A note on the equivalence of three major propagator algorithms for computational stability and efficiency
Tóm tắt
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.
Tài liệu tham khảo
Aki K and Richards P G (2002). Quantitative Seismology. 2nd ed. University Science Books, Sausalito, California, 261–269.
Buchen P W and Ben-Hador R (1996). Free-mode surfacewave computations. Geophys J Int124: 869–887.
Chapman C H (2003). Yet another elastic plane-wave, layermatrix algorithm. Geophys J Int154: 212–223.
Chapman C H and Orcutt J A (1985). The computation of body wave synthetic seismograms in laterally homogeneous media. Rev Geophys23(2): 105–163.
Chapman C H and Phinney R A (1972). Diffracted seismic signals and their numerical solution. Meth Comp Phys12: 165–230.
Dunkin J W (1965). Computation of modal solutions in layered, elastic media at high frequencies. Bull Seismol Soc Am55(2): 335–358.
Ivansson S (1993). Delta-matrix factorization for fast propagation through solid layers in a fluid-solid medium. J Comp Phys108: 357–367.
Kennett B L N (1974). Reflections, rays and reverberations. Bull Seismol Soc Am64(6): 1 685–1 696.
Kennett B L N (1983). Seismic Wave Propagation in a Stratified Medium. Cambridge University Press, Cambridge, 25–31, 126–136.
Kennett B L N (2001). The Seismic Wavefield. Vol I: Introduction and Theoretical Development. Cambridge University Press, Cambridge, 208–215, 260–270.
Kind R and Odom R I (1983). Improvements to layer matrix methods. J Geophys53: 127–130.
Müller G (1985). The reflectivity method: A tutorial. J Geophys58: 153–174.
Panza G F (1985). Synthetic seismograms: the Rayleigh waves modal summation. J Geophys58: 125–145.
Pitteway M L V (1965). The numerical calculation of wave-fields, reflection coefficients and polarizations for long radio waves in the lower ionosphere. Phil Trans R Soc Lond A 257(1079): 219–241.
Randall G E (1989). Efficient calculation of differential seismograms for lithospheric receiver functions. Geophys J Int99: 469–481.
Thrower E N (1965). The computation of the dispersion of elastic waves in layered media. J Sound Vib2(3): 210–226.
Wang R (1999). A simple orthonormalization method for stable and efficient computation of Green’s functions. Bull Seismol Soc Am89: 733–741.
Wang R and Kümpel H-J (2003). Poroelasticity: efficient modeling of strongly coupled, slow deformation processes in a multilayered half-space. Geophysics68(2): 705–717.
Wang R, Lorenzo-Martín F and Roth F (2003). Computation of deformation induced by earthquakes in a multi-layered elastic crust — FORTRAN programs EDGRN/EDCMP. Comp Geosc29: 195–207.
Wang R, Lorenzo-Martín F and Roth F (2006). PSGRN/PSCMP: A new code for calculating co- and post-seismic deformation, geoid and gravity changes based on the viscoelastic-gravitational dislocation theory. Comp Geosc32: 527–541.
Woodhouse J H (1980). Efficient and stable methods for performing seismic calculations in stratified media. In: Dziewonski A M and Boschi E eds. Proc. Int. School of Physics ‘Enrico Fermi’, Course LXXVIII, Physics of the Earth’s Interior. North-Holland, Amsterdam, 127–151.