Dynamical similarity and density (non-) proportionality in experimental tectonics

- We reassess Hubbert's (1937) density proportionality rule for scale models.
- Density proportionality is not always required in systems without inertia.
- In many cases the rule unnecessarily restricts the choice of analog materials for scale models.

The utility of analog laboratory models for tectonic processes relies on their dynamical similarity to their natural prototypes. Dynamical similarity is often thought to require that the density distribution in the model be a constant (position-independent) multiple of that in the prototype, a principle due to Hubbert (1937). To clarify the status of this rule, we nondimensionalize the equations and boundary/initial conditions governing simple models of three paradigmatic processes: gravity tectonics, compressional tectonics, and free subduction. The results show that density proportionality, while compatible with dynamical similarity, is not always required by it in systems with negligible inertia, a category that includes most geological and tectonic processes. The density proportionality rule is therefore unnecessarily restrictive in many cases, implying that the range of analog materials that can be used to construct properly scaled models is wider than commonly recognized.