### ASA 124th Meeting New Orleans 1992 October

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

**Johannes P. L. Mourik
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Anton G. Tijhuis
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*Faculty of Elec. Eng., Delft Univ. of Technol., P.O. Box 5031, 2600 GA
Delft, The Netherlands
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**Maarten V. De Hoop
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*Schlumberger Cambridge Res., High Cross, Madingley Rd., Cambridge CB3 0EL,
England
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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.