Ray-centred coordinate systems in anisotropic media

Whereas the ray-centred coordinates for isotropic media by Popov and Pšenčík are uniquely defined by the selection of the basis vectors at one point along the ray, there is considerable freedom in selecting the ray-centred coordinates for anisotropic media. We describe the properties common to all ray-centred coordinate systems for anisotropic media and general conditions, which may be imposed on the basis vectors. We then discuss six different particular choices of ray-centred coordinates in an anisotropic medium. This overview may be useful in choosing the ray-centred coordinates best suited for a particular application. The equations are derived for a general homogeneous Hamiltonian of an arbitrary degree and are thus applicable both to the anisotropic-ray-theory rays and anisotropic common S-wave rays.     

Upper mantle beneath the Eger Rift (Central Europe): plume or asthenosphere upwelling?

We present the first results of a high-resolution teleseismic traveltime tomography and seismic anisotropy study of the lithosphere–asthenosphere system beneath the western Bohemian Massif. The initial high-resolution tomography down to a depth of 250 km did not image any columnar low-velocity anomaly which could be interpreted as a mantle plume anticipated beneath the Eger Rift, similar to recent findings of small plumes beneath the French Massif Central and the Eifel in Germany. Alternatively, we interpret the broad low-velocity anomaly beneath the Eger Rift by an upwelling of the lithosphere–asthenosphere transition. We also map lateral variations of seismic anisotropy of the mantle lithosphere from spatial variations of P -wave delay times and the shear wave splitting. Three major domains characterised by different orientations of seismic anisotropy correspond to the major tectonic units—Saxothuringian, Moldanubian and the Teplá-Barrandian—and their fabrics fit to those found in our previous studies of mantle anisotropy on large European scales.     

Recurrence-time and frequency-slip statistics of slip events on the creeping section of the San Andreas fault in central California

An important question in seismic hazard assessments is the frequency-size and recurrence interval statistics at a point on a fault. Does a point on a fault obey the same statistics as earthquakes in a region do? This is a difficult question to answer because the number of repetitive earthquakes on a particular fault that have been observed is small. In order to overcome this difficulty we consider slip events on the creeping section of the San Andreas fault in central California. Sequences of up to 100 events are obtained from creepmeter records. We compare the statistical distribution of recurrence times with the Brownian passage-time, lognormal, and Weibull distributions and using goodness-of-fit tests find that the Weibull is the preferred distribution. We also consider the frequency–amplitude distribution of slip events. We find that the data clearly do not obey a Gutenberg–Richter distribution. Instead there is a uniform distribution of event sizes for a large fraction of events.     

Identification of symmetry planes in weakly anisotropic elastic media

A procedure is proposed to obtain symmetry properties of weakly anisotropic (WA) elastic media by giving 15 WA parameters of qP wave in an arbitrary Cartesian coordinate system. The 15 WA parameters, which linearly depend on 21 elastic elements, form a complete set to determine the symmetry planes in WA materials. The procedure is based on the eigenvalue problems of two matrices. One of the matrices consists of the Voigt and dilatational matrices, and the other is an acoustic tensor defined by an irreducible, completely symmetric and traceless, fourth-rank tensor resulting from decomposition of the fourth-rank elastic tensor. If the eigenvectors are taken as the axes of a new coordinate system (called symmetry Cartesian coordinate system), the transformation of WA parameters from an arbitrary Cartesian coordinate system to a symmetry Cartesian coordinate system can reduce the number of distinct WA parameters of elastic materials except in triclinic medium.