By the early 1970s, the basics of plate tectonics were known. Although much understanding remained to be gained, as a topic of research, plate tectonics no longer defined the forefront of earth science. Not only had it become a foundation on which to build, but also the methods used to reveal it became tools to take in new directions. For me as a seismologist studying earthquakes and active processes, the deformation of continents offered an obvious topic to pursue. Obviously examining the deformation of continents and ignoring the widespread geologic evidence of both ongoing and finite deformation of crust would be stupid. I was blessed with the opportunity to learn from and collaborate with two of the best, Paul Tapponnier and Clark Burchfiel. Continental deformation differed from plate tectonics both because deformation was widespread but more importantly because crust shortens (extends) horizontally and thickens (thins), processes that can be ignored where plate tectonics - the relative motion of rigid plates - occurs. Where a plate boundary passes into a continent, not only must the forces that move plates do work against friction or other dissipative processes, but where high terrain is created, they must also do work against gravity, to create gravitational potential energy in high terrain. Peter Bird and Kenneth Piper and Philip England and Dan McKenzie showed that a two-dimensional thin viscous sheet with vertically averaged properties enabled both sources of resistance to be included without introducing excessive complexity and to be scaled by one dimensionless number, what the latter pair called the Argand number. Increasingly over the past thirty years, emphasis has shifted toward the role played by the mantle lithosphere, because of both its likely strength and its negative buoyancy, which makes it gravitationally unstable. Despite progress since realizing that rigid plates (the essence of plate tectonics) provides a poor description of continental

Recent numerical studies of convection in the earth's mantle have included various features of plate tectonics. This paper describes three methods of modeling plates: through material properties, through force balance, and through a thin power-law sheet approximation. The results obtained are compared using each method on a series of simple calculations. From these results, scaling relations between the different parameterizations are developed. While each method produces different degrees of deformation within the surface plate, the surface heat flux and average plate velocity agree to within a few percent. The main results are not dependent upon the plate modeling method and herefore are representative of the physical system modeled.

Plate N Sheet 4.10.02 Keygenl