Massachusetts Institute of Technology. Earth Resources Laboratory
Abstract
We present a boundary integral equation formulation for the problem of wave propagation
in a borehole of irregular cross-section. The method consists in representing the
wave field diffracted at the borehole-rock interface by the radiation from a distribution
of surface sources applied along the borehole wall. The wave field in the borehole fluid
and in the elastic rock are then expressed using the discrete wavenumber method. The
application of the boundary conditions at discretized locations along the borehole wall
leads to a linear system of equations. The inversion of this system yields the required
source distribution.
We have used the method to investigate the effect of changes in borehole diameter
on the pressure wave field inside the borehole. The results show that when the change
is smooth, the records obtained ahead of the discontinuity location are not affected
by its presence. In the case of a steep variation, however, a significant amount of the
Stoneley wave energy is reflected. When the borehole diameter is different at the source
and at the receiver levels, the microseismograms obtained are somewhat of an average
between the ones that would be recorded in boreholes of constant radius equal to the
radius at the source and at the receiver. The presence of small-scale fluctuations in
borehole diameter reduces the amplitude of the Stoneley wave and decreases its velocity
and the pseudo-Rayleigh wave velocity.Massachusetts Institute of Technology. Full Waveform Acoustic Logging ConsortiumSociete Nationale Elf Aquitain
