| Summary: | The propagation of guided waves in a fluid-filled borehole with an open horizontal
fracture is investigated both theoretically and experimentally. The fracture is modeled
as a fluid layer that separates the domain of propagation into two regions. For
the solution of the problem, we use a hybrid method to generate wave modes in the
two regions. The modes are then summed to match the boundary conditions at the
fracture surfaces. A singularity problem arises in matching the surface conditions and
is regularized using a physical model based on the conservation of mass. Using the
theory developed in this study, we study the transmission and reflection characteristics
of borehole guided waves (Le., Stoneley and pseudo-Rayleigh waves) due to the
fracture. At low frequencies, the effects of a fracture on the Stoneley wave are dominated by the fluid flow into the fracture. As frequency increases, mode conversion at
the fracture becomes significant. Above the cut-off frequency of the pseudo-Rayleigh
wave, part of the incident Stoneley wave is converted to pseudo-Rayleigh waves, which
is demonstrated by synthetic microseismograms. The pseudo-Rayleigh wave is substantially
affected by the fracture. Because this wave requires the formation shear strength to sustain its propagation, even a thin fracture with zero shear strength can
significantly attenuate the wave amplitude and produce strong reflection. This effect
is more pronounced towards the cut-off frequencies than away from the frequencies.
Consequently, the lack of pseudo-Rayleigh energy across a fracture may be used as a
sensitive indicator in fracture detection and characterization.
Ultrasonic experiments have been performed to measure the transmission of guided
waves across laboratory borehole fracture models. For the Stoneley waves, we performed
the experiment below the cut-off frequency of the pseudo-Rayleigh wave and the
experimental results are in good agreement with the theory. For the pseudo-Rayleigh
wave, we performed the experiment in a higher frequency range. The experiment has
verified the substantial effects of a fracture on this wave mode. The weak early arrivals
of the transmitted waves have also been observed for thin as well as thick fractures.
This confirms the theoretical prediction that the transmission of the pseudo-Rayleigh
wave is the smallest towards the cut-off frequencies. The measured transmission coefficients agree with theoretical results.
In summary, we have presented an analysis on the guided wave propagation across
a borehole horizontal fracture. The wave characteristics in the vicinity of a fracture
as described in this study may be used to provide useful information for the detection
and characterization of borehole fractures using acoustic logging techniques.
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