Numerical solutions of rotational normal modes of a triaxial two-layered anelastic Earth

Shen, Wenbin; Yang, Zhuo; Guo, Zhiliang; Zhang, Wenying

doi:10.1016/j.geog.2019.03.001

Cited by 5 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The diurnal ones are used for FCN and FICN, and the static ones are used for CW and ICW. For compliances in Models 1 and 2, the static values of

κ

ξ

γ

, and

β

are from the Group I recommendations of Shen et al (), and the other five static compliances and the corresponding diurnal compliances are from D09, with diurnal values of

κ

ξ

γ

, and

β

scaled from static values according to D09. For additional compliances in Models 1, 2, and 3, we deploy the parameters from D09.…”

Section: Model Input Parametersmentioning

confidence: 99%

“…Chen and Shen () (hereafter CS10) formulated a triaxial two‐layered Earth rotation theory and provided CW and FCN normal modes solutions. Based on the complex compliances formulation of triaxial two‐layered Earth rotation frame by Sun and Shen (), Shen et al () further considered the electromagnetic coupling between the mantle and fluid core and analyzed the sensibility of the compliances and electromagnetic coupling parameters on the rotational CW and FCN normal modes.…”

Section: Introductionmentioning

confidence: 99%

“…Chen and Shen (2010) (hereafter CS10) formulated a triaxial two-layered Earth rotation theory and provided CW and FCN normal modes solutions. Based on the complex compliances formulation of triaxial two-layered Earth rotation frame by Sun and Shen (2016), Shen et al (2019) further considered the electromagnetic coupling between the mantle and fluid core and analyzed the sensibility of the compliances and electromagnetic coupling parameters on the rotational CW and FCN normal modes. Mathews et al (1991a) (hereafter MBHS1991) formulated a rotationally symmetric three-layered Earth rotation theory with pressure and gravitational couplings considered and stated that two more normal modes will be induced because of the inner core, namely, the Free Inner Core Nutation (FICN) and Inner Core Wobble (ICW).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Formulation of a Triaxial Three‐Layered Earth Rotation: Theory and Rotational Normal Mode Solutions

Guo

Shen

2020

JGR Solid Earth

Self Cite

View full text Add to dashboard Cite

In this study, we formulated a triaxial three‐layered anelastic Earth rotation theory considering various core‐mantle couplings, including the pressure and gravitational couplings acting on the elastic inner core by the outer core and mantle, and the viscoelectromagnetic couplings between the outer core and mantle and between the outer and inner cores. With this formulation, using the eigenvalue method, we solved four rotational normal modes, including the Chandler Wobble (CW), Free Core Nutation (FCN), Free Inner Core Nutation (FICN), and the Inner Core Wobble (ICW). The triaxiality of the actual Earth has notable effects on rotational normal modes, that is, 0.005, 0.0, −0.071, and 1.174 d (mean solar days), respectively, for the CW, FCN, FICN, and ICW. In the case that the triaxiality is bigger, for instance, if the Earth's equatorial dynamical ellipticity were 5.22×10−4, which is 1 order of magnitude larger than the presently determined ellipticity ( 2.2×10−5), the CW and ICW periods will be lengthened by 3.579 and 94.912 d, and the FICN period will be decreased by 0.591 d. Based on our present knowledge, the numerical solutions of the four normal modes under the new rotation frame suggest that the periods of CW, FCN, FICN, and ICW are, respectively, 432.2, 429.9, 934.0, and 2,718.7 d. Our theory for Earth can be extended to other planets in our solar system.

show abstract

“…The diurnal ones are used for FCN and FICN, and the static ones are used for CW and ICW. For compliances in Models 1 and 2, the static values of

κ

ξ

γ

, and

β

are from the Group I recommendations of Shen et al (), and the other five static compliances and the corresponding diurnal compliances are from D09, with diurnal values of

κ

ξ

γ

, and

β

scaled from static values according to D09. For additional compliances in Models 1, 2, and 3, we deploy the parameters from D09.…”

Section: Model Input Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Formulation of a Triaxial Three‐Layered Earth Rotation: Theory and Rotational Normal Mode Solutions

Guo

Shen

2020

JGR Solid Earth

Self Cite

View full text Add to dashboard Cite

show abstract

Internal co-seismic displacement and strain changes inside a homogeneous spherical Earth

Dong

Cheng

Wen

et al. 2021

Geophysical Journal International

View full text Add to dashboard Cite

Summary In this study, we devised a new set of analytical foundation solutions to compute the internal co-seismic displacement and strain changes caused by four independent point sources (strike-slip, dip-slip, horizontal tensile, and vertical tensile) inside a homogeneous spherical Earth model. Our model provides constraints on the deformation properties at depth, and reveals that the internal co-seismic deformation is larger than that on the surface. The deformation near the source is convergent with our formulae. For the internal deformation at radial section plane, the patterns of horizontal displacements ${u_\theta },{u_\phi }$ and strain changes ${e_{rr}},{e_{\theta \theta }},{e_{\phi \phi }},{e_{\theta \phi }}$ caused by strike-slip and tensile sources appear symmetric at the equidistance above and below the source. Their amplitudes are not identical but with a small discrepancy actually. Unlike these, the patterns of radial displacements ${u_r}$ for strike-slip and tensile sources exhibit point symmetry with the equidistance from the source. Also, the corresponding amplitudes are slightly different. The displacements ${u_\theta },{u_\phi }$ and strain changes ${e_{rr}},{e_{\theta \theta }},{e_{\phi \phi }},{e_{\theta \phi }}$ caused by dip-slip also appear the same properties as ${u_r}$ of strike-slip source. The magnitudes of the displacements and strain changes depend on the source types. The curvature effect on the near-field surface deformations is small, and it increases with the studied depth. But for the far-field deformation caused by the strike-slip source (ds = 20 km), the curvature effect can be as large as 77 per cent when the epicentral distance approximates to 1778 km.

show abstract

Core–mantle topographic coupling: a parametric approach and implications for the formulation of a triaxial three-layered Earth rotation

Zhang

Shen

2021

Geophysical Journal International

View full text Add to dashboard Cite

Summary We propose a parametric approach to the topographic (TOP) coupling between the mantle and outer core for refinement of the latest triaxial three-layered Earth rotation theory. Based on three models of the core-mantle boundary (CMB) topography, we obtain the axial components of the TOP torque as −2.08 × 1019 Nm, −2.72 × 1018 Nm and −1.97 × 1017 Nm, respectively. Under the frame of the triaxial three-layered Earth rotation theory, we solve the corresponding periods of Free Core Nutation as −(329.83 ± 28.12), −(457.54 ± −) and −(428.23 ± 1.09) mean solar days (d), respectively. The other three normal modes, namely, Chandler Wobble, Inner Core Wobble and Free Inner Core Nutation, are almost not affected by the TOP coupling of the CMB, their period values being 433.24, 2718.69 and 934.02 d, respectively. Calculations show that the TOP torque is highly sensitive to the adopted model of the topography, which is known to be robust. Taking into account the normal modes of the triaxial three-layered Earth rotation, the results of the CMB topography obtained by seismic tomography can be constrained in the future to a certain extent. In this study, considering the TOP coupling with the appropriate topography model, the estimates for the dynamic ellipticity ef of the fluid core lie between 0.0026340 and 0.0026430, values that are 3.56 per cent higher than the hydrostatic equilibrium value.

show abstract

Numerical solutions of rotational normal modes of a triaxial two-layered anelastic Earth

Cited by 5 publications

References 20 publications

Formulation of a Triaxial Three‐Layered Earth Rotation: Theory and Rotational Normal Mode Solutions

Formulation of a Triaxial Three‐Layered Earth Rotation: Theory and Rotational Normal Mode Solutions

Internal co-seismic displacement and strain changes inside a homogeneous spherical Earth

Core–mantle topographic coupling: a parametric approach and implications for the formulation of a triaxial three-layered Earth rotation

Contact Info

Product

Resources

About