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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.
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. 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. If 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.