Evidence that coupling to magma chambers controls the volume history and velocity of laterally propagating intrusions

In this paper, I present a simple analytical solution for the unsolved problem of a propagating dike coupled to a magma chamber. As recognized by Segall et al. (2001), the flow of the magma from a chamber to a dike is described by an ordinary differential equation for the unknown pressures of chamber and dike. The most intuitive assumption on magma exchange is that the volume gained by the intrusion equals the volume lost by the chamber. This constraint, however, implies a chamber so large that its pressure does not drop during the feeding process and an incompressible magma that does not expand or vesiculate as it intrudes. Models assuming constant driving pressure fail to explain observations. Here, mass conservation constrains pressure as magma flows from the chamber to the dike and the compressibilities of magma and sources control volume changes. These assumptions allow me to decouple the equations and solve the system analytically. The model predicts that chamber and dike volume change exponentially with time as V(t) = V∞[1 − exp(−t/τ)]. The asymptotic volume V∞ and the timescale τ are found to be functions of rock, magma, chamber and dike parameters and of the initial pressure conditions. Assuming that the intrusion is shaped as an elongating cuboid, its velocity is found to change as v = v0exp(−t/τ), where v0 is the initial dike velocity. The model is successfully tested against the best observations available for lateral dike propagation events: the volume history of chamber and dike during the 2000 Miyakejima intrusion (Japan) and dike velocity during the 1978 Krafla event (Iceland) and during some intrusions following the 2005 event in Afar (Ethiopia). This paper confirms and extends the results of a previous study by Rivalta and Segall (2008), who found the final ratio between dike volume and the volume withdrawn from the chamber to be rV = 1 + 4μβm/3 > 1, where μ is the host rock rigidity and βm is the magma compressibility. Here, I demonstrate that the formula for rV holds at any time during the intrusion, not just at the end. This model confirms that some magma chambers behave as stiff magma‐tanks, able to inflate large dikes as balloons, and demonstrates that high volume ratios are unlikely if the chamber has a pure sill shape. Fitting observations with the model allows us to estimate several dike, chamber, magma and rock parameters.