Degree Of Velocity Anisotropy Research Articles

Velocity anisotropy of Upper Jurassic organic-rich shales, Norwegian Continental Shelf

This study investigates the seismic velocity anisotropy of two organic-rich shales from the Norwegian Continental Shelf. The tested organic-rich shale samples were from the Upper Jurassic Draupne and Hekkingen formations collected from two wells (16/8-3S and 7125/1-1) drilled in the central North Sea and western Barents Sea, respectively. The two tested shales are different in organic matter richness and thermal maturation, and they have experienced different burial histories. The shale core plugs were tested in a triaxial cell under controlled pore pressure. Seismic velocities ([Formula: see text] and [Formula: see text]) were measured along different orientations with respect to layering to identify the complete tensor of the rock elastic moduli, and to investigate the velocity anisotropy as a function of increasing effective stress. The measured velocity values exhibit strong anisotropy for the two tested organic-rich shales. The anisotropy for both shales is strongest for [Formula: see text]. Seismic velocities follow an increasing trend as the effective stress increases. The anisotropy decreases somewhat with increasing consolidation, probably due to the closing of preexisting fractures and microcracks. The reduction of anisotropy is more evident for the P-wave because it decreases from 0.32 to 0.25 for the Draupne sample and from 0.28 to 0.24 for the Hekkingen sample when the vertical effective stress increases from 26 to 50 MPa. In general, the Hekkingen sample indicates slightly higher velocity values than the Draupne sample due to more compaction and lower porosity. In spite of major differences between the two shale formations in terms of organic matter content, maturity and burial history, they indicate almost the same degree of velocity anisotropy. The outcomes of this study can contribute to better imaging of organic-rich Draupne and Hekkingen shales by constraining the rock-physics properties.

Chaotic mixing and the secular evolution of triaxial cuspy galaxy models built with Schwarzschild’s method

We use both N-body simulations and integration in fixed potentials to explore the stability and the long-term secular evolution of self-consistent, equilibrium, non-rotating, triaxial spheroidal galactic models. More specifically, we consider Dehnen models built with the Schwarzschild method. We show that short-term stability depends on the degree of velocity anisotropy (radially anisotropic models are subject to rapid development of radial-orbit instability). Long-term stability, on the other hand, depends mainly on the properties of the potential, and in particular, on whether it admits a substantial fraction of strongly chaotic orbits. We show that in the case of a weak density cusp (gamma=1 Dehnen model) the N-body model is remarkably stable, while the strong-cusp (gamma=2) model exhibits substantial evolution of shape away from triaxiality, which we attribute to the effect of chaotic diffusion of orbits. The different behaviour of these two cases originates from the different phase space structure of the potential; in the weak-cusp case there exist numerous resonant orbit families that impede chaotic diffusion. We also find that it is hardly possible to affect the rate of this evolution by altering the fraction of chaotic orbits in the Schwarzschild model, which is explained by the fact that the chaotic properties of an orbit are not preserved by the N-body evolution. There are, however, parameters in Schwarzschild modelling that do affect the stability of an N-body model, so we discuss the recipes how to build a `good' Schwarzschild model.

The dynamical distance and intrinsic structure of the globular clusterωCentauri

We determine the dynamical distance D, inclination i, mass-to-light ratio M/L and the intrinsic orbital structure of the globular cluster ω Cen, by fitting axisymmetric dynamical models to the ground-based proper motions of van Leeuwen et al. and line-of-sight velocities from four independent data-sets. We bring the kinematic measurements onto a common coordinate system, and select on cluster membership and on measurement error. This provides a homogeneous data-set of 2295 stars with proper motions accurate to 0.20 mas yr -1 and 2163 stars with line-of-sight velocities accurate to 2 km s -1 , covering a radial range out to about half the tidal radius. We correct the observed velocities for perspective rotation caused by the space motion of the cluster, and show that the residual solid-body rotation component in the proper motions (caused by relative rotation of the photographic plates from which they were derived) can be taken out without any modelling other than assuming axisymmetry. This also provides a tight constraint on I) tan i. The corrected mean velocity fields are consistent with regular rotation, and the velocity dispersion fields display significant deviations from isotropy. We model ω Cen with an axisymmetric implementation of Schwarzschild's orbit superposition method, which accurately fits the surface brightness distribution, makes no assumptions about the degree of velocity anisotropy in the cluster, and allows for radial variations in M/L. We bin the individual measurements on the plane of the sky to search efficiently through the parameter space of the models. Tests on an analytic model demonstrate that this approach is capable of measuring the cluster distance to an accuracy of about 6 per cent. Application to w Cen reveals no dynamical evidence for a significant radial dependence of M/L, in harmony with the relatively long relaxation time of the cluster. The best-fit dynamical model has a stellar V-band mass-to-light ratio M/L V = 2.5 ±0.1 M ○. /L ○. and an inclination i = 50° ± 4°, which corresponds to an average intrinsic axial ratio of 0.78 ± 0.03. The best-fit dynamical distance D = 4.8 ± 0.3 kpc (distance modulus 13.75 ± 0.13 mag) is significantly larger than obtained by means of simple spherical or constant-anisotropy axisymmetric dynamical models, and is consistent with the canonical value 5.0 ± 0.2 kpc obtained by photometric methods. The total mass of the cluster is (2.5 ± 0.3) x 10 6 M ○. . The best-fit model is close to isotropic inside a radius of about 10 arcmin and becomes increasingly tangentially anisotropic in the outer region, which displays significant mean rotation. This phase-space structure may well be caused by the effects of the tidal field of the Milky Way. The cluster contains a separate disk-like component in the radial range between 1 and 3 arcmin, contributing about 4% to the total mass.

Dynamically hot galaxies. I - Structural properties

Results are reported from an analysis of the structural properties of dynamically hot galaxies which combines central velocity dispersion, effective surface brightness, and effective radius into a new 3-space (k), in which the axes are parameters that are physically meaningful. Hot galaxies are found to divide into groups in k-space that closely parallel conventional morphological classifications, namely, luminous ellipticals, compacts, bulges, bright dwarfs, and dwarf spheroidals. A major sequence is defined by luminous ellipticals, bulges, and most compacts, which together constitute a smooth continuum in k-space. Several properties vary smoothly with mass along this continuum, including bulge-to-disk ratio, radio properties, rotation, degree of velocity anisotropy, and 'unrelaxed'. A second major sequence is comprised of dwarf ellipticals and dwarf spheroidals. It is suggested that mass loss is a major factor in hot dwarf galaxies, but the dwarf sequence cannot be simply a mass-loss sequence, as it has the wrong direction in k-space.

Electromagnetic beam modes driven by anisotropic electron streams.

A theory is presented which provides an explanation for recent laboratory observations of a 'new electromagnetic' mode in a non-Maxwellian high-beta plasma' and suggests a likely relevance of these modes to space plasmas. Unstable parallel-propagating waves, which can be beam modes or whistlers, depending mainly on the degree of velocity anisotropy in a weak electron beam, are found. In the beam-mode limit relevant to the experiment, this is a kinetic Weibel instability, enhanced by a parallel magnetic field. The frequency of the mode can be above or below the electron cyclotron frequency.

The anisotropic reflectivity technique: anomalous reflected arrivals from an anisotropic upper mantle

Anomalous body wave arrivals due to anisotropy in a subcrustal layer are investigated using synthetic seismograms. Previously, seismograms of such anomalous phases could only be calculated for plane wavefronts, which simulated teleseismic waves. An extension of the reflectivity technique to anisotropic structures now permits the use of a curved wavefront from a local or regional source. Explosion and double couple sources at the surface are used to generate P- and SV-waves, which are incident on simple stratified models of an anisotropic upper mantle. The anisotropic subcrustal layer possesses the same degree of velocity anisotropy as has been found under Western Germany. Anomalous P to SH converted waves, and shear wave splitting, are evident on the synthetic seismograms. Characteristics of the anomalous arrivals which depend on the velocity—depth structures of the models are discussed. It is shown how the velocity contrasts at the base of an anisotropic layer may allow shear wave splitting to remain undetected even for a high degree of anisotropy. These results from simple models seem to indicate that anomalous arrivals on individual three-component seismograms are seldom likely to be of large enough amplitude to be useful for the analysis of upper mantle anisotropy.