  Landscape paradigm is ubiquitous in physics and other natural sciences, but
it has to be supplemented with both quantitative and qualitatively meaningful
tools for analyzing the topography of a given landscape. We here consider
dynamic explorations of the relief and introduce as basic topographic features
``wells of duration $T$ and altitude $y$''. We determine an intrinsic
exploration mechanism governing the evolutions from an initial state in the
well up to its rim in a prescribed time, whose finite-difference approximations
on finite grids yield a constructive algorithm for determining the wells. Our
main results are thus (i) a quantitative characterization of landscape
topography rooted in a dynamic exploration of the landscape, (ii) an
alternative to stochastic gradient dynamics for performing such an exploration,
(iii) a constructive access to the wells and (iv) the determination of some
bare dynamic features inherent to the landscape. The mathematical tools used
here are not familiar in physics: They come from set-valued analysis
(differential calculus of set-valued maps and differential inclusions) and
viability theory (capture basins of targets under evolutionary systems) which
have been developed during the last two decades; we therefore propose a minimal
appendix exposing them at the end of this paper to bridge the possible gap.
