Antonello Piombo

A model for the formation of lava tubes by roofing over a channel

The formation of lava tubes is a common phenomenon on some basaltic volcanoes, such as Etna. A model for tube formation by roofing of a channel is proposed and involves first describing lava as a Bingham liquid flowing down a slope. It is further assumed that lava flows in a channel with rectangular cross section: as a result of heat loss into the atmosphere, a crust is gradually formed on the upper surface of the flow and this crust eventually welds to the channel levees. We assume that a lava tube is formed when such a crust is sufficiently thick to resist the drag of the underlying flow and to sustain itself under its own weight. The minimum thickness of the crust satisfying such conditions depends on the tensile strength and shear strength of the crust itself. Assuming that the growth of the crust produces a downflow linear increase of the shear stress at the interface between flowing lava and the crust, the distance is evaluated between the eruption vent and the point where the tube is formed. The model predicts that if the flow rate is constant, the thickness of the flow increases as the crust fragments grow and weld to each other, and the velocity of the crust decreases to zero. Once the lava tube is formed, the initial flow rate can be achieved by a flow thickness smaller than the vertical size of the tube, with the same viscous dissipation: this may explain why under steady state conditions, the lava level inside a tube is frequently lower than the roof of the tube itself.

Effect of Stress Perturbations on the Dynamics of a Complex Fault

A plane fault containing two asperities subject to a constant strain rate by the motion of tectonic plates is considered. The fault is modelled as a discrete dynamical system where the average values of stress, friction and slip on each asperity are considered. The state of the fault is described by the slip deficits of the asperities. We study the behaviour of the system in the presence of stress perturbations that are supposed to be due to dislocations of neighbouring faults. The fault complexity entails consequences that are not present in the case of a homogeneous fault. A stress perturbation not only changes the occurrence time of the following earthquake but may also sensitively change the slip amplitude and area, hence the seismic moment, of the earthquake, as well as the position of its hypocentre. The greatest changes take place when simultaneous slip of asperities is involved. A Coulomb stress value can be assigned to each asperity. The change in the difference between the Coulomb stresses of the two asperities is a measure of how much the system gets closer to or farther from the condition for simultaneous slip. As an example, we consider the effect of the 1960 Great Chilean Earthquake on the two-asperity fault that produced the 2010 Maule earthquake and calculate the changes in the moment rate and in the total seismic moment. It results that, in the absence of the 1960 earthquake, the Maule earthquake would have occurred several decades later and would have involved a different sequence of modes, so that the moment rate function would have been very different, with a longer duration and a greater seismic moment.

Role of Mechanical Erosion in Controlling the Effusion Rate of Basaltic Eruptions

In many basaltic eruptions, observations show that the effusion rate of magma has a typical dependence on time: the effusion rate curves show first a period of increasing and later a decreasing phase by a maximum value. We present a model to explain this behavior by the emptying of a magma reservoir through a vertical cylindrical conduit with elliptical cross section, coupled with the its widening due to mechanical erosion, produced by the magma flow. The model can reproduce the observed dependence on time of effusion rate in basaltic eruptions. Eruption duration and the maximum value of effusion rate depend on the size of magma chamber, on lava viscosity and strongly on erosion rate per unit traction.

Propagation of an aseismic dislocation through asperities with smooth borders

Abstract A 2-D model is presented for the propagation of a Somigliana dislocation along a fault with nonuniform friction. Fault slip is driven by a uniform ambient shear stress, slowly increasing with time. The dislocation is nucleated in the lowest-friction region of the fault plane and is confined by the surrounding higher-friction regions (asperities). The case studied involves asperities which have smooth borders, characterized by a constant friction gradient. For values of ambient shear stress near to the weak-zone friction, the propagation of dislocation is slowed down by the presence of asperities. Only when it goes beyond the border does the dislocation front move at increasing velocity. The model shows that, at a given value of ambient shear stress, the slip amplitude is larger in the case of finite and constant friction gradient than in the case of asperities with sharp borders. Unlike the propagation velocity, slip rate is ever increasing during the dislocation process. The model shows to what extent a dislocation is influenced by the distribution of friction on the fault. A detailed knowledge of slip rate and slip history is needed to understand the mechanism of frictional instability on faults.

Displacement and stress fields around a fault jog: Effects on fault mechanics

Abstract We consider a fault surface which differs slightly from a plane due to a jog. The fault is placed in an elastic space and is subject to a uniform stress field. The orientation of the fault is such that the normal traction is greater on the jog determining a higher static friction. A considerable increase in friction and the formation of a strong asperity can occur due to repeated slip episodes on the fault. Slip produces an elastic deformation of the fault faces in correspondence of the asperity, causing an increase in normal traction and hence in friction. This process can be described as a tensile Somigliana dislocation, accompanied by partial fracturing of the fault face material, which can produce fault gouge.