Physics
Scientific paper
Feb 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980pepi...21...75s&link_type=abstract
Physics of the Earth and Planetary Interiors, Volume 21, Issue 2-3, p. 75-82.
Physics
2
Scientific paper
The Finite Element method is particularly adaptable to inhomogeneous modelling, because each element of the model is treated independently. The eigenvalue problem is formulated in terms of stiffness and mass matrices, an eigenvector, and gravity and rotation vectors. If the unperturbed (i.e. laterally homogeneous) solution is assumed for the eigenvector, an approximate solution for the eigenfrequency can be found directly, and Rayleigh's Principle guarantees that errors are of second order. Thus the change in eigenfrequency when lateral inhomogeneities are introduced can be estimated rather easily without attempting the full solution of the eigenvalue problem. Modelling the Earth with elements of the order of 100 km in size is well within the capability of present-day computers. Examples of the technique include some low-order torsional modes, in both a spherical and an ellipsoidal Earth model.
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