# Dynamics of volcanic plumbing systems and magma emplacement in the Earth's crust

**Olivier Galland**, Forsker in PGP-Geo, will present his laboratory work on the "*Dynamics of volcanic plumbing systems and magma emplacement in the Earth's crust*"

Drawing illustrating the complexity of volcanic plumbing systems

During this seminar, I will develop two themes:

**Dynamics of dikes versus cone sheets in volcanic systems**

Igneous sheet intrusions of various shapes, such as dikes and cone sheets, coexist as parts of complex volcanic plumbing systems likely fed by common sources. How they form is fundamental regarding volcanic hazards, but yet no dynamic model simulates and predicts satisfactorily their diversity. Here we present scaled laboratory experiments that reproduced dikes and cone sheets under controlled conditions. Our models show that their formation is governed by a dimensionless ratio (P_{1}), which describes the shape of the magma source, and a dynamic dimensionless ratio (P_{2}), which compares the viscous stresses in the flowing magma to the host-rock strength. Plotting our experiments against these two numbers results in a phase diagram evidencing a dike and a cone-sheet field, separated by a sharp transition that fits a power law. This result shows that dikes and cone sheets correspond to distinct physical regimes of magma emplacement in the crust. For a given host-rock strength, cone sheets preferentially form when the source is shallow, relative to its lateral extent, or when the magma influx velocity (or viscosity) is high. Conversely, dikes form when the source is deep compared to its size, or when magma influx rate (or viscosity) is low. Both dikes and cone sheets may form from the same source, the shift from one regime to the other being then controlled by magma dynamics, *i.e.,* different values of P_{2}. The extrapolated empirical dike-to-cone sheet transition is in good agreement with the occurrence of dikes and cone sheets in various natural volcanic settings.

**Analytical model igneous sill emplacement**

We develop a new axisymmetric analytic model of surface uplift upon sills and laccoliths, based on the formulation of a thin bending plate lying on an elastic foundation. In contrast to most former models also based on thin bending plate formulation, our model accounts for (i) axi-symmetrical uplift, (ii) both upon and outside the intrusion. The model accounts for shallow intrusions, *i.e*. the ratio *a/h*>5 where *a* and *h* are the radius and depth of the intrusion, respectively. The main parameter of the model is the elastic length* **l*, which is a function of the elastic properties of the bending plate and of the elastic foundation. The model exhibits two regimes depending on the ratio *a/l*. When *a/l*<5, the uplift spreads over a large domain compared to that of the intrusion. In contrast, when *a/l*>5, the uplift is mostly restricted upon the intrusion. When the elastic foundation is very stiff, our model converges towards that of a clamped plate. We discuss three possible applications of our model: (i) The model can be used to describe sill propagation by introducing a propagation criterion. For realistic values, our model reproduces well the behavior of horizontal intrusions simulated in experiments; (ii) The model can also be used to compute the critical size of saucer-shaped sills. It shows, for instance, that a soft elastic foundation favors the horizontal spreading of sills before they form inclined sheets; (iii) We show that the classical Mogi point source model cannot be used to constrain sill properties from the surface uplift. We thus propose that our model can be used as a valuable alternative to both simple analytical models like Mogi's and more complex numerical models used to analyze ground deformation resulting from sill intrusions in active volcanoes.