Gaussian packets in the computation of seismic wavefields

SUMMARY A method of computing synthetic seismograms by means of the three-parametric summation of Gaussian packets over space is proposed. The expansion of the wavefield specified in terms of a complex-valued amplitude and a phase function into Gaussian packets is very similar to the expansion into Gaussian beams, with the additional summation over points along the rays. Initial conditions for the wavefield, for which the initial directions of the rays are time independent (e.g. the point source), are assumed. The summation is performed in the frequency domain. The synthetic seismograms are then evaluated by the Fast Fourier transform for any source time function. The method should not require a substantial increase of the computational time with respect to the ray and Gaussian beam methods.

[1]  C. H. Chapman,et al.  Body-wave seismograms in inhomogeneous media using Maslov asymptotic theory , 1982 .

[2]  V. Červený,et al.  Gaussian beam synthetic seismograms , 1985 .

[3]  A. Katchalov,et al.  Gaussian beam methods and theoretical seismograms , 1988 .

[4]  V. Červený,et al.  Applications of dynamic ray tracing , 1988 .

[5]  V. Červený,et al.  Synthetic body wave seismograms for three-dimensional laterally varying media , 1984 .

[6]  K. Fuchs,et al.  Computation of Synthetic Seismograms with the Reflectivity Method and Comparison with Observations , 1971 .

[7]  C. H. Chapman,et al.  An introduction to Maslov's asymptotic method , 1985 .

[8]  Luděk Klimeš,et al.  Discretization error for the superposition of Gaussian beams , 1986 .

[9]  Luděk Klimeš,et al.  Expansion of a high-frequency time-harmonic wavefield given on an initial surface into Gaussian beams , 1984 .

[10]  Benjamin S. White,et al.  Gaussian wave packets in inhomogeneous media with curved interfaces , 1987, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[11]  V. Červený.  Synthetic body wave seismograms for laterally varying layered structures by the Gaussian beam method , 1983 .

[12]  Vlastislav Červený,et al.  Ray method in seismology , 1977 .

[13]  V. Červený,et al.  Paraxial ray approximations in the computation of seismic wavefields in inhomogeneous media , 1984 .

[14]  L. Klimeš.  The Relation between Gaussian Beams and Maslov Asymptotic Theory , 1984 .

[15]  M. M. Popov,et al.  Computation of wave fields in inhomogeneous media — Gaussian beam approach , 1982 .

[16]  V. M. Babich,et al.  Complex space-time ray method and “quasiphotons” , 1984 .