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.

The Earth’s Free Spherical Oscillations of the Great Japan Earthquake

2012 ◽  
Vol 622-623 ◽  
pp. 1664-1669 ◽  
Author(s):  
Ye Wu ◽  
Yong Ge Wan ◽  
Liang Ding
Keyword(s):  
Free Oscillation ◽  
Low Frequency ◽  
Earth Model ◽  
Frequency Signal ◽  
The Earth ◽  
Oscillation Modes ◽  
Spectral Splitting ◽  
Earth’S Free Oscillations ◽  
Earth’S Free Oscillation ◽  
Digital Seismic Network

An M9.0 earthquake struck Japan on March 11, 2011 and the strong earthquake made continuous oscillation of the Earth. We first studied the Earth’s free oscillations using observations of VHZ channel of China Digital Seismic Network (CDSN). Since the frequency response of seismograph in CDSN suppresses the information of low frequency signal, we do not need to remove the solid tide in our data processing. We extracted 72 clear spherical modes of (0S0,0S2to0S72) of the Earth’s free oscillation and 21 harmonic modes and they are consistent and nearly same with the frequencies of the modes of Preliminary Reference Earth Model (PREM). Spectral splitting phenomenon is observed obviously in0S2,0S3,0S4and1S2free oscillation modes.

The Earth’s Free Spherical Oscillations of the Chile Earthquake

2012 ◽  
Vol 622-623 ◽  
pp. 1674-1681
Author(s):  
Ye Wu ◽  
Shu Yang ◽  
Liang Ding
Keyword(s):  
Free Oscillation ◽  
Low Frequency ◽  
Earth Model ◽  
The Earth ◽  
Oscillation Modes ◽  
Chile Earthquake ◽  
Spectral Splitting ◽  
Earth’S Free Oscillations ◽  
Earth’S Free Oscillation ◽  
Digital Seismic Network

An M8.8 earthquake struck Chile on February 27, 2010 and the strong earthquake made continuous oscillation of the Earth. We studied the Earth’s free oscillations using observations of VHZ channel of China Digital Seismic Network (CDSN). Since the frequency response of seismograph in CDSN suppresses the information of low frequency signal, we do not need to remove the solid tide in our data processing. We extracted 76 clear spherical modes of (0S0, 0S2 to 0S76) of the Earth’s free oscillation and 78 harmonic modes and they are consistent and nearly same with the frequencies of the modes of Preliminary Reference Earth Model (PREM). Spectral splitting phenomenon is observed obviously in 0S2, 0S3, 0S4 and 1S2 free oscillation modes.

The influence of rotation on the free oscillations of the Earth

1975 ◽  
Vol 279 (1292) ◽  
pp. 583-624 ◽  
Keyword(s):  
Rigid Body ◽  
Normal Mode ◽  
Body Force ◽  
Normal Modes ◽  
Earth Model ◽  
Static Response ◽  
The Earth ◽  
Rigid Body Modes ◽  
Effects Of Rotation ◽  
Zero Frequency

We pursue an abstract investigation of the theory of the infinitesimal free elasticgravitational oscillations of a fairly general rotating Earth model. By considering in some detail the transition to the non-rotating case, we are able to delineate certain of the intrinsic effects of rotation on the normal mode eigensolutions, and to show how profoundly rotation alters the fundamental mathematical and physical properties of these eigensolutions. In particular, we show that the displacement eigenfunctions of a rotating Earth model are not mutually orthogonal, and that the corresponding normal modes of oscillation cannot in general be represented by pure standing waves. We consider the excitation of the normal modes of oscillation of a rotating Earth model by a transient imposed body force distribution, and we show that the complex dynamical amplitude of each normal mode may, in many geophysical applications, be determined separately, in spite of the lack of orthogonality among the displacement eigenfunctions. The calculation of the associated static response after the decay of the normal modes of oscillation is, on the other hand, complicated considerably by the absence of orthogonality. We specifically examine the influence of rotation on the zero-frequency rigid body translational and rotational modes of any non-rotating Earth model, and show how to account for the corresponding rigid body modes of any rotating Earth model in excitation calculations.

A new 3-D mantle density model from recent normal-mode measurements

2021 ◽  
Author(s):  
Rûna van Tent ◽  
Arwen Deuss ◽  
Andreas Fichtner ◽  
Lars Gebraad ◽  
Simon Schneider ◽  
...  
Keyword(s):  
Normal Mode ◽  
Lower Mantle ◽  
Velocity Structure ◽  
Normal Modes ◽  
Shear Velocity ◽  
Boundary Region ◽  
Splitting Function ◽  
The Pacific ◽  
Compositional Variations ◽  
Body Tides

<p>Constraints on the 3-D density structure of Earth’s mantle provide important insights into the nature of seismically observed features, such as the Large Low Shear Velocity Provinces (LLSVPs) in the lower mantle under Africa and the Pacific. The only seismic data directly sensitive to density variations throughout the entire mantle are normal modes: whole Earth oscillations that are induced by large earthquakes (M<sub>w</sub> > 7.5). However, their sensitivity to density is weak compared to the sensitivity to velocity and different studies have presented conflicting density models of the lower mantle. For example, Ishii & Tromp (1999) and Trampert et al. (2004) have found that the LLSVPs have a larger density than the surrounding mantle, while Koelemeijer et al. (2017) used additional Stoneley-mode observations, which are particularly sensitive to the core-mantle boundary region, to show that the LLSVPs have a lower density. Recently, Lau et al. (2017) have used tidal tomography to show that Earth's body tides prefer dense LLSVPs.</p><p>A large number of new normal-mode splitting function measurements has become available since the last density models of the entire mantle were published. Here, we show the models from our inversion of these recent data and compare our results to previous studies. We find areas of high as well as low density at the base of the LLSVPs and we find that inside the LLSVPs density varies on a smaller scale than velocity, indicating the presence of compositionally distinct material. In fact, we find low correlations between the density and velocity structure throughout the entire mantle, revealing that compositional variations are required at all depths inside the mantle.</p>

scholarly journals A new catalogue of toroidal-mode overtone splitting function measurements

2020 ◽  
Author(s):  
Simon Schneider ◽  
Arwen Deuss
Keyword(s):  
Normal Mode ◽  
Large Scale ◽  
Velocity Structure ◽  
Normal Modes ◽  
Splitting Function ◽  
Data Set ◽  
Toroidal Mode ◽  
Function Coefficient ◽  
Fiji Island ◽  
Shear Wave Velocity Structure

Abstract Spectra of whole Earth oscillations or normal modes provide important constraints on Earth’s large scale structure. The most convenient way to include normal mode constraints in global tomographic models is by using splitting functions or structure coefficients, which describe how the frequency of a specific mode varies regionally. Splitting functions constrain 3D variations in velocity, density structure and boundary topography. They may also constrain anisotropy, especially when combining information from spheroidal modes, which are mainly sensitive to P-SV structure, with toroidal modes, mainly sensitive to SH structure. Spheroidal modes have been measured extensively, but toroidal modes have proven to be much more difficult and as a result only a limited number of toroidal modes have been measured so far. Here we expand the splitting function studies by Resovsky and Ritzwoller (1998) and Deuss et al. (2013), by focusing specifically on toroidal mode overtone observations. We present splitting function measurements for 19 self-coupled toroidal modes of which 13 modes have not been measured before. They are derived from radial and transverse horizontal component normal mode spectra up to 5 mHz for 91 events with MW ≥ 7.4 from the years 1983-2018. Our data include the Tohoku event of 2011 (9.1MW), the Okhotsk event of 2013 (8.3MW) and the Fiji Island event from 2018 (8.2MW). Our measurements provide new constraints on upper and lower mantle shear wave velocity structure and in combination with existing spheroidal mode measurements can be used in future inversions for anisotropic mantle structure. Our new splitting function coefficient data set will be available online.

Acoustic Green's Function Approximations

1998 ◽  
Vol 06 (04) ◽  
pp. 435-452 ◽  
Author(s):  
Robert P. Gilbert ◽  
Zhongyan Lin ◽  
Klaus Hackl
Keyword(s):  
Inverse Problem ◽  
Normal Mode ◽  
Eigenvalue Problems ◽  
Normal Modes ◽  
Modal Parameters ◽  
Mindlin Plate ◽  
Ocean Bottom ◽  
Hankel Transformation ◽  
Poroelastic Materials ◽  
Function Approximations

Normal-mode expansions for Green's functions are derived for ocean–bottom systems. The bottom is modeled by Kirchhoff and Reissner–Mindlin plate theories for elastic and poroelastic materials. The resulting eigenvalue problems for the modal parameters are investigated. Normal modes are calculated by Hankel transformation of the underlying equations. Finally, the relation to the inverse problem is outlined.

scholarly journals Splitting function measurements for Earth's longest period normal modes using recent large earthquakes

2011 ◽  
Vol 38 (4) ◽  
pp. n/a-n/a ◽  
Author(s):  
Arwen Deuss ◽  
Jeroen Ritsema ◽  
Hendrik van Heijst
Keyword(s):  
Normal Modes ◽  
Splitting Function ◽  
Large Earthquakes

Experimental Study for Extraction of Normal Modes

1995 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Normal Modes ◽  
Measurement Data ◽  
Mode Shapes ◽  
Complex Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Incomplete System ◽  
Coupled Structures

Abstract A frequency-domain technique to extract the normal mode from the measurement data for highly coupled structures is developed. The relation between the complex frequency response functions and the normal frequency response functions is derived. An algorithm is developed to calculate the normal modes from the complex frequency response functions. In this algorithm, only the magnitude and phase data at the undamped natural frequencies are utilized to extract the normal mode shapes. In addition, the developed technique is independent of the damping types. It is only dependent on the model of analysis. Two experimental examples are employed to illustrate the applicability of the technique. The effects due to different measurement locations are addressed. The results indicate that this technique can successfully extract the normal modes from the noisy frequency response functions of a highly coupled incomplete system.

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