Borehole Wave Propagation In Isotropic And Anisotropic Media II: Isotropic Formation
Author(s)
Cheng, Ningya; Cheng, C. H.; Toksoz, M. N.
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Other Contributors
Massachusetts Institute of Technology. Earth Resources Laboratory
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In this paper we apply the 3-D finite difference method to simulate borehole wave
propagations in an isotropic formation. The scheme is tested in a fluid-filled borehole
surrounded by the homogeneous elastic formation. The finite difference synthetics results
are in good agreement with the discrete wavenumber solutions for both monopole
and dipole sources in hard as well as soft formation. These tests also show the good
performance of Higdon's absorbing boundary condition for the body waves as well as
the guided waves.
In the isotropic borehole formation, the following results are obtained:
1. Off-centered dipole sources generate almost the same waveforms as the centered
dipole source. The slight amplitude differences are due to the different values of the
excitation function at the different source positions. The off-centered monopole
shows a larger Stoneley wave than the centered one.
2. In an elliptic borehole, where the source is in line with the minor axis of ellipse,
the dipole waveforms have similar waveforms to the circular borehole with the
same radius as the minor axis. This corresponds to the odd flexural mode. The
waveform similarity demonstrates that the odd flexural mode is insensitive to the
major axis. When the dipole is in line with the major axis of the ellipse, the
waveforms shift to the low frequency range. The waveforms are dominated by the
even flexural mode.
3. For a borehole near a horizontal bed, the monopole log can be used to detect it by
using refracted P waves from the bed boundary. Because a dipole is a directional
source, when it is parallel to the bed, there is little effect of the bed on the
waveforms, and when it is perpendicular to the bed, there are strong flexural wave
interferences. For a borehole which penetrates a 45 degree tilted layer interface,
the monopole log has less reflection and transmission than the horizontal interface.
The dipole log also transmits less flexural waves across the tilted boundary than
the horizontal one. The horizontally layered formation seismograms clearly show
the two flexural modes in the different layers. There are no clear flexural wave
reflections in both cases.
Date issued
1994Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;1994-03