Q. 80: Do your numerical models assume rigid ‘slabs’ of cold lithosphere or viscous flow?

CPT Q. #80 – 101 Q&A on Catastrophic Plate Tectonics

Question: 80. Does your model assume rigid “slabs” of cold lithosphere or viscous flow? If rigid, what is the free body diagram you assume for the forces and motions involved? Brown provides such a free body diagram for his assertions and I would like to analyze yours as well. If you assume viscous flow, then could you please similarly provide a free body diagram of the subduction process that pulls the cold lithosphere downward?

Response: My models assume a viscous description of the rock deformations. The viscosity depends on temperature and stress, and rock strength can vary by many orders of magnitude over the computational domain. The numerical codes utilize what is called the finite element method. The computational domain is subdivided into a large number of computational cells or elements. Conservation of mass and conservation of energy is enforced in each of the cells individually. Similarly, all the forces acting individually on each cell are required to balance throughout the computational grid at every time step. So whether one considers a single cell or an arbitrary grouping of cells, a strict balance of all the forces acting upon the volume in question is enforced at every instant in time. These forces include gravitational body force, the forces involved in the viscous deformation of the solid rock, and the forces associated with spatial changes in pressure. So the numerical solutions I have included in my papers represent in a very genuine and literal sense what you are referring to as ‘free-body diagrams’. The very essence of the numerical technique I use enforces a balance of forces on every cell at every time step. But this is not trivial. For a TERRA grid with 10 million cells, this means solving 40 million simultaneous equations for 40 million unknowns every time step (three components of force plus pressure for each cell). But computers can do this now relatively routinely.

These methods have been checked and cross-checked by many individuals over many years in many diverse applications. Not only do my programs show, without any room for doubt, that cold lithosphere has a strong tendency to detach from the surface and sink into the deeper mantle, dozens to hundreds of other similar programs also do the same. There is nothing mysterious about the process. Let me just comment in passing that two problems with Walt Brown’s simplistic diagrams is that they (a) do not allow for volumetric deformation and (b) do not account for the fact that the region below the plates is at least a thousand (or more likely ten thousand) times weaker than the plate itself.

To reiterate, all the plots I have published showing cold material peeling away from the upper boundary represent just what you are requesting, namely, results based on a continuing precise balancing of all the forces involved, including the forces arising from the volumetric deformation of the solid rock material everywhere in the domain as well as those resulting from spatial variations in the pressure field. Without using some sort of numerical method, how do you envision accounting for these two absolutely crucial aspects of the analysis?