Commun. Comput. Phys.,
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Volume 3.

Spectral-Element and Adjoint Methods in Seismology

Jeroen Tromp 1*, Dimitri Komatitsch 2, Qinya Liu 3

1 Seismological Laboratory, California Institute of Technology, Pasadena, California 91125, USA.
2 Department of Geophysical Modeling and Imaging, University of Pau, 64013 Pau Cedex, France.
3 Scripps Institution of Oceanography, University of California San Diego, La Jolla CA 92093-0225, USA.

Received 14 September 2006; Accepted (in revised version) 6 June 2007
Available online 14 September 2007


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 {\em 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 {\em inverse problem}.

AMS subject classifications: 74S05, 74S30, 86A15, 86A22

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Key words: Spectral-element method, adjoint methods, seismology, inverse problems, numerical simulations.

*Corresponding author.
Email: (J. Tromp), dimitri.komatitsch (D. Komatitsch), (Q. Liu)

The Global Science Journal