Magmatic Lensing: A Mechanism for the Growth of Large Crustal Magma Chambers

We present a model for the growth and thermal evolution of large crustal magma reservoirs, based upon the focusing of rising dikes towards a pressurized and buoyant melted region (the magma chamber). Dikes propagate orthogonally to the least compressive (local) principle stress, which in turn is determined by the regional stress trajectories created by the magma chamber and far field stresses. Therefore, there exists a capture radius at depth that is potentially much larger than the dimensions of the chamber, forming a system that we call a "magmatic lens." This phenomenon allows influx of magma to compete with the processes of cooling, crystallization and viscous relaxation of stresses to form large chambers. In time, these magma chambers may either 1) grow through melting and influx until excess overpressure causes eruption, 2) exist stably, or 3) freeze and shrink until magma lensing no longer occurs. We find analytical solutions for the stress fields of two-dimensional, viscoelastic, pressurized, and buoyant inclusions of circular and elliptic geometry, with and without a free surface, to model a lower or mid-crustal magma chamber. We then couple an algorithm for dike propagation with a thermal code that takes into account melting, crystallization, and a nonlinear melt fraction curve for both chamber and country rock to simulate magma lensing dynamically. This allows us to map the relationship between eruption-forming chamber overpressures, lower crustal estimates for melt flux, and the effects of regional extension.