APPLICATIONS OF ORTHOGONALITY THEORY OF DISCRETE NORMAL MODES TO THE IDENTIFICATION OF FREE OSCILLAT

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Owing to the loss of the orthogonality relations of discrete normal modes of free oscillations of the Earth in practical analysis, not only stacking method fails to give the desired results, but also stripping method may lead to large errors and even mis-identifications for certain normal modes. For this reason, a method in which the data from many earthquakes are used and appropriately weighted in order to make the orthogonality relations of discrete normal modes approximately satisfied is put forward. In addition, the conditions under which the orthogonality relations of discrete normal modes hold exactly within the range of a given degree and order have been found. Owing to the loss of the orthogonality relations of discrete normal modes of free oscillations of the earth in practical analysis, not only stacking method fails to give the desired results, but also also stripping method may lead to large errors and even mis-identifications for certain normal For this reason, a method in which the data from many earthquakes are used and appropriately weighted in order to make the orthogonality relations of discrete normal modes approximately satisfied is put forward. In addition, the conditions under which the orthogonality relations of discrete normal modes hold exactly within the range of a given degree and order have been found.
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