The sinking of gravitationally unstable lithosphere beneath high-elevation plateaus is proposed to be a key driver of their uplift, and is proposed to have occurred globally, including beneath the Andes, Tibet, Anatolia, Colorado Plateau, and Nevadaplano. Where the lithosphere is actively sinking, geophysical imaging affords a snapshot of this process. However, the transience of these events leaves faint imprints on the surface. Once unstable lithosphere has sunk, little evidence of this process remains, besides (in some cases) low-volume magmatism that typically has low preservation potential. This talk will explore an alternative archive: the surface sedimentary record. Numerical geodynamic models predict that lithosphere removal can lead to transient topographic changes that could be preserved in the surface record, particularly in deposits of lakes or playas that are subsequently inverted. The question is, can we find evidence in the geologic record of such a dynamic topographic response to lithospheric dripping?