Inferring rheology from free-surface observations

We develop direct inversion methods for inferring the rheology of a fluid from observations its shallow flow. First, evolution equation free-surface flow an inertia-less current with general constitutive law is derived. The relationship between volume flux and basal stress, $\tau_b$ encapsulated by single function $F(\tau_b)$, which depends only on law. method consists (i) determining stress evolution, (ii) comparing to constrain $F$ (iii) $F$. Examples are presented both steady transient flows demonstrating that wide range laws can be directly obtained. For in velocity known, we derive different method, circumvents need calculate flux.