HR: 14:10h
AN: S33E-03    [Abstracts]
TI: Extending high-frequency wave asymptotics to low frequencies
AU: * Fomel, S
EM: sergey.fomel@beg.utexas.edu
AF: University of Texas at Austin, University Station, Box X, Austin, TX 78713-8924, United States
AU: Tcheverda, V
EM: chev@uiggm.nsc.ru
AF: Institute of Geophysics SB RAS, prosp. Koptyuga 3, Novosibirsk, 630090, Russian Federation
AB: Recent successful applications of full waveform solutions have renewed the interest in using low frequency information in seismology. In this paper, we attempt to fill the gap between the ray theory or the high-frequency asymptotic description of wave propagation and the full waveform theory. We show that it is possible to extend the traditional high-frequency solutions to lower frequencies by including additional terms in the phase function that provide a non-liner dependence of phase on frequency. We suggest a particular functional form of this dependence: u(\mathbf{x},ω) ≈ A(\mathbf{x}) e^{i \sqrt{ω2 T2(\mathbf{x}) + B(\mathbf{x}) T(\mathbf{x})}}, where u is the wavefield, \mathbf{x} is a space coordinate, ω is frequency, A is the wave amplitude, T is the traveltime, and B is a new correction factor connected with other parameters by special differential equations. We compare our approximation with full waveform solutions using both exact analytical techniques and numerical experiments. The comparison shows that, although the suggested approximation does not extend all the way to zero frequency, it provides a reasonably accurate extension of the ray theory for describing low-frequency effects in the range of frequencies used in seismic exploration. We discuss possible applications of our theory in seismic imaging, tomography, and full waveform inversion.
DE: 0560 Numerical solutions (4255)
DE: 0902 Computational methods: seismic
DE: 0935 Seismic methods (3025, 7294)
DE: 3285 Wave propagation (0689, 2487, 4275, 4455, 6934)
DE: 7260 Theory
SC: Seismology [S]
MN: 2007 Fall Meeting