Seafloor displacements across the mid-ocean ridge eruption cycle modulated by mush zone viscosity

Mid-ocean ridges (MORs) are extremely active volcanic systems where dike intrusions and eruptions recur on decadal time scales. Their submarine setting has long made in-situ observations of active deformation extremely challenging, hindering insight into sub-seafloor deformation sources. Recent progress in seafloor geodesy is rapidly changing this state of affairs, by providing measurements of rapid seafloor displacements throughout the MOR eruption cycle. These novel datasets therefore call for the development of new models to fully realize their potential. Importantly, MOR plumbing systems have been particularly well imaged and typically comprise shallow reservoirs termed axial melt lenses (AMLs) lying above, and embedded within a lower crustal mush zone. Leveraging this knowledge, we design 2-D (forward) finite-element models of the active seafloor deformation that should characterize a cycle of steady AML inflation followed by an instantaneous dike intrusion and AML drainage. The AML lies at the base of an elastic lithosphere, and atop a Maxwell viscoelastic mush zone, with viscosity η_M, that reaches Moho depths and is laterally confined to the axial domain. The underlying asthenosphere is viscoelastic with a viscosity of 10¹⁸ Pa.s. 

Our models treat AMLs as a tensile dislocation that opens at a specified rate, corresponding to a constant replenishment flux. AML replenishment manifests as distributed seafloor uplift. When  η_M ≥ 10¹⁸ Pa.s, our models resemble elastic half-space end-members. Lower values of η_M however exert a damping effect on seafloor uplift rates, which slow down significantly from beginning to end of a replenishment phase. When the AML suddenly drains and/or when a dike suddenly opens, low mush zone viscosities result in a transient phase of post-drainage and post-diking relaxation, manifesting as steadily vanishing seafloor uplift and seafloor subsidence, respectively. 

We use our numerical simulations to revisit estimates of AML inflation at the East Pacific Rise (9°50′N) using seafloor uplift rates (up to ~7 cm/yr) measured by Nooner et al. (2014) between 2009 and 2011, i.e., 4 to 6 years following the 2005-2005 eruption. If we assume a strong mush (η_M >10¹⁸ Pa.s), the observed uplift requires an AML replenishment rate of ~150 m³/yr per meter along the ridge axis, whereas a very weak mush (η_M <10¹⁶ Pa.s) requires rates as large as ~350 m³/yr/m. Interestingly, the observed cross-axis profile of seafloor displacements appears incompatible with our post-eruption relaxation models, implying either that such relaxation did not take place, or that it was effectively over within 4 years. If the latter is true, then the effective viscosity of the axial mush zone should be close to, or slightly less than 10¹⁶ Pa.s, consistent with micro-mechanical models of gabbroic mush flow, and large-scale thermo-mechanical models of MOR thermal structure.