Shear-wave Anisotropy in the Earth’s Inner Core

Earth’s inner core anisotropy is widely used to infer the deep Earth's evolution and present dynamics. Many compressional-wave anisotropy models have been proposed based on seismological observations. In contrast, inner-core shear-wave (J-wave) anisotropy – on a par with the compressional-wave anisotropy – has been elusive. Here we present a new class of the J-wave anisotropy observations utilizing earthquake coda-correlation wavefield. We establish that the coda-correlation feature I2-J, sensitive to J-wave speed, exhibits time and amplitude changes when sampling the inner core differently. J-waves traversing the inner core near its center travel faster for the oblique than equatorial angles relative to the Earth’s rotation axis by at least ~5 s. The simplest explanation is the J-wave cylindrical anisotropy with a minimum strength of ~0.8%, formed through the lattice-preferred-orientation mechanism of iron. Although we cannot uniquely determine its stable iron phase, the new observations rule out one of the body-centered-cubic iron models.

New measurements of long-period radial modes using large earthquakes

SUMMARY Radial modes, nS0, are long-period oscillations that describe the radial expansion and contraction of the whole Earth. They are characterized only by their centre frequency and quality factor Q, and provide crucial information about the 1-D structure of the Earth. Radial modes were last measured more than a decade ago using only one or two earthquakes. Here, we measure radial modes using 16 of the strongest and deepest earthquakes of the last two decades. By introducing more earthquake data into our measurements, we improve our knowledge of 1-D attenuation, as we remove potential earthquake bias from our results. For mode 0S0, which is dominated by compressional energy, we measure a Q value of 5982, much higher than previously measured, and requiring less bulk attenuation in the Earth than previously thought. We also show that radial modes cross-couple (resonate) strongly to their nearest spheroidal mode due to ellipticity and inner core cylindrical anisotropy. Cross-coupling improves the fit between data and synthetics, and gives better estimates of the centre frequency and attenuation value of the radial modes. Including cross-coupling in our measurements results in a systematic shift of the centre frequencies of radial modes towards the Preliminary Reference Earth Model. This shift in centre frequencies, has implications for the strength of the radial anisotropy present in the uppermost inner core, with our cross-coupling results agreeing with lower values of anisotropy than the ones inferred from just measuring the modes in self-coupling (isolation). Furthermore, cross-coupling between radial modes and angular-order two modes provides constraints on cylindrical inner core anisotropy, that will help us improve our knowledge of the 3-D structure of the inner core.

Modeling of anisotropic base plate of a ballastless railway track under dynamic influences

Introduction. Due to dynamic loading, the upper structure of the railway track is subject to deformation over the entire construction and operation period. This paper focuses on the development of a mathematical model of the base plate of a general-type ballastless railway track structure without relying on specific existing technological solutions used for such elements. The effect of the actually given vertical component of the rolling stock velocity arising from the deviation from the design position of the long-welded rails on the dynamic deflection of the plate and the contact force of cylindrical anisotropy and the initial rate of dynamic interaction is studied. The proposed model makes it possible to take into account the effect of elastic waves originating in the contact area between the wheel and the rail that move at their final speeds after contact. The actual issue researched in this paper is the reinforcement of the ballastless railway base plate for the prevention of severe damage in the base plate. Materials and methods. A mathematical model has been developed to describe the dynamic behavior of a reinforced concrete plate of a ballastless railway track taking into account the specifics of load application from rolling stock wheel sets. Results. Detailed presentation of the research results in the form of analytical expressions and dependence diagrams of dynamic and kinematic parameters of the structure behavior can have practical application when designing rapid transit and high-speed railway lines both in Russia and abroad. Conclusions. The obtained results can be used for carrying out full-fledged research of dynamic behavior of the track bed under mobile loading, for checking the local durability of plates under shock impact, for researching and selecting optimal rigidity parameters for the track bed.

Constraining 1-D inner core attenuation through measurements of strongly coupled normal mode pairs

SUMMARY We measured inner core normal mode pair 10S2–11S2, which cross-couples strongly for 1-D structure and is sensitive to shear wave velocity, and find that our measurements agree with a strongly attenuating inner core. In the past, this mode pair has been used to try to resolve the debate on whether the inner core is strongly or weakly attenuating. Its large spectral amplitude in observed data, possible through the apparent low attenuation of 10S2, has been explained as evidence of a weakly attenuating inner core. However, this contradicted body waves and other normal modes studies, which resulted in this pair of modes being excluded from inner core modelling. Modes 10S2 and 11S2 are difficult to measure and interpret because they depend strongly on the underlying 1-D model used. This strong dependence makes these modes change both their oscillation characteristics and attenuation values under a small 1-D perturbation to the inner core model. Here, we include this effect by allowing the pair of modes to cross-couple or resonate through 1-D structure and treat them as one hybrid mode. We find that, unlike previously thought, the source of 10S2 visibility is its strong cross-coupling to 11S2 for both 1-D elastic and anelastic structure. We also observe that the required 1-D perturbation is much smaller than the 2 per cent vs perturbation previously suggested, because we simultaneously measure 3-D structure in addition to 1-D structure. Only a 0.5 per cent increase in inner core vs or a 0.5 per cent decrease in inner core radius is required to explain 10S2–11S2 observations and a weakly attenuating inner core is not needed. In addition, the 3-D structure measurements of mode 10S2 and its cross-coupling to 11S2 show the typical strong zonal splitting pattern attributed to inner core cylindrical anisotropy, allowing us to add further constrains to deeper regions of the inner core.

Scientifically substantiated technology for reverse extrusion of products made of anisotropic tubular billets

The theoretical research results of the reverse extrusion of a heavy-walled tubular billet made of orthotropic material having a cylindrical anisotropy of stress-strain properties are presented. The assessment of force modes and limiting potentialities of the reverse extrusion of anisotropic tubular billets is carried out.

ETHOD OF COMPENSATING LOADS FOR SOLVING OF ANISOTROPIC MEDIUM PROBLEMS

The work applies the method of compensating loads (MCL) for solution of statics and vibrations problems of plates with cylindrical anisotropy. For receiving of basic and compensating solutions Nielsen’s equation is used. The solution expressed in terms of Bessel functions is obtained. Such way can be used in con-sideration of symmetric, antisymmetric and unsymmetric flexure of orthotropic circular plates resting on an elastic Winkler’s subgrade. The similar method can be also utilized for examination of the symmetric vibrations of the orthotropic circular plates as well as for the cases of vibrations with one or a few nodal diameters. The solutions are obtained in closed form in terms of the cylindrical functions.