The spectral-element method in seismology

Dimitri Komatitsch, Seiji Tsuboi, Jeroen Tromp

Research output: Chapter in Book/Report/Conference proceedingChapter

106 Scopus citations


We present the main properties of the spectral-element method, which is well suited for numerical calculations of synthetic seismograms for three-dimensional Earth models. The technique is based upon a weak formulation of the equations of motion and combines the flexibility of a finite-element method with the accuracy of a pseudospectral method. The mesh is composed of hexahedral elements and honors the main discontinuities in the Earth model. The displacement vector is expressed in each element in terms of high-degree Lagrange interpolants, and integrals are computed based upon Gauss-Lobatto-Legendre quadrature, which leads to an exactly diagonal mass matrix and therefore drastically simplifies the algorithm. We use a fluid-solid coupling formulation that does not require iterations at the core-mantle or inner-core boundaries. The method is efficiently implemented on parallel computers with distributed memory based upon a message-passing methodology. We present two large-scale simulations for a realistic three-dimensional Earth model computed on the Japanese Earth Simulator at periods of 5 s and longer.

Original languageEnglish (US)
Title of host publicationSeismic Earth
Subtitle of host publicationArray Analysis of Broadband Seismograms, 2005
EditorsGuust Nolet, Alan Levander
PublisherBlackwell Publishing Ltd.
Number of pages23
ISBN (Electronic)9781118666333
ISBN (Print)9780875904221
StatePublished - 2005

Publication series

NameGeophysical Monograph Series
ISSN (Print)0065-8448
ISSN (Electronic)2328-8779

All Science Journal Classification (ASJC) codes

  • Geophysics


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