ASA 124th Meeting New Orleans 1992 October

3aUW16. Efficient computation of synthetic seismograms in piecewise continuously layered fluids.

Johannes P. L. Mourik

Anton G. Tijhuis

Faculty of Elec. Eng., Delft Univ. of Technol., P.O. Box 5031, 2600 GA Delft, The Netherlands

Maarten V. De Hoop

Schlumberger Cambridge Res., High Cross, Madingley Rd., Cambridge CB3 0EL, England

An efficient numerical scheme is presented for generating synthetic seismograms in continuously layered fluids with a countable set of discontinuities. The acoustic equations describing the wave propagation in such a configuration are subjected to a Fourier transform with respect to time and a Hankel transform with respect to the radial coordinate in the plane of symmetry. This reduces the scattering problem to a one-dimensional contrast integral equation over a finite domain, with a degenerate kernel. The latter equation must be solved for many values of the transform-domain variables. In view of this, a space discretization is introduced that is independent of these variables. The discretized form of the integral equation, inherent in a straightforward compression of the integral kernel, thus obtained is solved recursively with a procedure that closely resembles the invariant embedding technique. At each level, in the inhomogeneous medium, the outcome of the recursion can be converted into a transmission operator by a closing operation that represents the transition to a homogeneous half-space. The key advantage of this scheme is that discontinuities in the medium properties can be handled without special precautions. Further, it is shown that the inverse Hankel transform can be carried out with a specially designed composite Gaussian quadrature rule independent of frequency. Representative numerical results will be presented.