Depth of the brittle-ductile transition in a transcurrent boundary zone

A model is proposed which describes the boundary zone between two transcurrent plates as a viscoelastic body, with rheological properties changing with depth. In this model, the brittle-ductile transition is defined as the depth at which the time derivative of shear stress changes from positive to negative values. Variations of this depth are studied as functions of geothermal gradient, rheological parameters and strain rate, using a power law rheology with exponent ranging from 1 to 4. Stress relaxation in the ductile zone is controlled by a local characteristic time, which depends on petrology, temperature and, in the case of non-Newtonian rheology, on strain rate. The composition and the hydration degree of crustal rocks may also sensibly influence the depth of the brittle-ductile transition. The model predictions are compared with observations regarding the San Andreas, Imperial Valley and North Anatolian Faults: it is found that values ofn from 1 to 3 are more appropriate to reproduce the transition depth inferred by the seismicity distribution.     

Asperity distribution of the 1964 Great Alaska earthquake and its relation to subsequent seismicity in the region

The 1964 Alaska earthquake was the second largest seismic events in the 20th century. The aim of this work is the use of surface deformation data to determine asperity and slip distributions on the fault plane of the Alaska earthquake: these distributions are calculated by a Monte Carlo method. To this aim, we decompose the fault plane in a large number of small square asperity units with a side of 25 km; this allows us to obtain plane surfaces with an irregular shape. In the first stage, each asperity unit is allowed to slip a constant amount or not to slip at all, providing the geometry of the dislocation surface that best reproduces the observed displacements. To this purpose, a large number of slip distributions have been tried by the use of the Monte Carlo method. The slip amplitude is the same for all the asperities and is equal to the average fault slip inferred from the seismic moment. In the second stage, we evaluate the slip distribution in the dislocation area determined by the Monte Carlo inversion: in this case, we allow unit cells to undergo different values of slip in order to refine the initial dislocation model. The results confirm the previous finding that the slip distribution of the great Alaska earthquake was essentially made of two dislocation areas with a higher slip, the Prince William Sound and the Kodiak asperities. Analysis of the post-1964 seismicity in the rupture region shows a strong correlation between the larger earthquakes (M_w≥6) and the distribution of locked asperities following the 1964 event, which can be considered as an independent test of the validity of the model. We do not find slip values higher than 25 m for any of the patches, and we determine two separate high-slip zones: one correspondent to the Prince William Sound asperity, and one (18 m slip) to the Kodiak asperity. The slip distribution connected with the 1964 shock appears to be consistent with the following seismicity in the region.     

A dislocation model of microplate boundary ruptures n the presence of a viscoelastic asthenosphere

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 constant 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 half-pace model.     

A crack model of creep processes on deep sections of faults

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.     

Lava flow in tubes with elliptical cross sections

We develop a model of lava flow in a cylindrical tube with elliptical cross section. The lava is considered an isothermal, incompressible Newtonian fluid. We solve analytically the steady-state Navier–Stokes equation under a constant driving force, given by the component of gravity along the axis of the tube and obtain the velocity and stress field components in the fluid. The ratio between the flow rate of the elliptical tube and that of a circular tube, having the same cross sectional area, is found to be always less than 1 and to depend only on the value of eccentricity. The ratio decreases rapidly when the eccentricity becomes lower than about 0.5. The average flow velocity in a partially filled tube is calculated under the assumption of constant flow rate. In an elliptical tube, the shear traction is not uniform on the wall of the tube, but changes periodically with the position. It is maximum at the intersections with the minor axis and minimum at the intersections with the major axis, the ratio between the maximum and the minimum value being equal to the ratio between the lengths of the two axes. Assuming that the erosion rate of the wall of the tube is proportional to shear traction, we calculate the erosion of the wall as a function of time and find that its effect is such as to make the tube cross section closer to the circular shape.