Continental and mid-oceanic rifts commonly show a rift valley bounded by normal faults and uplifted shoulders. In this paper we numerically model the evolution of rift valley relief in a notched brittle lithosphere. Results show that the rift valley has a maximum valley relief, which is controlled by the competition between isostasy and lithospheric geometry. If the axial lithosphere is much thinner than the flanking lithosphere, the isostatic force will break outward dipping faults on the axis and stop the deepening of the rift valley. We call this the axial failure mode. On the other hand, if the thickness of axial lithosphere is close to that of the flanks, flexural bending will break new faults on the flanks and stop the valley deepening. We call this the flanking failure mode. Triggering of either mode gives the maximum valley depth, and the selection is controlled by the interplay between isostasy and lithospheric geometry. On the basis of these mechanisms we propose a scaling equation that relates the maximum valley depth to the geometry ( flanking thickness, axial thickness, and notch width) and strength ( friction angle and cohesion) of the lithosphere. The model explains along-axis variation of valley relief at mid-oceanic ridges by changes of the axial lithosphere thickness.
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