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A note on the equivalence of three major propagator algorithms for computational stability and efficiency |
Yanlu Ma1, 2, Rongjiang Wang3, Huilan Zhou4 |
1 Institute for Geology, Mineralogy and Geophysics, Ruhr-University, Bochum 44801, Germany
2 China Earthquake Networks Center, Beijing 100045, China
3 GeoForschungsZentrum Potsdam (GFZ), Telegrafenberg, D-14473 Potsdam, Germany
4 College of Earth Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, China |
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Abstract It is shown in this note that the three methods, the orthonormalization method, the minor matrix method and the recursive reflection-transmission matrix method are closely related and solve the numerical instability in the original Thomson-Haskell propagator matrix method equally well. Another stable and efficient method based on the orthonormalization and the Langer block-diagonal decomposition is presented to calculate the response of a horizontal stratified model to a plane, spectral wave. It is a numerically robust Thomson-Haskell matrix method for high frequencies, large layer thicknesses and horizontal slownesses. The technique is applied to calculate reflection-transmission coefficients, body wave receiver functions and Rayleigh wave dispersion.
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Received: 30 September 2011
Published: 10 February 2012
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Fund:National Natural Science Foundation of China (Nos. 40374009 and 40574024) |
Corresponding Authors:
Yanlu Ma
E-mail: yanlu.ma@rub.de
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