Use Of Spectral Theory Of Matrices To Study Seismic Movements
AbstractTo the worldwide efforts made for understand the dynamics of seismic movements, a significant contribution was made by the research group of Massachusetts Institute of Technology. Such a contribution was given in 1983 by L. R. Lines and S. Treitel, . Starting from ideas contained in this paper , we present here, in all mathematical details, how the stages of development of earthquake can be characterized. The impulse response of the main filter that characterizes the seismic movement is obtained by minimizing a second moment norm. This is made by Lagrange multipliers method. The obtained impulse responses are found to be eigenvectors of some matrix, named moment of inertia matrix. The properties of this matrix are specified. A simple example to emphasize the theory, including the deduction of relations between the main parameters of the earthquake is given, using discrete convolution and deconvolution. Several conclusions are finally presented.
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Bibliographic InfoArticle provided by Romanian-American University in its journal Journal of Information Systems and Operations Management.
Volume (Year): 5 (2011)
Issue (Month): 2 (December)
earthquake; second moment norm minimization; Lagrange multipliers method; eigenvalues and eigenvectors of a matrix;
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