Univ. London Royal Holloway

Field studies indicate that nearly all eruptions in volcanic edifices and rift zones are supplied with magma through fractures (dykes) that are opened by magmatic overpressure. While (inferred) dyke injections are frequent during unrest periods, volcanic eruptions are, in comparison, infrequent, suggesting that most dykes become arrested at certain depths in the crust, in agreement with field studies. The frequency of dyke arrest can be partly explained by the numerical models presented here which indicate that volcanic edifices and rift zones consisting of rocks of contrasting mechanical properties, such as soft pyroclastic layers and stiff lava flows, commonly develop local stress fields that encourage dyke arrest. During unrest, surface deformation studies are routinely used to infer the geometries of arrested dykes, and some models (using homogeneous, isotropic half-spaces) infer large grabens to be induced by such dykes. Our results, however, show that the dyke-tip tensile stresses are normally much greater than the induced surface stresses, making it difficult to explain how a dyke can induce surface stresses in excess of the tensile (or shear) strength while the same strength is not exceeded at the (arrested) dyke tip. Also, arrested dyke tips in eroded or active rift zones are normally not associated with dyke-induced grabens or normal faults, and some dykes arrested within a few metres of the surface do not generate faults or grabens. The numerical models show that abrupt changes in Young's moduli(stiffnesses), layers with relatively high dyke-normal compressive stresses (stress barriers), and weak horizontal contacts may make the dyke-induced surface tensile stresses too small for significant fault or graben formation to occur in rift zones or volcanic edifices. Also, these small surface stresses may have no simple relation to the dyke geometry or the depth to its tip. Thus, for a layered crust with weak contacts, straightforward inversion of surface geodetic data may lead to unreliable geometries of arrested dykes in active rift zones and volcanic edifices.

The main magma source for eruptions on Etna (Italy) is poorly constrained. Here we use data on the size distributions of volcanic fissures/feeder-dykes, crater cones, dyke thicknesses, and lava flows to estimate the average magma volume flowing out of the chamber during eruptions and the volume of the chamber. For the past four centuries the average magma volume leaving the chamber during each eruption is estimated at 0.064 km3. From the theory of poroelasticity the estimated chamber volume is then between 69 and 206 km3. For comparison, a sill-like, circular chamber (an oblate ellipsoid) 1 km thick and 14 km in diameter would have a volume of about 154 km3. The elastic strain energy stored in the host rock during inflation of such a chamber is about 2.8 × 1014 J. Estimating the surface energy of a typical dyke-fracture as about 107 J m-2, the results suggest that the stored strain energy is sufficient to generate a dyke-fracture with an area of about 28 km2. The average strike-dimension of volcanic fissures/feeder-dykes in Etna is about 2.7 km. It follows that the estimated strain energy is sufficient to generate a feeder-dyke with a strike-dimension of 2-3 km and with a dip-dimension as great as 10 km, agreeing with the maximum estimated depth of the magma chamber.

No eruption, no caldera collapse, and no landslide can take place in a volcano unless its state of stress is suitable for the associated type of rock failure. The state of stress, in turn, results in deformation, and both stress and deformation depend on the mechanical properties of the rocks that constitute the volcano. Understanding stress and deformation in volcanoes is thus of fundamental importance for understanding unrest periods and for accurate forecasting volcano failure, such as may result in large-scale lateral and vertical collapses and eruptions.