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Spectral-element and adjoint methods in seismology. (English) Zbl 1183.74320
Summary: 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 of 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 enable seismologists to tackle the inverse problem.

74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
86A15 Seismology (including tsunami modeling), earthquakes
86A22 Inverse problems in geophysics