An example of erosion crater: The Hazera Makhtesh (Negev Desert): View of the Hazera Crater from its western flank. Note the only outlet valley in the southeastern cliff (center-right).
Location geological map of the Negev Craters. The blue area in the upper-right corner is the Dead Sea. The Hazera is the smallest in the upper-center of the map, its brown color indicates the weak early Cretaceous core sandstones, whereas green indicates the overlying hard marine carbonates from late Cretaceous.
TISC. I calculated the fluvial erosion on top of a dome-like uplift of a thin hard layer (orange) covering a soft layer (green).
Model results (at 0, 6, 15 and 25 My).Top panels: Drainage network (chanels with more than .1 m3/s of mean water discharge) and lithology (planform view illuminated from North: brown color used for the hard layer; green for the soft layer; yellow for sediments). Lower panels: cross section from E to W showing the thickness or the hard, brown layer. The initial surface (t=0) is flat, with a hard layer overlaying a buried anticline. At t=1 Myr the uplift starts with a maximum rate at the centre of the domain. Drainage self-organizes according to this uplift. At t=6My the weak layer is reached by one of the fluvial channels. The last stage shows the final crater geometry.
Simulation of erosion
Water coming from precipitation is assumed to flow following the maximum slope. Sediment carrying capacity is a function of mean water discharge and slope and determines whether a stream is eroding or depositing. Suspended sediments resulting from erosion are transported through the fluvial network until they are posited or they leave the model domain (mass conservation).
Tectonic uplift is simulated calculating the effect of a deep load pushing upwards an elastic layer.
See this paper about the Negev craters:
[pdf] Ezra Zilberman, 2000, Formation of "Makhteshim" - unique erosion cirques in the Negev, southern Israel, Israel Journal of Earth Sciences V49
See this page on crater erosion on Mars: