A scheme to treat the singularity in global seismic wavefield simulation using pseudospectral method with staggered grids

Yanbin Wang, Hiroshi Takenaka

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The pseudospectral method has been applied to the simulation of seismic wave propagation in 2-D global Earth model. When a whole Earth model is considered, the center of the Earth is included in the model and then singularity arises at the center of the Earth where r = 0 since the 1/r term appears in the wave equations. In this paper, we extended the global seismic wavefield simulation algorithm for regular grid mesh to staggered grid configuration and developed a scheme to solve the numerical problems associated with the above singularity for a 2-D global Earth model defined on staggered grid using pseudospectral method. This scheme uses a coordinate transformation at the center of the model, in which the field variables at the center are calculated in Cartesian coordinates from the values on the grids around the center. It allows wave propagation through the center and hence the wavefield at the center can be stably calculated. Validity and accuracy of the scheme was tested by compared with the discrete wavenumber method. This scheme could also be suitable for other numerical methods or models parameterized in cylindrical or spherical coordinates when singularity arises at the center of the model.

Original languageEnglish
Pages (from-to)121-127
Number of pages7
JournalEarthquake Science
Volume23
Issue number2
DOIs
Publication statusPublished - Apr 2010
Externally publishedYes

Fingerprint

finite difference method
grids
Earth (planet)
simulation
Wave propagation
wave propagation
Seismic waves
wave equation
Wave equations
seismic wave
numerical method
cylindrical coordinates
Cartesian coordinates
method
spherical coordinates
Numerical models
coordinate transformations
Numerical methods
seismic waves
wave equations

Keywords

  • Pseudospectral method
  • Seismic modeling
  • Staggered grid
  • Wave propagation
  • Whole earth

ASJC Scopus subject areas

  • Geophysics
  • Geotechnical Engineering and Engineering Geology
  • Geology

Cite this

A scheme to treat the singularity in global seismic wavefield simulation using pseudospectral method with staggered grids. / Wang, Yanbin; Takenaka, Hiroshi.

In: Earthquake Science, Vol. 23, No. 2, 04.2010, p. 121-127.

Research output: Contribution to journalArticle

@article{aab9da450aa24812afd65021c9881504,
title = "A scheme to treat the singularity in global seismic wavefield simulation using pseudospectral method with staggered grids",
abstract = "The pseudospectral method has been applied to the simulation of seismic wave propagation in 2-D global Earth model. When a whole Earth model is considered, the center of the Earth is included in the model and then singularity arises at the center of the Earth where r = 0 since the 1/r term appears in the wave equations. In this paper, we extended the global seismic wavefield simulation algorithm for regular grid mesh to staggered grid configuration and developed a scheme to solve the numerical problems associated with the above singularity for a 2-D global Earth model defined on staggered grid using pseudospectral method. This scheme uses a coordinate transformation at the center of the model, in which the field variables at the center are calculated in Cartesian coordinates from the values on the grids around the center. It allows wave propagation through the center and hence the wavefield at the center can be stably calculated. Validity and accuracy of the scheme was tested by compared with the discrete wavenumber method. This scheme could also be suitable for other numerical methods or models parameterized in cylindrical or spherical coordinates when singularity arises at the center of the model.",
keywords = "Pseudospectral method, Seismic modeling, Staggered grid, Wave propagation, Whole earth",
author = "Yanbin Wang and Hiroshi Takenaka",
year = "2010",
month = "4",
doi = "10.1007/s11589-010-0001-x",
language = "English",
volume = "23",
pages = "121--127",
journal = "Earthquake Science",
issn = "1674-4519",
publisher = "Seismological Society of China",
number = "2",

}

TY - JOUR

T1 - A scheme to treat the singularity in global seismic wavefield simulation using pseudospectral method with staggered grids

AU - Wang, Yanbin

AU - Takenaka, Hiroshi

PY - 2010/4

Y1 - 2010/4

N2 - The pseudospectral method has been applied to the simulation of seismic wave propagation in 2-D global Earth model. When a whole Earth model is considered, the center of the Earth is included in the model and then singularity arises at the center of the Earth where r = 0 since the 1/r term appears in the wave equations. In this paper, we extended the global seismic wavefield simulation algorithm for regular grid mesh to staggered grid configuration and developed a scheme to solve the numerical problems associated with the above singularity for a 2-D global Earth model defined on staggered grid using pseudospectral method. This scheme uses a coordinate transformation at the center of the model, in which the field variables at the center are calculated in Cartesian coordinates from the values on the grids around the center. It allows wave propagation through the center and hence the wavefield at the center can be stably calculated. Validity and accuracy of the scheme was tested by compared with the discrete wavenumber method. This scheme could also be suitable for other numerical methods or models parameterized in cylindrical or spherical coordinates when singularity arises at the center of the model.

AB - The pseudospectral method has been applied to the simulation of seismic wave propagation in 2-D global Earth model. When a whole Earth model is considered, the center of the Earth is included in the model and then singularity arises at the center of the Earth where r = 0 since the 1/r term appears in the wave equations. In this paper, we extended the global seismic wavefield simulation algorithm for regular grid mesh to staggered grid configuration and developed a scheme to solve the numerical problems associated with the above singularity for a 2-D global Earth model defined on staggered grid using pseudospectral method. This scheme uses a coordinate transformation at the center of the model, in which the field variables at the center are calculated in Cartesian coordinates from the values on the grids around the center. It allows wave propagation through the center and hence the wavefield at the center can be stably calculated. Validity and accuracy of the scheme was tested by compared with the discrete wavenumber method. This scheme could also be suitable for other numerical methods or models parameterized in cylindrical or spherical coordinates when singularity arises at the center of the model.

KW - Pseudospectral method

KW - Seismic modeling

KW - Staggered grid

KW - Wave propagation

KW - Whole earth

UR - http://www.scopus.com/inward/record.url?scp=77953420611&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953420611&partnerID=8YFLogxK

U2 - 10.1007/s11589-010-0001-x

DO - 10.1007/s11589-010-0001-x

M3 - Article

AN - SCOPUS:77953420611

VL - 23

SP - 121

EP - 127

JO - Earthquake Science

JF - Earthquake Science

SN - 1674-4519

IS - 2

ER -