### Abstract

We present a method for modelling seismic wave propagation in a whole-earth model by solving the elastodynamic equations in 2-D cylindrical coordinates (r, 0) using the Fourier pseudospectral method (PSM). In solving the 2-D cylindrical elastodynamic equations for a whole-earth model, a singularity arises at the centre (r = 0) of the earth. To avoid the singularity, we develop a scheme that uses extension of field variables in the radial direction, with which computation of the wavefield at the centre is avoided, so that the wave propagation through the centre can be calculated. The time interval used in the calculation is determined by the smallest lateral grid spacing around the centre in the model. In a cylindrical coordinate system, the smallest lateral grid spacing is generally so small that the calculation is too time-consuming to be realistically carried out even on a supercomputer. We adopt a multidomain scheme to increase the smallest lateral grid spacing and avoid the oversampling of the physical domain around the centre of the earth. A smoothing scheme in the wavenumber domain is also proposed, which enables us to use a large enough time interval to allow the calculation for the whole-earth model on a desktop workstation. The waveforms calculated by the present method are compared with those obtained by the Direct Solution Method (DSM) to demonstrate their high accuracy. This method significantly reduces the computer memory and computation time required and makes it possible to study the effects of small-wavelength heterogeneities that can be approximated as azimuthally symmetric on wave propagation in the earth. We apply the present method to study the effects of local heterogeneity in the earth by adding a low-velocity perturbation above the core-mantle boundary (CMB) to the IASP91 earth model.

Original language | English |
---|---|

Pages (from-to) | 689-708 |

Number of pages | 20 |

Journal | Geophysical Journal International |

Volume | 145 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Core
- Core phases
- Pseudospectral method
- Seismic modelling
- Wave propagation
- Whole earth

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics

### Cite this

*Geophysical Journal International*,

*145*(3), 689-708. https://doi.org/10.1046/j.1365-246X.2001.01413.x

**Modelling seismic wave propagation in a two-dimensional cylindrical whole-earth model using the pseudospectral method.** / Wang, Yanbin; Takenaka, Hiroshi; Furumura, Takashi.

Research output: Contribution to journal › Article

*Geophysical Journal International*, vol. 145, no. 3, pp. 689-708. https://doi.org/10.1046/j.1365-246X.2001.01413.x

}

TY - JOUR

T1 - Modelling seismic wave propagation in a two-dimensional cylindrical whole-earth model using the pseudospectral method

AU - Wang, Yanbin

AU - Takenaka, Hiroshi

AU - Furumura, Takashi

PY - 2001

Y1 - 2001

N2 - We present a method for modelling seismic wave propagation in a whole-earth model by solving the elastodynamic equations in 2-D cylindrical coordinates (r, 0) using the Fourier pseudospectral method (PSM). In solving the 2-D cylindrical elastodynamic equations for a whole-earth model, a singularity arises at the centre (r = 0) of the earth. To avoid the singularity, we develop a scheme that uses extension of field variables in the radial direction, with which computation of the wavefield at the centre is avoided, so that the wave propagation through the centre can be calculated. The time interval used in the calculation is determined by the smallest lateral grid spacing around the centre in the model. In a cylindrical coordinate system, the smallest lateral grid spacing is generally so small that the calculation is too time-consuming to be realistically carried out even on a supercomputer. We adopt a multidomain scheme to increase the smallest lateral grid spacing and avoid the oversampling of the physical domain around the centre of the earth. A smoothing scheme in the wavenumber domain is also proposed, which enables us to use a large enough time interval to allow the calculation for the whole-earth model on a desktop workstation. The waveforms calculated by the present method are compared with those obtained by the Direct Solution Method (DSM) to demonstrate their high accuracy. This method significantly reduces the computer memory and computation time required and makes it possible to study the effects of small-wavelength heterogeneities that can be approximated as azimuthally symmetric on wave propagation in the earth. We apply the present method to study the effects of local heterogeneity in the earth by adding a low-velocity perturbation above the core-mantle boundary (CMB) to the IASP91 earth model.

AB - We present a method for modelling seismic wave propagation in a whole-earth model by solving the elastodynamic equations in 2-D cylindrical coordinates (r, 0) using the Fourier pseudospectral method (PSM). In solving the 2-D cylindrical elastodynamic equations for a whole-earth model, a singularity arises at the centre (r = 0) of the earth. To avoid the singularity, we develop a scheme that uses extension of field variables in the radial direction, with which computation of the wavefield at the centre is avoided, so that the wave propagation through the centre can be calculated. The time interval used in the calculation is determined by the smallest lateral grid spacing around the centre in the model. In a cylindrical coordinate system, the smallest lateral grid spacing is generally so small that the calculation is too time-consuming to be realistically carried out even on a supercomputer. We adopt a multidomain scheme to increase the smallest lateral grid spacing and avoid the oversampling of the physical domain around the centre of the earth. A smoothing scheme in the wavenumber domain is also proposed, which enables us to use a large enough time interval to allow the calculation for the whole-earth model on a desktop workstation. The waveforms calculated by the present method are compared with those obtained by the Direct Solution Method (DSM) to demonstrate their high accuracy. This method significantly reduces the computer memory and computation time required and makes it possible to study the effects of small-wavelength heterogeneities that can be approximated as azimuthally symmetric on wave propagation in the earth. We apply the present method to study the effects of local heterogeneity in the earth by adding a low-velocity perturbation above the core-mantle boundary (CMB) to the IASP91 earth model.

KW - Core

KW - Core phases

KW - Pseudospectral method

KW - Seismic modelling

KW - Wave propagation

KW - Whole earth

UR - http://www.scopus.com/inward/record.url?scp=0034978232&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034978232&partnerID=8YFLogxK

U2 - 10.1046/j.1365-246X.2001.01413.x

DO - 10.1046/j.1365-246X.2001.01413.x

M3 - Article

AN - SCOPUS:0034978232

VL - 145

SP - 689

EP - 708

JO - Geophysical Journal International

JF - Geophysical Journal International

SN - 0956-540X

IS - 3

ER -