• Corpus ID: 208527131

The computation of seismic normal modes with rotation as a quadratic eigenvalue problem

@article{Shi2019TheCO,
  title={The computation of seismic normal modes with rotation as a quadratic eigenvalue problem},
  author={Jia Shi and Ruipeng Li and Yuanzhe Xi and Yousef Saad and Maarten V. de Hoop},
  journal={arXiv: Computational Physics},
  year={2019}
}
A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core. The relevant elastic-gravitational system of equations, including the Coriolis force, is subjected to a mixed finite-element method, while self-gravitation is accounted for with the fast multipole method (FMM). To solve the resulting quadratic eigenvalue problem (QEP), the approach utilizes… 

References

SHOWING 1-10 OF 93 REFERENCES

A Rayleigh-Ritz-method-based approach to computing seismic normal modes in rotating terrestrial planets

A Rayleigh-Ritz-based Continuous Galerkin method based approach is presented to compute the seismic normal modes of rotating terrestrial planets. The method is not restricted to terrestrial planets,

A Rayleigh-Ritz method based approach to computing seismic normal modes in the presence of an essential spectrum.

A Rayleigh-Ritz with Continuous Galerkin method based approach is presented to compute the normal modes of a planet in the presence of an essential spectrum. The essential spectrum is associated with

Computing Planetary Interior Normal Modes with a Highly Parallel Polynomial Filtering Eigensolver

TLDR
To the authors' knowledge, this is the first time that the direct calculation of the normal modes of 3-D strongly heterogeneous planets, in particular, Earth and Mars, is made feasible via a combination of multiple matrix-free methods and a separation of the essential spectra.

Coupled free oscillations of an aspherical, dissipative, rotating Earth: Galerkin theory

Variational theory based on self-adjoint equations of motion cannot fully represent the interaction of the earth's seismic free oscillations in the presence of lateral structure, attenuation, and

The Normal Modes of a Rotating, Elliptical Earth

Summary It is possible to calculate precisely the theoretical eigen-frequencies of any Earth model which is non-rotating, spherically symmetric, and which has an isotropic static stress field and

Normal modes and seismograms in an anelastic rotating Earth

In order to account for rotation and anelastic effects in the normal modes of the Earth, a structure of the space of normal modes different from those generally used in the elastic self-adjoint case

An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra

  • F. GilbertA. Dziewoński
  • Geology
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1975
A cyclic process of refining models of the mechanical structure of the Earth and models of the mechanism of one or more earthquakes is developed. The theory of the elastic-gravitational free

Exact free oscillation spectra, splitting functions and the resolvability of Earth's density structure

Seismic free oscillations, or normal modes, provide a convenient tool to calculate low-frequency seismograms in heterogeneous Earth models. A procedure called ‘full mode coupling’ allows the seismic

Modelling of coupled normal modes of the Earth: the spectral method

SUMMARY Modelling of coupled free oscillations or seismograms in an earth with small-scale lateral heterogeneities (a few hundred kilometres) is presently impossible without strong approximations,

The subspace projection method for constructing coupled-mode synthetic seismograms

SUMMARY Subspace projection is an algorithm to calculate synthetic long-period seismograms from weakly coupled free oscillations. The algorithm exploits the fact that seismic motion on a slowly
...