could be demonstrated to occur at high pressures and temperatures, and these difficulties persist [e.g., ...