Fourth-Order Finite Difference Acoustic Logs In A Transversely Isotropic Formation
Name
1993.2 Cheng_Cheng_Toksoz.pdf
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710.95 KB
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Checksum (MD5)
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Author(s)
Cheng, N. Y.
Cheng, C. H.
Toksoz, M. N.
Date Issued
1993
Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;1993-02
Abstract
In this paper we present a finite difference scheme for seismic wave propagation in
a fluid-filled borehole in a transversely isotropic formation. The first-order hyperbolic
differential equations are approximated explicitly on a staggered grid using an algorithm
that is fourth-order accurate in space and second-order accurate in time. The grid
dispersion and grid anisotropy are analyzed. Grid dispersion and anisotropy are well
suppressed by a grid size of 10 points per wavelength. The stability condition is also
obtained from the dispersion analysis. This finite difference scheme is implemented
on the nCUBE2 parallel computer with a grid decomposition algorithm. The finite
difference synthetic waveforms are compared with those generated using the discrete
wavenumber method. They are in good agreement. The damping layers effectively
absorbed the boundary reflections. Four vertically heterogeneous borehole models: a
horizontal layered formation, a borehole with a radius change, a semi-infinite borehole,
and a semi-infinite borehole with a layer, are studied using the finite difference method. Snapshots from the finite difference results provide pictures of the radiating wavefields.
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