35. X. Kong and P. Bird (1995) SHELLS: A thin-shell program for modeling neotectonics of regional or global lithosphere with faults, J. Geophys. Res., 100, B11, 22,129-22,131.

Abstract. The thin-plate method of modeling neotectonics uses isostasy and vertical integration of lithospheric strength to reduce three-dimensional problems to two dimensions. We introduce new thin-shell continuum elements and fault elements which satisfy the completeness and compatibility requirements, and permit extension of these methods to the lithospheres of spherical planets. Even a coarse grid of these elements with elastic rheology can reproduce low-order toroidal free oscillations. In the program SHELLS, a realistic frictional/dislocation-creep rheology is handled by iteration; this method converges to solutions which can be numerically tested to confirm that they satisfy both local equilibrium and the balance of torques on whole plates. Because this code can incorporate both natural plate shapes (with internal faults) and realistic rheologies, it yields models that are readily tested by their predictions of geodetic velocities, stresses, and fault slip rates.

P.S. Although SHELLS is available from the AGU archives, my download folder /neotec/SHELLS offers a newer version in which some bugs are fixed and a different linearization of the rheology gives improved convergence of solutions. P. Bird 2000.09.19

Geometric construction of velocity at a point inside one of our new spherical thin-shell elements. Green arrows show horizontal velocities at the 3 nodes at the corners of the spherical triangle (transparent; outlined by three black arcs of great circles). Velocity is linearly interpolated within a virtual plane triangle (yellow) which cuts through the sphere; the result is the blue velocity vector. Then, velocity is projected radially to the surface, with amplification, to produce the red vector. If the 3 nodal velocities are consistent with a common Euler pole, then the element moves without straining, and the red velocity vector is horizontal. In other cases, we discard the small radial component of the interpolated velocity.