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Abstract The Turkana Depression, located between the Ethiopian and East African plateaus, displays an anomalous rift architecture. It is missing the narrow, magma‐rich morphology observed in the Main Ethiopian Rift that cuts through the Ethiopian Plateau. Instead, diffuse faulting and isolated volcanic centers are widespread over several hundred kilometers. Turkana has also experienced less magmatism over the last 30 Myr than adjacent plateaus, despite having a thin crust and residing above a mantle that is inferred to be hot and partially molten. We hypothesize that lithospheric weakening has been the key control on magma transport across the lithosphere in the Turkana Depression and subsequent rift development. Using poro‐viscoelastic–viscoplastic models of melt transport, we show that magma extraction across a thin, weakened lithosphere is slower than across a thick, elastic lithosphere. Our results suggest that pre‐rift lithospheric strength can explain the magma‐poor character of Turkana for most of its tectonic history. 

SUMMARY To reach Earth’s surface, magma must ascend from the hot, ductile asthenosphere through cold and brittle rock in the lithosphere. It does so via fluid-filled fractures called dykes. While the continuum mechanics of ductile asthenosphere is well established, there has been little theoretical work on the cold and brittle regime where dyking and faulting occurs. Geodynamic models use plasticity to model fault-like behaviour; plasticity also shows promise for modelling dykes. Here we build on an existing model to develop a poro-viscoelastic–viscoplastic theory for two-phase flow across the lithosphere. Our theory addresses the deficiencies of previous work by incorporating (i) a hyperbolic yield surface, (ii) a plastic potential with control of dilatancy and (iii) a viscous regularization of plastic failure. We use analytical and numerical solutions to investigate the behaviour of this theory. Through idealized models and a comparison to linear elastic fracture mechanics, we demonstrate that this behaviour includes a continuum representation of dyking. Finally, we consider a model scenario reminiscent of continental rifting and demonstrate the consequences of dyke injection into the cold, upper lithosphere: a sharp reduction in the force required to rift.