On the tesseral-harmonics resonance problem in artificial-satellite theory

The longitude-dependent part of the geopotential usually gives rise only to short-period effects in the motion of an artificial satellite. However, when the motion of the satellite is commensurable with that of the earth, the path of the satellite repeats itself relative to the earth and perturbations build up at each passage of the satellite in the same spot, so that there can be important long-period effects. In order to take these effects into account in deriving a theoretical solution to the equations of motion of an artificial satellite, it is necessary to select terms in the longitude-dependent part of the geopotential that will contribute significantly to the perturbations. Attempts made to obtain a selection that is valid in a general case, regardless of the initial eccentricity of the orbit and of the order of the resonance, are reported. The solution to the equations of motion of an artificial satellite, in a geopotential thus determined, is then derived by using Hori's method by Lie series, which, by its properties regarding canonical invariance, has proved advantageous in the classical theory

On the Tesseral-Harmonics Resonance Problem in Artificial-Satellite Theory, Part 2

Equations were derived for the perturbations on an artificial satellite when the motion of the satellite is commensurable with that of the earth. This was done by first selecting the tesseral harmonics that contribute the most to the perturbations and then by applying Hori's method by use of Lie series. Here, are introduced some modifications to the perturbations, which now result in better agreement with numerical integration

On moment‐length scaling of large strike slip earthquakes and the strength of faults

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94719/1/grl15585.pd

Observations of changing anisotropy across the southern margin of the African LLSVP

We present evidence for the presence of complex anisotropy in the lowermost mantle from 3-D waveform modelling of observed core-diffracted shear waves that sample the southern edge of the African Large Low Shear Velocity Province (LLSVP). The anomalously strong amplitude of the SV component for the shear core-diffracted phase at large distances indicates the presence of anisotropy. We measure shear wave splitting parameters to determine which part of the elastic tensor is constrained by this particular data set. The modelling is performed using the spectral element method. The anisotropy is strong outside the LLSVP, weakens or rotates close to its boundary, and appears to be absent inside the LLSVP. The presence of the LLSVP margin may cause flow in the mantle to change direction. The occurrence of strong anisotropy in the region of fast seismic velocities is compatible with lattice-preferred orientation in post-perovskite due to accommodation of flow through dislocation creep

Short wavelength topography on the inner-core boundary

Constraining the topography of the inner-core boundary is important for studies of core–mantle coupling and the generation of the geodynamo. We present evidence for significant temporal variability in the amplitude of the inner core reflected phase PKiKP for an exceptionally high-quality earthquake doublet, observed postcritically at the short-period Yellowknife seismic array (YK), which occurred in the South Sandwich Islands within a 10-year interval (1993/2003). This observation, complemented by data from several other doublets, indicates the presence of topography at the inner-core boundary, with a horizontal wavelength on the order of 10 km. Such topography could be sustained by small-scale convection at the top of the inner core and is compatible with a rate of super rotation of the inner core of ≈0.1–0.15° per year. In the absence of inner-core rotation, decadal scale temporal changes in the inner-core boundary topography would provide an upper bound on the viscosity at the top of the inner core

Towards Inverting Seismic Waveform Data for Temperature and Composition in the Earth's Upper Mantle

B: Unraveling the physical state of the upper mantle, including the transition zone, is one of the key factors for understanding the Earth's mantle dynamics. Knowledge of mantle temperature and composition is mainly based on the interpretation of seismological observations based on insights from mineral physics. Despite the progress made to image the 3-D seismic structure of the upper mantle, its interpretation in terms of physical parameters is still challenging and it requires a truly interdisciplinary approach. Due to the better knowledge of the elastic and anelastic properties of mantle minerals at high temperatures and pressures, such an approach is now becoming feasible. We propose a new waveform inversion procedure, based on a formalism previously developed at Berkeley for global elastic and anelastic tomography, and using our existing collection of long-period fundamental and higher mode surface waveforms. Here, we incorporate mineral physics data at an early stage of the process to directly map lateral variations in temperature and composition, using recent estimates of the temperature and composition derivatives of seismic velocities (∂lnV/∂lnT,C). Anelasticity introduces a non-linear dependence of the seismic velocities with temperature throughout the upper mantle, and phase-transitions confer a non-linear character to the compositional derivatives as well, therefore the kernels should be re-computed after each iteration of the inversion. We discuss ways to address the non-linearities, as well as uncertainties in the partial derivatives. In addition to constraining the lateral variations in temperature or composition, the models can have implications on the average structure of the upper mantle. The most-common accepted physical 1-D structure had problems to satisfactorily fit seismic travel time data, requiring a slower TZ to improve the fit. However, these data do not have sufficient coverage (and resolution) in the TZ. A complementary outcome of our models will be to shed light on whether the seismic data require a modification of the physical structure in the transition zone and if the three-dimensional heterogeneity introduces a significant shift of the average physical structure away from adiabatic pyrolite

A Refined Approach to Model Anisotropy in the Lowermost Mantle

© 2018 Institute of Physics Publishing. All rights reserved. Seismic anisotropy in the lowermost mantle has been attributed to texture development during mantle convection. This study models texture evolution in a subducting slab impinging on the core-mantle boundary. Using a 3-dimensional geodynamic model with tracers recording the deformation history, a visco-plastic self-consistent (VPSC) model for polycrystal deformation, and relying on experimentally determined slip systems, aggregate grains with volume fractions of 60% orthorhombic silicate perovskite (MgSiO3), 20% cubic calcium perovskite (CaSiO3), and 20% cubic ferropericlase ((Mg,Fe)O) were deformed plastically and developed crystal preferred orientation. Forward and reverse perovskite (Pv)-postperovskite (PPv) phase transitions were included by allowing for likely orientation variant selections. Grain orientations, P (compression) and S (shear) wave velocity pole figures were calculated for each phase as well as the aggregate. The results show that dominant (001) slip on PPv can produce strong texture and shear wave anisotropy of 0.01-3.07% with VSH >VSV which agrees with seismological observations in selected areas of the D" layer

Time-reversal method and cross-correlation techniques by normal mode theory: a three-point problem

International audienceSince its beginning in acoustics, the Time-Reversal method (hereafter referred as TR) has been explored by different studies to locate and characterize seismic sources in elastic media. But few authors have proposed an analytical analysis of the method, especially in the case of an elastic medium and for a finite body such as the Earth. In this paper, we use a normal mode approach (for general 3-D case and degenerate modes in 1-D reference model) to investigate the convergence properties of the TR method. We first investigate a three-point problem, with two fixed points which are the source and the receiver and a third one corresponding to a changing observation point. We extend the problem of a single channel TR experiment to a multiple channel and multiple station TR experiment. We show as well how this problem relates to the retrieval of Green's function with a multiple source cross-correlation and also the differences between TR method and cross-correlation techniques. Since most of the noise sources are located close to the surface of the Earth, we show that the time derivative of the cross-correlation of long-period seismograms with multiple sources at the surface is different from the Green's function. Next, we show the importance of a correct surface-area weighting of the signal resent by the stations according to a Voronoi tessellation of the Earth surface. We use arguments based on the stationary phase approximation to argue that phase-information is more important than amplitude information for getting a good focusing in TR experiment. Finally, by using linear relationships between the time-reversed displacement (resp. strain wavefields) and the components of a vector force source (resp. a moment tensor source), we show how to retrieve force (or moment tensor components) of any long period tectonic or environmental sources by time reversal

The Aromatase Gene (CYP19A1) Variants and Circulating Hepatocyte Growth Factor in Postmenopausal Women

Background: Estrogen and androgen have been linked to the regulation of circulating hepatocyte growth factor (HGF), an adipose tissue-derived cytokine. It is possible that the CYP19A1 gene which alters sex hormones production may influence HGF levels. We examined the association between the CYP19A1 gene variants and plasma HGF concentrations. Design We evaluated 45 common and putative functional variants of CYP19A1 and circulating levels of HGF among 260 postmenopausal women who later developed colorectal cancer from the Women's Health Initiative Observational Cohort. As the distribution of HGF levels was highly skewed, we transformed HGF concentrations for all women into a log-, ranked-, or normal score-scale value. Multiple linear regression with adjustment for age was used to evaluate the associations. Results: We observed an association between the rs7172156, rs1008805, rs6493494, rs749292, and rs11636639 variants and HGF levels in ranked and normal score scales (corrected p values ≤0.02), although the association of these 5 SNPs with log-scale HGF was not significant (corrected p values ≥0.16). The associations remained unchanged after additional adjustment for hormone therapy use and estradiol levels. These 5 SNPs, which were in linkage disequilibrium (pairwise D′≥97%, r2≥56%), constituted a block with 2 common haplotypes accounting for 82% frequency. The most common haplotype, TCCCA, was associated with lower ranked- or normal score-transformed HGF levels (corrected p values ≤0.001), whereas the second most common haplotype, CTTCA, was associated with higher ranked- or normal score-transformed HGF levels (corrected p values ≤0.02). Conclusion: Our findings of a potential association between the CYP19A1 variants and circulating HGF levels warrant confirmation in studies with larger sample size