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Seismic Wave Propagation in and Around Boreholes
Tiepeng Zhou
Submitted
to the Department of Earth, Atmospheric, and Planetary Sciences on September
1, 1995 in partial fulfillment of the requirements for the degree of Doctor
of Philosophy
Abstract
Seismic imaging applications using a source or receiver in a borehole are
significantly complicated by the coupling of the wavefields propagating in
the formation with those in a borehole. In particular, a borehole source can
generate a very large amplitude Stoneley wave, and a borehole receiver will
record both incoming body waves and tube waves generated by the interaction
of these waves with the receiver borehole. These problems are particularly
severe when the source and the receiver are in the same borehole, the single-well
imaging configuration. In this thesis we have explored ways of using conventional,
staggered-grid finite difference codes to model these wave propagation effects
to help understand data that may be collected in such experiments.
The most fundamental problem in simulating these effects with finite difference
algorithms is that both the borehole and the surrounding medium must be discretized,
and a modeling scheme that must finely discretize the small borehole (diameter
about 0.20 m) will not be able to incorporate large models (on the order of
100 m) around the borehole because of the sheer size of the resulting discretized
model.. We therefore show results of tests demonstrating that it is possible
to relax these constraints somewhat in two ways: (1) at the lower frequencies
(i.e. wavelength in the formation is relatively large compared to the borehole),
the borehole need not be discretized as finely to accurately reproduce the
same effects on source wavefields as a fine discretization, and (2) as long
as the wavelength remains fairly large compared to the borehole, the size
of the borehole can be increased without significantly altering the radiation
pattern. Both finite difference and stationary phase radiation pattern results
confirm the second point.
The second issue we address is the problem of tube waves recorded in single-well
imaging experiments. One way of helping to suppress the effects of these waves
on receivers, especially hydrophones, is to place damping devices within the
borehole between source and receivers. We use the finite difference method
to simulate the effects of dampers of various velocities and lengths. In general,
the larger the velocity contrast between the damper and the fluid, the more
the tube wave is suppressed. Likewise, a longer damper will also better suppress
the tube wave. In contrast, at least for realistic values, the center frequency
of the source does not influence the effectiveness of the damper very much.
One very important consideration we prove with the calculations is that the
use of multiple dampers is very effective, suggesting that an effective procedure
in the field may involve placing two or more dampers between the source and
the receiver.
