is described by the mean anomaly l or equivalently the mean longitude ϵ l ϩ . Collectively these variables are called orbital elements. In the Kepler problem, where a single planet orbits a spherical star, all the elements of the planet except the mean longitude are fixed, which is why the elements are useful quantities. We use the masses and a, e, and i from the JPL ephemeris DE200 (Table 2). 6.

No abstract

Ongoing plate convergence between India and Eurasia provides a natural laboratory for studying the dynamics of continental collision, a fi rst-order process in the evolution of continents, regional climate, and natural hazards. In southeastern Tibet, the fast directions of seismic anisotropy determined using shear-wave splitting analysis correlate with the surfi cial geology including major sutures and shear zones and with the surface strain derived from the global positioning system velocity fi eld. These observations are consistent with a clockwise rotation of material around the eastern Himalayan syntaxis and suggest coherent distributed lithospheric deformation beneath much of southeastern Tibet. At the southeastern edge of the Tibetan Plateau we observe a sharp transition in mantle anisotropy with a change in fast directions to a consistent E-W direction and a clockwise rotation of the surface velocity, surface strain fi eld, and fault network toward Burma. Around the eastern Himalayan syntaxis, the coincidence between structural crustal features, surface strain, and mantle anisotropy suggests that the deformation in the lithosphere is mechanically coupled across the crust-mantle interface and that the lower crust is suffi ciently strong to transmit stress. At the southeastern margin of the plateau in Yunnan province, a change in orientation between mantle anisotropy and surface strain suggests a change in the relationship between crustal and mantle deformation. Lateral variations in boundary conditions and rheological properties of the lithosphere play an important role in the geodynamic evolution of the Himalayan orogen and Tibetan Plateau and require the development of three-dimensional models that incorporate lateral heterogeneity.

S U M M A R YWe apply the Automated Multimode Inversion of surface and S-wave forms to a large global data set, verify the accuracy of the method and assumptions behind it, and compute an S vvelocity model of the upper mantle (crust-660 km). The model is constrained with ∼51 000 seismograms recorded at 368 permanent and temporary broadband seismic stations. Structure of the mantle and crust is constrained by waveform information both from the fundamentalmode Rayleigh waves (periods from 20 to 400 s) and from S and multiple S waves (higher modes). In order to enhance the validity of the path-average approximation, we implement the automated inversion of surface-and S-wave forms with a three-dimensional (3-D) reference model. Linear equations obtained from the processing of all the seismograms of the data set are inverted for seismic velocity variations also relative to a 3-D reference, in this study composed of a 3-D model of the crust and a one-dimensional (1-D), global-average depth profile in the mantle below. Waveform information is related to shear-and compressional-velocity structure within approximate waveform sensitivity areas. We use two global triangular grids of knots with approximately equal interknot spacing within each: a finely spaced grid for integration over sensitivity areas and a rougher-spaced one for the model parametrization.For the tomographic inversion we use LSQR with horizontal and vertical smoothing and norm damping. We invert for isotropic variations in S-and P-wave velocities but also allow for S-wave azimuthal anisotropy-in order to minimize errors due to possible mapping of anisotropy into isotropic heterogeneity. The lateral resolution of the resulting isotropic upper-mantle images is a few hundred kilometres, varying with data sampling.We validate the imaging technique with a 'spectral-element' resolution test: inverting a published global synthetic data set computed with the spectral-element method using a laterally heterogeneous mantle model we are able to reconstruct the synthetic model accurately. This test confirms both the accuracy of the implementation of the method and the validity of the JWKB and path-average approximations as applied in it.Reviewing the tomographic model, we observe that low-S v -velocity anomalies beneath mid-ocean ridges and backarc basins extend down to ∼100 km depth only, shallower than according to some previous tomographic models; this presents a close match to published estimates of primary melt production depth ranges there. In the seismic lithosphere beneath cratons, unambiguous high velocity anomalies extend to ∼200 km. Pronounced low-velocity zones beneath cratonic lithosphere are rare; where present (South America; Tanzania) they are neighboured by volcanic areas near cratonic boundaries. The images of these low-velocity zones may indicate hot material-possibly of mantle-plume origin-trapped or spreading beneath the thick cratonic lithosphere.

We used three-dimensional inverse scattering of core-reflected shear waves for large-scale, high-resolution exploration of Earth's deep interior (D′′) and detected multiple, piecewise continuous interfaces in the lowermost layer (D′′) beneath Central and North America. With thermodynamic properties of phase transitions in mantle silicates, we interpret the images and estimate in situ temperatures. A widespread wave-speed increase at 150 to 300 kilometers above the coremantle boundary is consistent with a transition from perovskite to postperovskite. Internal D′′ stratification may be due to multiple phase-boundary crossings, and a deep wave-speed reduction may mark the base of a postperovskite lens about 2300 kilometers wide and 250 kilometers thick. The core-mantle boundary temperature is estimated at 3950 ± 200 kelvin. Beneath Central America, a site of deep subduction, the D′′ is relatively cold (DT = 700 ± 100 kelvin). Accounting for a factor-of-two uncertainty in thermal conductivity, core heat flux is 80 to 160 milliwatts per square meter (mW m A t a depth of~2890 km, the core-mantle boundary (CMB) separates turbulent flow of liquid metals in the outer core from slowly convecting, highly viscous mantle silicates. The 200-to 300-km-thick thermochemical boundary layer on the mantle sidethe so-called D′′ layer-is enigmatic (1, 2), but a recently discovered phase transition from perovskite (pv) to postperovskite (ppv) in (Mg,Fe)SiO 3 (3-5) begins to explain seismologically observed complexity [e.g., (6)]. If the ppv transition occurs, one can, in principle, estimate in situ variations in temperature from the pressure-temperature dependence (that is, the Clapeyron slope) and the seismologically inferred location of the associated interface (7). Steep (conductive) thermal gradients in D′′ can produce multiple crossings of the phase boundary, and identification of associated seismic signals offers new opportunities for constraining (local) core heat flux (8, 9).Seismic (transmission) tomography delineates smooth changes in wave speed associated with mantle convection (Fig. 1A), but one must focus on the scattered wave field to image interfaces associated with transitions in mineralogy or composition. Scattering of PKP (the main P wave propagating through the core) in D′′, first recognized in the early 1970s (10), has been used to constrain stochastic models of deep mantle structure [e.g., (11)], but the most detailed and accurate constraints on D′′ structure to date have come from forward modeling of shear waves reflected at or near the CMB (12, 13). This approach has its drawbacks, however. First, it requires prior knowledge about the target structure and often assumes relatively simple geometries, the uniqueness of which is not easily established. Second, it relies on signal associated with near-and postcritical incidence, which limits radial resolution and the CMB regions that can be studied (14). The small distance window can also reduce the available source-receiver azimuths, which can degrade imaging in dir...