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SUMMARY There is evidence that magma chambers are not fed by a continuous flow, but in the form of discrete magma batches. The possibility is considered that the chamber is fed by a magma bubble ascending through the region underneath, driven by buoyancy force. Due to the high ambient temperatures, it is assumed that the bubble moves through a viscoelastic medium with temperature-dependent viscosity. The motion of a spherical magma bubble and its inflow into the chamber are studied. The bubble volume is assumed to be at least equal to magma volumes in typical effusive eruptions on Mount Etna, corresponding to bubble radii of a few hundred metres. Under some simplifying assumptions, the problem is solved analytically. The bubble velocity is directly proportional to the square of its radius and inversely to the viscosity of surrounding rocks, but it is independent of magma viscosity. Velocity can reach values of the order of tens of metres per year in the proximity of the chamber. Since the characteristic time for heat diffusion is several hundred years, the bubble can cover several kilometres with only moderate cooling. During ascent, forced convection takes place in the bubble. Equations for convection streamlines are obtained and traveltimes of magma are calculated, giving a mixing time of the order of hundred years below the chamber. Inflow of the bubble in the magma chamber produces a pulse in flow rate. Under reasonable assumptions, pulse shape and duration are calculated analytically. Pulse duration can be several tens of years and can give rise to a sequence of eruptions, depending on the size of the bubble and the critical overpressure for eruption.

SUMMARY Atmospheric shock waves are a common phenomenon in explosive volcanic eruptions. We consider the motion of a spherical shock wave generated by a point source in the strong shock approximation. The shock front corresponds to discontinuities in the gas velocity, density, pressure and temperature, which are calculated as functions of the energy of the explosion. The problem is solved analytically for the distributions of velocity, density, pressure and temperature in the atmosphere as functions of the distance from the source. The motion of the shock wave being supersonic, the solution is valid for a few seconds after the explosion, corresponding to a distance of few kilometres. The acoustic effect of the shock wave, expressed by the peak sound pressure level, is calculated and may reach hundreds of decibels. The pressure waveform that could be recorded in the vicinity of the volcano is calculated and compared with typical waveforms in weak shock conditions. The change in the refractive index of air due to density inhomogeneity is calculated and the conditions under which a condensation cloud is formed behind the shock front are investigated.

SUMMARY Volcanic rocks forming sills, dykes or lava flows may display a magnetic anisotropy derived from the viscous flow during their emplacement. We model a sill as a steadystate flow of a Bingham fluid, driven by a pressure gradient in a horizontal conduit. The magma velocity as a function of depth is calculated from the motion and constitutive equations. Vorticity and strain rate are determined for a reference system moving with the fluid. The angular velocity and the orientation of an ellipsoidal magnetic grain immersed in the fluid are calculated as functions of time or strain. Magnetic susceptibility is then calculated for a large number of grains with a uniform distribution of initial orientations. It is shown that the magnetic lineation oscillates in the vertical plane through the magma flow direction, and that the magnetic foliation plane changes periodically from horizontal to vertical. The results are compared with the magnetic fabric of Ferrar dolerite sills (Victoria Land, East Antarctica) derived from low-field susceptibility measurements.

Summary, A microplate is modelled as an elastic plate with two long strike-slip boundaries, lying over a Maxwell-type viscoelastic asthenosphere. The microplate is subjected to a constagt and uniform shear strain rate by the opposite motions of two adjoining larger plates. After the occurrence of an earthquake at one of the microplate boundaries, the time evolution of shear stress at the other boundary is studied. It is found that stress build-up at the second boundary is delayed due to stress diffusion governed by the asthenosphere relaxation. Earthquake occurrence at this latter boundary would be delayed depending upon both the microplate width and the ratio between the Maxwell relaxation time of the asthenosphere and a characteristic time required for tectonic strain to recover rupture conditions. It turns out that the parameters which determine the occurrence of seismic activity along the microplate boundaries are more strictly constrained in the presence of a viscoelastic asthenosphere than in the case of an elastic halfspace model.

A crack model in antiplane shear configuration is shown representing creep processes interpreted in terms of ‘viscous’ deformation of a narrow plastic layer, characterized by inhomogeneous rheological properties, embedded within a homogeneous elastic medium. The evolution in time of slip and stress over the crack plane is studied through a truncated expansion in Chebyshev polynomials, and convergence is proved to be fast in the simple examples considered. Finite‐stress solutions are found which are compatible with constitutive relations of elasto‐plastic materials and furthermore these allow us to simulate creep propagation and stress transfer between locked and unlocked fault segments. This model provides a simple interpretation of the shallow depth of the seismogenic layer observed in several areas of the world and lends itself to modelling creep processes during either post‐seismic rebound or pre‐seismic stress buildup. Stress transfer is accomplished mostly by the slow extension of the creeping section. During a seismic cycle it is envisaged that different regimes dominate over deep, intermediate and shallow sections of faults: (i) slow pre‐seismic stress build‐up accompanied by creep and stress migration toward intermediate depths; (ii) brittle fracture over shallow and intermediate sections of faults; (iii) post‐seismic rebound over intermediate and deep sections of faults. The present crack model, while providing finite‐stress solutions, allows a better understanding of how stress may accommodate at different depths over a fault plane during a seismic cycle.

Summary. A strike-slip plate boundary is considered with non-uniform strength. Depth-dependent slip on the fault surface is assumed to occur aseismically in the lower fault section, in response to a basal shear stress, and seismically in the brittle upper section. The upper fault section acts as a barrier, preventing aseismic slip from reaching shallower depths. If, however, friction decreases in the proximity of the Earth's surface, brittle fracture may occur beyond the barrier. It is found that, when friction in the uppermost fault section exceeds the applied shear stress, fault slip occurs there with a smaller amplitude than at larger depth. This may explain the discrepancies, which have been sometimes reported, between fault offsets observed at the Earth's surface and fault offsets inferred from seismograms by using simpler dislocation models.

Summary. We consider a long strike-slip fault in a lithosphere modelled as an elastic slab. To the base of the slab a shear stress distribution is applied which simulates the viscous drag exerted by the asthenosphere. The resulant stress on the fault plane may directly fracture the lithosphere in its brittle upper portion; alternatively it may give rise at first to a stable aseismic sliding in the lower portion. In the latter case, stress concentration due to the deep aseismic slip is the relevant feature of the pre-seismic stress acting on the upper section of the lithosphere. The two cases are examined by use of dislocation theory and their observable effects compared. Different depths of the aseismic slip zone and the presence or absence of a uniform friction on the seismic fault are allowed for. If the model is applied to the San Andreas fault region, where a steady sliding condition actually seems to be present at shallow depth, it turns out that the slip amplitudes commonly associated with large earthquakes are consistent with average basal stress values which can be substantially lower than a few bars, a value often quoted as the steady state basal stress due to a velocity gradient in the upper asthenosphere.