pure and applied geophysics

, Volume 114, Issue 5, pp 863–875 | Cite as

On the excitation of the earth's seismic normal modes

  • N. J. Vlaar


The excitation of the earth's normal modes is formulated as an initial value problem. The static state of the earth, stressed from its hydrostatic reference situation, is considered as the initial state. The initial state is relaxed, at the time of the earthquake, by the removal of the forces maintaining the departure from hydrostatic equilibrium. Expressions are derived for the coefficients giving the relative excitation of the individual modes for the cases where these forces are compensating volume forces or compensating tractions on the faces of a dislocation. It is demonstrated that a point slip dislocation has a body force equivalent in the form of a double couple with a deviatoric moment tensor. However, for a source with volume change no moment tensor equivalent can be found. The volume change, apart from an elastic effect which can be represented by an isotropic moment tensor, has a direct gravitational effect on the excitation. This effect is due to a balanced force field consisting of a point force at the source and a continuous distribution of volume forces throughout the earth. The latter distribution, if not taken into account, may give rise to artificial phases in the frequency spectrum of the normal modes.


Normal Mode Moment Tensor Slip Dislocation Hydrostatic Equilibrium Volume Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. G. E. Backus andJ. F. Gilbert (1967),Numerical applications of a formalism for geophysical inverse problems, Geophys. J.R. astr. Soc.13, 247–267.Google Scholar
  2. F. A. Dahleen (1972),Elastic dislocation theory for a self-gravitating elastic configuration with an initial static stress field, Geophys, J.R. astr. Soc.28, 223–226.Google Scholar
  3. F. Gilbert (1970).Excitation of the normal modes of the earth by earthquake sources, Geophys. J.R. astr. Soc.22, 223–226.Google Scholar
  4. F. Gilbert andA. M. Dziewonski (1975),An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra, Phil. Trans. R. Soc. London, Ser. A,278, 187–269.Google Scholar
  5. B. V. Kostrov (1970),The theory of the focus for tectonic earthquakes, Izv. Earth Phys.4, 84–101.Google Scholar
  6. H. Takeuchi andM. Saito (1972),Seismic surface waves inMethods in Computational Physics, Vol. 11 (Academic Press, New York-London, 1972).Google Scholar

Copyright information

© Birkhäuser Verlag 1976

Authors and Affiliations

  • N. J. Vlaar
    • 1
  1. 1.Vening Meinesz LaboratoryUtrechtThe Netherlands

Personalised recommendations