A perturbation theory for Love waves in anelastic media

Summary. We give a systematic formulation and a rigorous justification of a perturbation technique for the computation of the eigenvalues and eigenfunctions of Love waves (and toroidal oscillations by an appropriate change for variables) in an anelastic medium with a constitutive law modelling geophysical media of current interest such as the Kelvin—Voigt Solid, the Maxwell Solid, the Standard Linear Solid, and the Standard Linear Solid with a continuous spectrum of relaxation times. We develop expressions relating the eigenvalues of eigenfunctions for Love waves in a continuously varying vertically stratified anelastic half-space to the corresponding elastic eigenvalues and eigenfunctions. Analytically, our correspondence principle has the form of a regular perturbation expansion in terms of a parameter for both the eigenvalues and eigenfunctions. The identification of ɛ is motivated by the dissipativity principle of viscoelasticity theory. Moreover, we show that our correspondence principle applies respectively only in the high and low frequency range for the Maxwell and Kelvin—Voigt Solids. Outside of the applicable range of frequencies, our correspondence principle yields no useful information. For the family of Standard Linear Solids it is uniformly applicable for all non-zero frequencies.
We also derive an explicit formula to estimate the radius of convergence of our perturbation expansions. This estimate of the radius of convergence for each eigenvalue and eigenfunction is functionally defined by the constitutive model for the anelastic medium. The estimate is frequency dependent and depends on the separation distance between the eigenvalue and the remainder of the spectrum of the corresponding elastic problem.     

Volcanic style in the Strand Fiord Formation (Upper Cretaceous), Axel Heiberg Island, Canadian Arctic Archipelago

The Strand Fiord Formation is a volcanic unit of early Late Cretaceous age which outcrops on west-central and northwestern Axel Heiberg Island in the Canadian Arctic Archipelago. The formation is part of the thick Sverdrup Basin succession and immediately precedes the final basin foundering event. The Strand Fiord volcanics are encased in marine strata and thin southward from a maximum thickness of 789+ m on northwestern Axel Heiberg to a zero edge near the southern shore of the island. Tholeiitic icelandite flows are the main constituent of the formation with volcaniclastic conglomerates, sandstones, mudrocks and rare coal seams also being present. The lava flows range in thickness from 6 to 60 m and subaerial flows predominate. Both pahoehoe and aa lava types are common and the volcanic pile accumulated mostly by the quiet effusion of lavas. The volcaniclastic lithologies become more common near the southern and eastern edges of the formation and represent lahars and beach to shallow marine reworked deposits. The Strand Fiord volcanics are interpreted to represent the cratonward extension of the Alpha Ridge, a volcanic ridge that was active during the formation of the Amerasian Basin.     

Has the crab pulsar magnetic field grown after its birth?

We investigate the evolution of rotation period and spindown age of a pulsar whose surface magnetic field undergoes a phase of growth. Application of these results to the Crab pulsar strongly indicates that its parameters cannot be accounted for by the field growth theories.     

Astrometry from space: GAIA and planet detection

The proposed baseline GAIA mission will be able to detect the astrometric signature of Jupiter-size planets around of the order of a million stars, using either global or narrow-angle astrometry. If the mission can realize the higher astrometric accuracy that photon statistics allows for bright stars, lower-mass planets (from Earth size to ten times larger) can be found around ten to a few hundred stars.     

Influence of viscous dissipation on a hydromagnetic field

The effect of a transverse magnetic field and of the viscosity diffusion on the free-convection flow of an electrically-conducting incompressible fluid past a uniformally accelerated vertical plate is discussed. A finite difference method has been used to obtain a numerical solution. The influence of the various parameters on the flow field is discussed.     

Tensile stresses around boreholes due to transient fluid flow

We present solutions for the effective stress induced by gas flow through a porous solid into a borehole resulting from sudden pressure reduction. Tensile effective stress that exceeds the strength of the solid will lead to borehole failure. This has applications to the intentional creation of cavities, relevant to the efficient recovery of coalbed methane, and the avoidance of borehole stability problems in conventional gas production.