Spectral-element and adjoint methods in seismology

Jeroen Tromp, Dimitri Komatitsch, Qinya Liu

Research output: Contribution to journalReview articlepeer-review

380 Scopus citations


We provide an introduction to the use of the spectral-element method (SEM) in seismology. Following a brief review of the basic equations that govern seismic wave propagation, we discuss in some detail how these equations may be solved numerically based upon the SEM to address the forward problem in seismology. Examples of synthetic seismograms calculated based upon the SEM are compared to data recorded by the Global Seismographic Network. Finally, we discuss the challenge of using the remaining differences between the data and the synthetic seismograms to constrain better Earth models and source descriptions. This leads naturally to adjoint methods, which provide a practical approach to this formidable computational challenge and enables seismologists to tackle the inverse problem.

Original languageEnglish (US)
Pages (from-to)1-32
Number of pages32
JournalCommunications in Computational Physics
Issue number1
StatePublished - Jan 2008

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


  • Adjoint methods
  • Inverse problems
  • Numerical simulations
  • Seismology
  • Spectral-element method


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