Quasi-static crack models and the frictional stress threshold criterion for slip arrest

Summary. Two-dimensional crack problems in elastic homogeneous isotropic media are considered which describe rupture over a fault surface characterized by non-uniform stress drop. Solutions can be found in which the stress field is finite at the crack tips and the rupture surface is not assigned a priori , but is part of the solution. These crack models are found to be consistent with the frictional stress threshold criterion for slip arrest over pre-existing fault surfaces. A crack is found to stop when its contribution to the stress field is opposite to the stress drop at the crack tips. The quasi-static propagation of a crack up to the arrest configuration is studied in terms of the minimum energy principle. The crack spontaneously propagates in such a way as to make the value of the stress intensity factor at one tip equal to the value at the other tip. Furthermore a tip propagating in a region with higher friction is found to move more slowly than the other tip propagating in a region with lower friction. Simple criteria for fracture arrest are derived, in terms of a properly averaged stress drop. Piecewise constant stress drop profiles are explicitly considered yielding a variety of solutions which can be applied to modelling asperities or barriers over a fault plane. The evaluation of the amount of the energy released during the quasi-static crack propagation shows that stopping phases cannot be efficiently radiated if the crack comes to rest in a low friction region.     

Stress and temperature in subduction shear zones: Tonga and Mariana

Summary. Because there is secondary sea-floor spreading in the Tonga and Mariana subduction systems, the island arcs are separate plates. Horizontal forces on the two sides of the arc must balance, and the maximum force on the back-arc side can be calculated from a lithostatic ridge model. This, in combination with gravity data, allows calculation of the average shear stress in the top 100 km of the subduction shear zone. Stress in Tonga is 220±100 bar, and in the Mariana it is 165±75 bar. These low stresses are probably made possible by a fluid pore pressure almost equal to the least compressive stress.
Knowledge of stress allows approximate calculation of temperature in the shear zone by integration of a single differential equation. These temperatures are too low to activate most dehydration reactions in the subducted crust. As it approaches the volcanic line, this crust is at 150–350°C in Tonga and 150–300°C in the Mariana. Shear melting of the crust is ruled out, and conductive melting of the slab by contact with the asthenosphere meets with geochemical objections. Magmas in these systems are probably produced by partial melting of asthenosphere, triggered by a sudden release of water from the slab.     

Upper crustal shear velocity models from higher mode Rayleigh wave dispersion in Scotland

Summary. Group velocities for first and second higher mode Rayleigh waves, in the frequency range 0.8–4.8 Hz, generated from a local earthquake of magnitude 3.7 M _L in western Scotland, are measured at stations along the 1974 LISPB line. These provide detailed information about the crustal structure west of the line. The data divide the region into seven apparently homogeneous provinces. Averaged higher mode velocity dispersion curves for each province are analysed simultaneously using a linearized inversion technique, yielding regionalized shear velocity profiles down to a depth of 17 km into the upper crust. Shear wave velocity is between 3.0 and 3.4 km s⁻¹ in the upper 2 km, with a slow increase to around 3.8 km s⁻¹. P -wave models computed using these results agree with profiles from the LISPB and LUST refraction experiments.     

Coupled normal-mode sensitivity to inner-core shear velocity and attenuation

We have studied the response of normal modes to perturbations in inner-core shear velocity and attenuation, using fully coupled mode synthetics. Our results indicate that (i) mode pairs   _n S _l – _{n ±1} S _l   are strongly coupled by anelasticity, (ii) this coupling causes shear velocity perturbations to strongly affect the Q values of modes through exchange of inner-core characteristics, (iii) there is no evidence for a weakly attenuating inner core in shear, and (iv) the discrepancy between attenuation models returned from normal modes and body waves is small. These results suggest that inversions for inner-core attenuation and shear velocity should be performed simultaneously and should take account of the strong cross-coupling due to attenuation.     

Application of some dynamic properties of stick—slip to earthquakes

Summary . Quantitative comparison of dynamic parameters is made between stick—slip in the laboratory and earthquakes in the Earth. It is shown that the same theory is successfully applied for both earthquakes and stick—slip for rock samples for which slip occurs over the entire pre-existing fault, in so far as the physical processes of earthquakes are explained by the elastic rebound theory.     

Retrieving shear velocity structure from high-frequency toroidal modes of the Earth

Summary. For a smooth earth model, observations of a set of high-frequency toroidal modes at fixed slowness yield only a single piece of information, the tau value for that slowness. In this note, a procedure for obtaining the shear velocity structure from free oscillation data for an earth model with velocity discontinuities is developed, based on the method of tau inversion. The information content of the high-frequency modes is greater in this case, and the nature and depths of the discontinuities may be deduced. It is shown, for the real Earth, that the tau values obtained from free oscillation data are affected significantly by the presence of the Moho, but a simple iterative scheme may be used to remove this contamination. Brune's method of deducing mode frequencies from body wave pulses is shown to produce significant errors for a model with a pronounced Moho discontinuity, and the same iterative scheme may also be employed to correct for this effect.