Geophys. J. Int. zyxwvutsrqpo (1992) zyxwvutsrqp 109, 481-487 zyxwvutsrqp Models of convection-driven tectonic plates: a comparison of methods and results zyxwv Scott D. King,’* Carl W. Gable2 and Stuart A. Weinstein3t IGPP, Scripps Institution of Oceanography, UCSD, La Jolla, CA 92093, USA zyxwvut zlGPP, Earth and Environmental Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA and Department zy of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138. USA Depariment of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, MD 21218, USA Accepted 1991 November 8. Received 1991 November 6; in original form 1991 June 28 SUMMARY Recent numerical studies of convection in the Earth’s mantle have included various features of plate tectonics. A number of different methods for modelling ‘plate-like’ behaviour have been used. The differences in the methods of modelling plates may assume or predict significantly different plate deformation. We describe three methods of modelling plates through: material properties, force balance, and a thin power-law sheet approximation. We compare the results obtained using each method on a series of simple calculations. From these results we are able to develop scaling relations between the different parametrizations. 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 per cent. The main results are not dependent upon the plate modelling method and therefore are representative of the physical system we set out to model. Key words: convection, Earth’s mantle, plate tectonics. 1 INTRODUCTION A striking and unique feature of the dynamic Earth is that it’s surface is divided into tectonic plates (Le Pichon 1968; Morgan 1968). These plates behave like rigid caps on the Earth’s surface with surface deformation concentrated at the plate boundaries (e.g., Isacks, Oliver & Sykes 1968). Using boundary layer theory, Turcotte & Oxburgh (1967) demonstrated that cold sinking lithosphere may provide sufficient driving force to move plates at their observed velocities. However, calculations of infinite Prandtl number convection with uniform material properties (e.g., McKenzie, Roberts & Weiss 1974) or temperature- dependent viscosity (e.g., Nataf & Richter 1982) do not exhibit plate-like surface velocities. In general, plate-like surface velocities are only observed in convection calculations with the help of a plate generation method. There have been a number of investigations of plates in convective solutions and a variety of methods have been used to induce plate-like behaviour (e.g., Richter & McKenzie 1978; Kopitzke 1979; Davies 1988; Gurnis 1988; Gurnis & Hager 1989; King & Hager 1990; Gable, O’Connell & Travis 1991). However, only one brief * Now at: Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47906, USA. t Now at: Department of Geological Science, University of Michigan, Ann Arbor, MI 48109, USA. investigation comparing different methods has been undertaken (Davies 1989). It is difficult to compare results obtained using different methods, because results are often presented in terms of implementation specific parameters. In light of this, two important questions arise: do different methods have essentially the same result on the convective flow, and if so, is it possible to relate the material properties used in the various methods to observables such as heat flux and plate velocity? The importance of understanding the difference between the parametrizations is more than a study of numerical methods since the resulting plates are often quite different. In particular, the deformation of the plate assumed or predicted by different parametrizations can vary from a uniform velocity with no intraplate deformation to a velocity distribution with a broad zone of deformation. It is important, before we proceed, to present our criterion for judging a convective solution to have plate-like surface velocities. First, we will consider plates which have the same composition as the underlying mantle. Because of this, these plates will more closely resemble oceanic plates than continental plates which are compositionally different from the mantle. Second, plate interiors should have low strain-rates so that the surface velocities are nearly uniform. Furthermore, the majority of the deformation of plates takes place near the plate boundaries, therefore in the calculations the stresses and strain-rates should be largest near the plate boundaries. 481 Downloaded from https://academic.oup.com/gji/article/109/3/481/677588 by guest on 20 October 2022