GFZ German research centre for geo sciences

Theory of Elastic Waves

Gerhard Müller

Editors: Michael Weber (GFZ & Universität Potsdam), Georg Rümpker (Universität Frankfurt), Dirk Gajewski (Universität Hamburg)


When Gerhard Müller chose to leave us on 9 July 2002 because of his illness, we lost a teacher and colleague. Part of his legacy is several lecture notes which he had worked on for more then 20 years. These notes have become the backbone of teaching seismics and seismology at basically all German universities. When asked some years before his death if he had considered to translate "Theorie Elastischer Wellen" into English and publish it as a book, his answer was "I plan to do it when I am retired". We hope that our effort would have found his approval. 

We would like to thank R. and I. Coman, Universität Hamburg for preparing a first, German draft in LATEX of this script, A. Siebert (GFZ Potsdam) for her help in preparing the figures and our students for pointing out errors and asking questions. We would like to thank A. Priestley for proof-reading the script and turning Deutschlish into English and K. Priestley for his many comments.

We thank the GFZ Potsdam and the Dublin Institute for Advanced Studies for their support during a sabbatical of MW in Dublin, where most of this book was prepared. We would also thank the GFZ for continuing support in the preparation of this book.

M. Weber (Potsdam), G. Rümpker (Frankfurt), D. Gajewsk (Hamburg) - January 2007

This script is the revised and extended version of a manuscript which was used for several years in a 1- to 2-semester lecture on the theory of elastic waves at the universities of Karlsruhe and Frankfurt. The aim of this manuscript is to give students with some background in mathematics and theoretical physics the basic knowledge of the theory of elastic waves, which is necessary for the study of special literature in monographs and scientific journals. Since this is an introductory text, theory and methods are explained with simple models to keep the computational complexity and the formulae as simple as possible. This is why often liquid media instead of solid media are considered, and only horizontally  polarised waves (SH-waves) are discussed, when shear waves in layered, solid media are considered. A third example is that the normal mode \index{normal mode} theory for point sources is derived for an ideal wave guide with free or rigid boundaries. These simplifications occasionally hide the direct connection to seismology. In my opinion, there is no other approach if one aims at presenting theory and methods in detail and introducing at least some aspect from the wide field of seismology. After working through this script students should, I hope, be better prepared to read the advanced text books of Pilant (1979), Aki and Richards (1980, 2000), Ben-Menahem and Sing (1981), Dahlen and Tromp (1998), Kennett (2002) and Chapman (2004), which treat models as realistically as possible.

This manuscript has its emphasis in the wave seismic treatment of elastic body and surface waves in layered media. The understanding of the dynamic properties of these two wave types, i.e., their amplitudes, frequencies and impulse forms, are a basic prerequisite-requisite for the study of the structure of the Earth, may it be in the crust, the mantle or the core, and for the study of processes in the earthquake source. Ray seismics in inhomogeneous media and their relation with wave seismics are discussed in more detail than in earlier versions of the script, but seismologically interesting topics like eigen-modes of the Earth and extended sources of elastic waves are still not treated, since they would exceed the scope of an introductory lecture.

At several places of the manuscript, exercises are included, the solution of  these is an important part in understanding the material. One of the appendices tries to cover in compact form the basics of the Laplace and Fourier transform and of the delta function, so that these topics can be used in the main part of  the script.

I would like to thank Ingrid Hörnchen for the often tedious writing and correcting of this manuscript.

This file (64MB) + tew_2007.pdf (3.5MB) can also be downloaded via

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