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Published January 2008 | Published
Journal Article Open

Spectral-Element and Adjoint Methods in Seismology


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.

Additional Information

2008 Copyright Global Science Press. Reprinted with permission. Received 14 September 2006; Accepted (in revised version) 6 June 2007; Available online 14 September 2007. Broadband data were obtained from the IRIS Data Management Center. This material is based in part upon work supported by the National Science Foundation under grant EAR-0309576. This is contribution No. 9157 of the Division of Geological & Planetary Sciences (GPS), California Institute of Technology. The numerical simulations for this research were performed on Caltech's GPS Division Dell cluster. The software used to perform the spectral-element simulations shown in this article is freely available via www.geodynamics.org.

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