Spherical harmonic stacking for the singlets of Earth's normal modes of free oscillation

2014 ◽  
Vol 41 (15) ◽  
pp. 5428-5435 ◽  
Author(s):  
Benjamin F. Chao ◽  
Hao Ding
Keyword(s):  
Spherical Harmonic ◽  
Free Oscillation ◽  
Normal Modes

scholarly journals Split free oscillation amplitudes for the 1960 Chilean and 1964 Alaskan earthquakes

1977 ◽  
Vol 67 (3) ◽  
pp. 651-660 ◽  
Author(s):  
Robert J. Geller ◽  
Seth Stein
Keyword(s):  
Surface Waves ◽  
Volume Change ◽  
Free Oscillation ◽  
Additional Data ◽  
Normal Modes ◽  
Source Mechanisms ◽  
Split Mode ◽  
Theoretical Results

abstract Splitting of the Earth's normal modes was observed for both the 1960 Chilean and 1964 Alaskan earthquakes. The strong peaks in the observed spectrum of each split multiplet correspond to singlets with much higher amplitudes than the others. Using theoretical results we have derived elsewhere (Stein and Geller, 1977a), we are able to predict this pattern. We show that the source mechanisms inferred for these earthquakes from surface waves are consistent with the observed pattern of relative spectral amplitudes of the split modes. However other mechanisms, such as a slow isotropic volume change, are also consistent with the split-mode amplitudes and are excluded only by additional data.

scholarly journals On the oscillation spectra of ultra compact stars

1995 ◽  
Vol 451 (1942) ◽  
pp. 341-348 ◽  
Keyword(s):  
Energy Density ◽  
Spherical Harmonic ◽  
Compact Star ◽  
Normal Modes ◽  
Compact Stars ◽  
Real Difference ◽  
Characteristic Frequencies ◽  
Polar Mode ◽  
Uniform Energy Density ◽  
Oscillation Frequencies

Quasi-normal modes of ultra compact stars with uniform energy density have been calculated. For less compact stars, there is only one very slowly damped polar mode (corresponding to the Kelvin f-mode) for each spherical harmonic index l . Further long-lived modes become possible for a sufficiently compact star (roughly when M/R ≥ 1/3). We compare the characteristic frequencies of these resonant polar modes to the axial modes first found by Chandrasekhar & Ferrari ( Proc. R. Soc. Lond . A 434, 449 (1991)). We find that the two spectra approach each other as the star is made more compact. The oscillation frequencies of the corresponding polar and axial modes agree to within a percent for stars more compact than M/R = 0.42. At the same time, the damping times are slightly different. The results illustrate that there is no real difference between the origin of these axial and polar modes: They are essentially spacetime modes.

FrosPy: A Modular Python Toolbox for Normal Mode Seismology

2022 ◽  
Author(s):  
Simon Schneider ◽  
Sujania Talavera-Soza ◽  
Lisanne Jagt ◽  
Arwen Deuss
Keyword(s):  
Normal Mode ◽  
Free Oscillation ◽  
Large Time ◽  
Reference Model ◽  
Normal Modes ◽  
Earth Model ◽  
Splitting Function ◽  
Quality Factor Q ◽  
Earth’S Free Oscillation ◽  
Q Values

Abstract We present free oscillations Python (FrosPy), a modular Python toolbox for normal mode seismology, incorporating several Python core classes that can easily be used and be included in larger Python programs. FrosPy is freely available and open source online. It provides tools to facilitate pre- and postprocessing of seismic normal mode spectra, including editing large time series and plotting spectra in the frequency domain. It also contains a comprehensive database of center frequencies and quality factor (Q) values based on 1D reference model preliminary reference Earth model for all normal modes up to 10 mHz and a collection of published measurements of center frequencies, Q values, and splitting function (or structure) coefficients. FrosPy provides the tools to visualize and convert different formats of splitting function coefficients and plot these as maps. By giving the means of using and comparing normal mode spectra and splitting function measurements, FrosPy also aims to encourage seismologists and geophysicists to learn about normal mode seismology and the study of the Earth’s free oscillation spectra and to incorporate them into their own research or use them for educational purposes.

Filtering methods for finite-time normal modes and atmospheric error growth

2000 ◽  
Vol 42 ◽  
pp. 1482
Author(s):  
Mozheng Wei ◽  
Jorgen S. Frederiksen ◽  
Steve Kepert
Keyword(s):  
Finite Time ◽  
Normal Modes ◽  
Error Growth

Gravitational Waves

2018 ◽  
Author(s):  
Michele Maggiore
Keyword(s):  
Black Hole ◽  
Perturbation Theory ◽  
Gravitational Waves ◽  
Transfer Functions ◽  
Normal Modes ◽  
Cosmological Perturbation ◽  
Tests Of General Relativity ◽  
Pulsar Timing ◽  
Tensor Perturbations ◽  
Stochastic Backgrounds

A comprehensive and detailed account of the physics of gravitational waves and their role in astrophysics and cosmology. The part on astrophysical sources of gravitational waves includes chapters on GWs from supernovae, neutron stars (neutron star normal modes, CFS instability, r-modes), black-hole perturbation theory (Regge-Wheeler and Zerilli equations, Teukoslky equation for rotating BHs, quasi-normal modes) coalescing compact binaries (effective one-body formalism, numerical relativity), discovery of gravitational waves at the advanced LIGO interferometers (discoveries of GW150914, GW151226, tests of general relativity, astrophysical implications), supermassive black holes (supermassive black-hole binaries, EMRI, relevance for LISA and pulsar timing arrays). The part on gravitational waves and cosmology include discussions of FRW cosmology, cosmological perturbation theory (helicity decomposition, scalar and tensor perturbations, Bardeen variables, power spectra, transfer functions for scalar and tensor modes), the effects of GWs on the Cosmic Microwave Background (ISW effect, CMB polarization, E and B modes), inflation (amplification of vacuum fluctuations, quantum fields in curved space, generation of scalar and tensor perturbations, Mukhanov-Sasaki equation,reheating, preheating), stochastic backgrounds of cosmological origin (phase transitions, cosmic strings, alternatives to inflation, bounds on primordial GWs) and search of stochastic backgrounds with Pulsar Timing Arrays (PTA).

Triatomic molecules

2018 ◽  
Author(s):  
John H. D. Eland ◽  
Raimund Feifel
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Electronic States ◽  
Triatomic Molecules ◽  
Doubly Charged Ions ◽  
Spectral Bands ◽  
Valence Electrons ◽  
Doubly Charged ◽  
Charged Ions ◽  
Double Ionisation

Double ionisation of the triatomic molecules presented in this chapter shows an added degree of complexity. Besides potentially having many more electrons, they have three vibrational degrees of freedom (three normal modes) instead of the single one in a diatomic molecule. For asymmetric and bent triatomic molecules multiple modes can be excited, so the spectral bands may be congested in all forms of electronic spectra, including double ionisation. Double photoionisation spectra of H2O, H2S, HCN, CO2, N2O, OCS, CS2, BrCN, ICN, HgCl2, NO2, and SO2 are presented with analysis to identify the electronic states of the doubly charged ions. The order of the molecules in this chapter is set first by the number of valence electrons, then by the molecular weight.

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