| Summary: | The theory of the Earth's normal modes provides a framework for the calculation of theoretical seismograms in spherically symmetric and in three-dimensional Earth models. In the spherically symmetric case, sometimes augmented by approximate, asáymptotic techniques to account for three-dimensional structure, normal mode theory provides a 'workhorse' practical method for calculating realistic theoretical seismograms. These form the basis of many different kinds of global seismological studies, including source studies and structural imaging using surface waves and body waves over a broad range of frequencies. In the case of three-dimensional Earth models, the theory of modal splitting and coupling again provides a powerful theoretical framework, although computational limitations make the complete application of the theory challenging. Approximate and less than complete versions of the theory have provided unique information on the Earth's three-dimensional structure, and further research promises much more in the future, as computational resources and data volumes increase, and as improved approximate and numerical approaches based on the normal mode approach are developed. Our understanding of the detailed structure of the Earth's vibrational spectrum at very long periods remains rather poor, which means that there is the likelihood that much remains to be discovered about the large-scale three-dimensional structure, that the study of very long period spectra can reveal. This chapter aims to give a concise account of the normal mode approach, providing a fairly self-contained treatment of some of the fundamentals of the theory and of its practical applications in seismology. © 2007 Elsevier B.V. All rights reserved.
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