scholarly journals Truncated co-seismic geoid and gravity changes in the domain of spherical harmonic degree

2004 ◽  
Vol 56 (9) ◽  
pp. 881-892 ◽  
Author(s):  
Wenke Sun ◽  
Shuhei Okubo
Keyword(s):  
Spherical Harmonic ◽  
Spherical Harmonic Degree ◽  
Gravity Changes ◽  
Harmonic Degree

scholarly journals Phase change in subducted lithosphere, impulse, and quantizing Earth surface deformations

Solid Earth ◽  
2015 ◽  
Vol 6 (3) ◽  
pp. 1075-1085
Author(s):  
C. O. Bowin ◽  
W. Yi ◽  
R. D. Rosson ◽  
S. T. Bolmer
Keyword(s):  
Angular Momentum ◽  
Phase Change ◽  
Spherical Harmonic ◽  
Plate Tectonics ◽  
Phase Changes ◽  
Metallic Nickel ◽  
Spherical Harmonic Degree ◽  
The Pacific ◽  
Seamount Chain ◽  
Harmonic Degree

Abstract. The new paradigm of plate tectonics began in 1960 with Harry H. Hess's 1960 realization that new ocean floor was being created today and is not everywhere of Precambrian age as previously thought. In the following decades an unprecedented coming together of bathymetric, topographic, magnetic, gravity, seismicity, seismic profiling data occurred, all supporting and building upon the concept of plate tectonics. Most investigators accepted the premise that there was no net torque amongst the plates. Bowin (2010) demonstrated that plates accelerated and decelerated at rates 10−8 times smaller than plate velocities, and that globally angular momentum is conserved by plate tectonic motions, but few appeared to note its existence. Here we first summarize how we separate where different mass sources may lie within the Earth and how we can estimate their mass. The Earth's greatest mass anomalies arise from topography of the boundary between the metallic nickel–iron core and the silicate mantle that dominate the Earth's spherical harmonic degree 2 and 3 potential field coefficients, and overwhelm all other internal mass anomalies. The mass anomalies due to phase changes in olivine and pyroxene in subducted lithosphere are hidden within the spherical harmonic degree 4–10 packet, and are an order of magnitude smaller than those from the core–mantle boundary. Then we explore the geometry of the Emperor and Hawaiian seamount chains and the 60° bend between them that aids in documenting the slow acceleration during both the Pacific Plate's northward motion that formed the Emperor seamount chain and its westward motion that formed the Hawaiian seamount chain, but it decelerated at the time of the bend (46 Myr). Although the 60° change in direction of the Pacific Plate at of the bend, there appears to have been nary a pause in a passive spreading history for the North Atlantic Plate, for example. This, too, supports phase change being the single driver for plate tectonics and conservation of angular momentum. Since mountain building we now know results from changes in momentum, we have calculated an experimental deformation index value (1–1000) based on a world topographic grid at 5 arcmin spacing and displayed those results for viewing.

scholarly journals Resonant Coupling between Solar Gravity Modes

1983 ◽  
Vol 66 ◽  
pp. 259-266
Author(s):  
W. Dziembowski
Keyword(s):  
Parametric Resonance ◽  
Spherical Harmonic ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Spherical Harmonic Degree ◽  
Strongly Coupled ◽  
Resonant Coupling ◽  
High Degree ◽  
Harmonic Degree ◽  
Solar Gravity

AbstractIt is shown that in consequence of the parametric resonance, g modes of low spherical harmonic degree l are strongly coupled to the modes of high degree. The coupling limits the growth of lowl modes to very small amplitudes. For g1, l = 1 mode, the final amplitude of the radial velocity is of the order of 10 cm s-1. A mixing of solar core as a result of a finite-amplitude development of linear instability of this mode is thus highly unlikely.

scholarly journals Multiwavelength studies of β Cephei stars

1994 ◽  
Vol 162 ◽  
pp. 17-18
Author(s):  
H. Cugier ◽  
A. Pigulski ◽  
G. Polubek ◽  
R. Monier
Keyword(s):  
Chemical Composition ◽  
Radial Velocity ◽  
Spherical Harmonic ◽  
Present Knowledge ◽  
Velocity Data ◽  
Spherical Harmonic Degree ◽  
Pulsating Stars ◽  
Radial Velocity Data ◽  
Harmonic Degree

As first pointed out by Moskalik and Dziembowski (1992) all β Cephei stars lie within the domain of H–R diagram where κ-mechanism effectively drives pulsations in the stellar layers with T ≈ 2×105 K. For most of these objects a chemical composition described by X = 0.70 and Z = 0.02 is sufficient to account for the pulsations, cf. Dziembowski and Pamyatnykh (1993). Recently, Cugier, Dziembowski and Pamyatnykh (1993) have investigated how the present knowledge about nonadiabatic observables of β Cephei stars affects methods of identification of the spherical harmonic degree, l. They found that good photometric and radial velocity data should result in unambiguous identification of l. Cugier, Dziembowski and Pamyatnykh also concluded that nonadiabatic observables can be used to obtain mean stellar parameters of pulsating stars.

Finite-frequency imaging of the global 410- and 660-km discontinuities using SS precursors

2019 ◽  
Vol 220 (3) ◽  
pp. 1978-1994
Author(s):  
Zhen Guo ◽  
Ying Zhou
Keyword(s):  
Transition Zone ◽  
Spherical Harmonic ◽  
Wave Speed ◽  
Global Scale ◽  
Finite Frequency ◽  
Spherical Harmonic Degree ◽  
Mantle Transition Zone ◽  
Global Models ◽  
Ss Precursors ◽  
Harmonic Degree

SUMMARY We report finite-frequency imaging of the global 410- and 660-km discontinuities using boundary sensitivity kernels for traveltime measurements made on SS precursors. The application of finite-frequency sensitivity kernels overcomes resolution limits in previous studies associated with large Fresnel zones of SS precursors and their interferences with other seismic phases. In this study, we calculate the finite-frequency sensitivities of SS waves and their precursors based on a single-scattering (Born) approximation in the framework of travelling-wave mode summation. The global discontinuity surface is parametrized using a set of triangular gridpoints with a lateral spacing of about 4°, and we solve the linear finite-frequency inverse problem (2-D tomography) based on singular value decomposition (SVD). The new global models start to show a number of features that were absent (or weak) in ray-theoretical back-projection models at spherical harmonic degree l > 6. The thickness of the mantle transition zone correlates well with wave speed perturbations at a global scale, suggesting dominantly thermal origins for the lateral variations in the mantle transition zone. However, an anticorrelation between the topography of the 410-km discontinuity and wave speed variations is not observed at a global scale. Overall, the mantle transition zone is about 2–3 km thicker beneath the continents than in oceanic regions. The new models of the 410- and 660-km discontinuities show better agreement with the finite-frequency study by Lawrence & Shearer than other global models obtained using SS precursors. However, significant discrepancies between the two models exist in the Pacific Ocean and major subduction zones at spherical harmonic degree >6. This indicates the importance of accounting for wave interactions in the calculations of sensitivity kernels as well as the use of finite-frequency sensitivities in data quality control.

scholarly journals Subduction to the lower mantle – a comparison between geodynamic and tomographic models

Solid Earth ◽  
2012 ◽  
Vol 3 (2) ◽  
pp. 415-432 ◽  
Author(s):  
B. Steinberger ◽  
T. H. Torsvik ◽  
T. W. Becker
Keyword(s):  
Cross Sections ◽  
Upper Mantle ◽  
Spherical Harmonic ◽  
Lower Mantle ◽  
Subduction Zones ◽  
Shear Velocity ◽  
Mantle Flow ◽  
Spherical Harmonic Degree ◽  
Geodynamic Model ◽  
Harmonic Degree

Abstract. It is generally believed that subduction of lithospheric slabs is a major contribution to thermal heterogeneity in Earth's entire mantle and provides a main driving force for mantle flow. Mantle structure can, on the one hand, be inferred from plate tectonic models of subduction history and geodynamic models of mantle flow. On the other hand, seismic tomography models provide important information on mantle heterogeneity. Yet, the two kinds of models are only similar on the largest (1000 s of km) scales and are quite different in their detailed structure. Here, we provide a quantitative assessment how good a fit can be currently achieved with a simple viscous flow geodynamic model. The discrepancy between geodynamic and tomography models can indicate where further model refinement could possibly yield an improved fit. Our geodynamical model is based on 300 Myr of subduction history inferred from a global plate reconstruction. Density anomalies are inserted into the upper mantle beneath subduction zones, and flow and advection of these anomalies is calculated with a spherical harmonic code for a radial viscosity structure constrained by mineral physics and surface observations. Model viscosities in the upper mantle beneath the lithosphere are ~1020 Pas, and viscosity increases to ~1023 Pas in the lower mantle above D". Comparison with tomography models is assessed in terms of correlation, both overall and as a function of depth and spherical harmonic degree. We find that, compared to previous geodynamic and tomography models, correlation is improved, presumably because of advances in both plate reconstructions and mantle flow computations. However, high correlation is still limited to lowest spherical harmonic degrees. An important ingredient to achieve high correlation – in particular at spherical harmonic degree two – is a basal chemical layer. Subduction shapes this layer into two rather stable hot but chemically dense "piles", corresponding to the Pacific and African Large Low Shear Velocity Provinces. Visual comparison along cross sections indicates that sinking speeds in the geodynamic model are somewhat too fast, and should be 2 ± 0.8 cm yr−1 to achieve a better fit.

scholarly journals The JPL lunar gravity field to spherical harmonic degree 660 from the GRAIL Primary Mission

2013 ◽  
Vol 118 (7) ◽  
pp. 1415-1434 ◽  
Author(s):  
Alex S. Konopliv ◽  
Ryan S. Park ◽  
Dah-Ning Yuan ◽  
Sami W. Asmar ◽  
Michael M. Watkins ◽  
...  
Keyword(s):  
Gravity Field ◽  
Spherical Harmonic ◽  
Lunar Gravity ◽  
Spherical Harmonic Degree ◽  
Lunar Gravity Field ◽  
Primary Mission ◽  
Harmonic Degree

scholarly journals Can the comprehensive model phase 4 (CM4) predict the geomagnetic diurnal field for days away from quiet time?

2016 ◽  
Vol 34 (10) ◽  
pp. 887-900 ◽  
Author(s):  
Elvis Onovughe
Keyword(s):  
Diurnal Variation ◽  
Spherical Harmonic ◽  
Geomagnetic Field ◽  
Predictive Ability ◽  
Small Scale ◽  
Comprehensive Model ◽  
Quiet Time ◽  
Spherical Harmonic Degree ◽  
Station Data ◽  
Harmonic Degree

Abstract. The most recent comprehensive model (CM4) of the geomagnetic field (Sabaka et al., 2004) has been used in conjunction with geomagnetic ground observatory station data to analyse and study the geomagnetic diurnal variation field for days away from quiet time and the CM4 prediction for these times. Even though much has been learnt about many components of the geomagnetic field, the diurnal variation field behaviour for days away from quiet time (moderately disturbed time) has not been intensively studied. Consequently, we analyse these, and the predictive ability of the CM4 for ground variations, and whether the CM4 prediction of the diurnal variation (whether at quiet time or away from quiet time) is valid outside the period of reference that from which the data were used in modelling. In carrying out the study, we compared the observatory station data and the CM4 prediction directly. Using the CM4 code, well-characterised internal and magnetospheric components were subtracted from the data, plots and global maps of the residual field generated and then compared with the CM4 to see how well the model performed in predicting the data at moderately disturbed time (Kp  ≤  5). The results show that the CM4 is valid and produces useful predictions outside the period covering the timespan of the model and during moderately disturbed time, despite the lack of active data in the original model dataset. The model predictability of the data increases as we move to higher spherical harmonic degree truncation, as the model–data misfit is reduced, but with increased roughness as a result of small-scale features incorporated. The observed results show that this relationship between the increase in spherical harmonic degree truncation and reduction in misfit can be restricted by data quality or quantity and global coverage or spread.

scholarly journals A Review of Observational Helioseismology

1990 ◽  
Vol 121 ◽  
pp. 253-264
Author(s):  
Thomas L. Duvall
Keyword(s):  
Spherical Harmonic ◽  
Solar Rotation ◽  
Resonant Cavity ◽  
Solar Interior ◽  
Radial Coordinate ◽  
Radial Part ◽  
Spherical Harmonic Degree ◽  
Spherical Harmonic Function ◽  
Recent Conference ◽  
Harmonic Degree

There have been several excellent reviews of observational helioseismology in recent years. These include the reviews by Harvey (1988), Libbrecht (1988), and van der Raay (1988) presented at a recent conference in Tenerife. The present effort will concentrate on the progress made on solar rotation recently.The Sun is a resonant cavity that supports many (~ 107) modes of oscillation. The modes that are most easily observed are the acoustic or p-modes. The eigenfunctions for these modes are:fnl(r) is the radial part of the separable eigenfunction where r is the radial coordinate measured from the center of the star. n is the number of radial nodes in the eigenfunction. Ylm (θ,ϕ) is the spherical harmonic function, where θ is the colatitude and ϕ is the longitude. The spherical harmonic degree l is the number of nodes of the spherical harmonic measured along a great circle that makes an angle with the equator. The azimuthal order m is the number of nodes around the equator. The frequency of the eigenmode, vnlm, depends on the mode. Much of our information derived about the solar interior from helioseismology comes from the measurement of these frequencies.

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