Coupled model of overpressure-driven dike deformation and volcanic conduit flow: implications for non-uniform dike deformation during effusive eruptions

Abstract Interactions between the elastic magma chamber and the variable flow resistance of conduits control volcanic eruptions. Recent geodetic observations have revealed complex conduit deformations, especially in inclined dikes, which traditional models have struggled to capture. In this study, we introduce a simplified coupled model that explicitly accounts for magma flow within a nonuniform, elastically deformable inclined dike conduit under the influence of edifice loading. Dimensional analysis reduces the governing equations to an advection–diffusion type equation, controlled by two key dimensionless parameters representing the relative deformability of the conduit and the contribution of gravitational and pressure gradient forces. Numerical simulations demonstrate that these parameters govern the regime of pressure propagation. Specifically, deformation driven by large overpressure can significantly increase effusion rates and induce response delays between different depths. Applying this model to the 2018 Kilauea eruption, we show that the observed response delays and the spatial pattern of deformation (simultaneous expansion and contraction) are well-reproduced in a regime, where advective effects dominate. Our findings provide a refined theoretical framework for understanding volcanic conduit behavior in complex geometries and could explain observed non-uniform deformation phenomena. Graphical abstract