Evaluation of stress and displacement fields due to an elliptical plane shear crack

Summary. Following the classic work of Eshelby, the slip and stress distributions due to an elliptical plane shear crack are evaluated. The relation between average (or maximum) slip on the crack and the (constant) static stress drop, for faults of different aspect ratios, is found. The slip vector is not parallel to the applied stress but makes a small angle to it, except when the stress is applied along the major or minor axis of the ellipse. The stress -distribution around the crack shows that in addition to the expected stress concentration along the crack edge, there are broad regions of stress increase off the crack plane for circular and elliptical cracks, similar to those known to exist for in-plane but not for antiplane shear cracks. Whether the stress- intensity factor at the end of one axis is greater or less than that at the end of the other axis ( k_a ≶ k_b ), depends on the condition: √ b/a ≶ (1 − v ) where a and b are the semi-axes of the ellipse, k_a and k_b are the stress-intensity factors at the end of the a- and b -axes and v is Poisson's ratio. The total stress-intensity factor varies smoothly along the edge of the ellipse from one axis to the other and it is found that this variation is rather small.     

Teleseismic body wave radiation from a seismic source in a layered medium

Summary. A simple method is presented which combines the reciprocity theorem and the flat layer theory to yield teleseismic body wave radiation from seismic sources embedded in the Earth's crust. The source is represented by its equivalent body forces and can be quite general. The effect of Yucca Flat geology on explosion signals is studied in detail. In particular, the m _b— M _s relation is shown to be dependent on detonation medium and source depth. Application to shallow earthquake faults demonstrates the strong influence of free surface and layering on the shape of P- and S-wave teleseismic spectra.     

Observation and modelling of fault-zone fracture seismic anisotropy – II. P-wave polarization anomalies

Summary. In Part I of this paper we modelled shear-wave splitting observed in crystalline rock bordering an active, normal fault-zone at Oroville, California, with Červený's ray-tracing system applied to anisotropic heterogeneous media using Hudson's formulation of elastic constants for a medium containing aligned cracks. In Part II we use the ray-tracing results of Part I to quantitatively interpret P -wave polarization anomalies observed in the three-component seismograms recorded in the Oroville fault zone. We show that the eigenvectors of the first-order Christoffel tensor defined by the ray-tracing slowness vector and Hudson's first-order anisotropic corrections to the isotropic elastic tensor correctly account for P -wave first motion that deviates from the ray vector.     

Dynamical rupture process on a three-dimensional fault with non-uniform frictions and near-field seismic waves

Summary. Dynamical rupture process on the fault is investigated in a quasi-three-dimensional faulting model with non-uniform distributions of static frictions or the fracture strength under a finite shearing pre-stress. The displacement and stress time functions on the fault are obtained by solving numerically the equations of motion with a finite stress—fracture criterion, using the finite difference method.
If static frictions are homogeneous or weakly non-uniform, the rupture propagates nearly elliptically with a velocity close to that of P waves along the direction of pre-stress and with a nearly S wave velocity in the direction perpendicular to it. The rise time of the source function and the final displacements are larger around the centre of the fault. In the case when the static frictions are heavily non-uniform and depend on the location, the rupture propagation becomes quite irregular with appreciably decreased velocities, indicating remarkable stick-slip phenomena. In some cases, there remain unruptured regions where fault slip does not take place, and high stresses remain concentrated up to the final stage. These regions could be the source of aftershocks at a next stage.
The stick—slip faulting and irregular rupture propagation radiate high-frequency seismic waves, and the near-field spectral amplitudes tend to show an inversely linear frequency dependence over high frequencies for heavily non-uniform frictional faults.     

Observation and modelling of fault-zone fracture seismic anisotropy - I. P, SV and SH travel times

Summary. Three-component VSP borehole seismograms taken in the vicinity of an active normal fault in California show strong systematic shear-wave splitting that increases with proximity to the fault. Using Červený's method of characteristics for ray tracing in anisotropic heterogeneous media and Hudson's formulation of elastic constants for media-bearing aligned fractures, we have fitted a suite of P, SV and SH hanging-wall and foot-wall travel times with a simple model of aligned fractures flanking the fault zone. The dominant fracture set is best modelled as parallel to the fault plane and increasing in density with approach to the fault. The increase in fracture density is non-uniform (power law or Gaussian) with respect to distance to the fault. Although the hanging-wall and the foot-wall rock are petrologically the same unit, the fracture halo is more intense and extensive in the hanging wall than in the foot wall. Upon approach to the fault plane, the fracture density or fracture-density gradient becomes too great for the seismic response to be computed by Hudson–Červený procedures (the maximum fracture density that can be modelled is about 0.08). Within this 25 m fracture domain it appears more useful to model the fault and near field fractures as a low-velocity waveguide. We observe production of trapped waves within the confines of the intense fracture interval.     

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.