| In the past decades volcano seismologists and geodesists have collected many observations
on the transient regime of dike emplacement that current models of dike propagation do not
explain. The cause of this failure has been already identified by several authors in the
common assumption that magma chambers can maintain their pressure constant while
feeding dikes. This assumption collides e.g. with the convex upward shape of the
volume evolution during the 1997 dike intrusion at KIlauea, as noted by Owen et
al. [2000] and Segall et al. [2001]. Segall et al. [2001] described the flow of the
magma from a chamber to a dike with an ordinary differential equation for the
unknown pressures of chamber and dike. The feeding of dikes is then associated to a
pressure drop in the magma chamber, controlled by magma bulk modulus and elastic
compressibility of surrounding rock. Here I present a model developing on that
intuition, which makes use of mass conservation (instead of volume conservation)
as a constraint for pressure, as magma flows from the chamber to the dike. This
ansatz allows to solve the problem analytically. The model predicts that chamber and
intrusion volume change exponentially with time as V (t) = V -[1 - exp(-t-Ï)].
Intrusion velocity is found to change as v = v0 exp(-t-Ï), where v0 is the initial dike
velocity. The asymptotic volume V - and the time scale Ï can be expressed in
terms of rock, magma, chamber and dike parameters and of the initial pressure
conditions. Fitting volume or velocity curves can provide independent constraints on
parameters difficult to retrieve otherwise. I validate my model with data from the 2000
Miyakejima intrusion (Japan), the 1978 Krafla event (Iceland) and from some intrusions
following the 2005 event in Afar (Ethiopia). The fit between model and observations is
excellent. This paper confirms and extends the results of a previous study [Rivalta
and Segall , 2008] that explained the volume imbalance found during some dike
intrusions. The final ratio between dike volume and the volume withdrawn from
the chamber was found to be rV = 1 + 4μβm-3 > 1, where μ is the host rock
rigidity and βm is the magma compressibility. This invalidates the most intuitive
assumption on magma exchange that the volume gained by the intrusion equals
the volume lost by the chamber(s). Here, I demonstrate that the formula for rV
holds at any time, not just at equilibrium. My model confirms that some magma
chambers behave as stiff magma-tanks, able to inflate large dikes as balloons, and
demonstrates that this is unlikely to occur if the chambers are simply shaped as sills. |