The principal purpose of this paper is to examine whether membrane stresses can support topographic loads on planetary elastic lithospheres. It is found that the ability of a spherical shell to support loads through membrane stresses is determined by the nondimensional parameter r = Ed/ApgR 2 where d is the thickness of the elastic lithosphere, AO is the density difference between the mantle and crust, and R is the radius of the planetary body. When this parameter is large membrane stresses can fully support topographic loads without flexure, and when it is small the influence of membrane stresses can be neglected. Solutions of the equation governing the behavior of a spherical shell are obtained for a topographic load expressed in terms of spherical harmonics. Spherical harmonic expansions of the measured gravity and topography for Mars and the moon are compared with the theory. It is found that for Mars the support of topography is primarily due to membrane stresses for n < 8 and for the moon for n < 17. For Mars the data for 4 _< n _< 7 give •-= 0.5. For the moon the data have considerable scatter that is attributed to the mascons but generally correlate with •-= 0.5. If bending stresses are neglected, the governing equation for the deflection of the spherical shell is Legendre's equation. A general solution is obtained for an axisymmetric load. This solution is applied to the Tharsis region on Mars. The 60-65% compensation of this region requires that •-= 0.6. The well defined fracture pattern surrounding the Tharsis region is attributed to tensional membrane stresses.

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We show how clustering as a general hierarchical dynamical process proceeds via a sequence of inverse cascades to produce self-similar scaling, as an intermediate asymptotic, which then truncates at the largest spatial scales. We show how this model can provide a general explanation for the behavior of several models that has been described as "self-organized critical," including forest-fire, sandpile, and slider-block models.

Many major faults, including a large fraction of the San Andreas, appear to be virtually quiescent between great earthquakes. The locked sections of the San Andreas near San Francisco and Los Angeles have little or no seismic activity on the primary fault trace, although secondary faults may be active. Stick‐slip behavior on a fault can be explained in terms of a static coefficient of friction, which is larger than the dynamic or sliding coefficient. In this paper we propose a modification of the friction hypothesis in which chemical lithification (cementation) occurs on the fault between earthquakes. As the stress on the fault increases it becomes large enough to break the cemented bonds between particles causing slip on the fault. We treat this problem quantitatively, assuming that pressure solution is responsible for the cementation. An advantage of this model is that the hydrostatic pressure approaches the lithostatic pressure during cementation so that low fault strengths are predicted.

The energy source for crustal deformation is isotopic heating and secular cooling of the mantle. In a true solid, heat would be lost to the surface by conduction; however, solid-state creep processes allow the Earth’s solid mantle to exhibit a fluid behaviour. Thus, thermal convection can convert heating into directed motion. Variations in temperature lead to variations in densitythrough thermal expansion and contraction. Although the resultant body forces are vertical, horizontal variations in temperature lead to horizontal body forces. At an ocean ridge the variations in the thickness of the lithosphere lead to the elevation of the ridge. The result is a substantial horizontal ridge push force.This force, along with the trench pull force on the descending lithosphere is the primary force driving plate tectonics. Lithospheric thinning must occur beneath continental rifts and plateau uplifts. I suggest that lithospheric thinning is caused by the diapiric penetration of hot asthenospheric rock to the crust/mantle boundary. This penetration may also cause lithospheric stoping and plateau uplifts. Lithospheric thinning leads to large tensional stresses above the zone of thinning. These forces are generally much larger than the compressional forces generated by crustal thinning. The forces generated by lithospheric thinning are quite large and may be responsible for the propagation of continental rifts. In island arcs and Andean type orogenic belts both lithospheric thinning and crustal thickening result in large tensional forces. Probably the most complex zone of crustal deformation is the continental collision. Variations in types of continental collisions are discussed.