Modeling of low‐frequency Stoneley‐wave propagation in an irregular borehole

A fast modeling method is formulated for low‐frequency Stoneley‐wave propagation in an irregular borehole. This fast modeling method provides synthetic waveforms which include the effects of two borehole irregularities, diameter changes (washout), and formation property changes. The essential physics of the low‐frequency Stoneley waves are captured with a simple 1-D model. A mass‐balance boundary condition and a propagator matrix are used to express Stoneley‐wave interactions with the borehole irregularities. The accuracy of the proposed method was confirmed through comparison with existing finite‐difference and boundary integral modeling methods that yielded cross‐correlations greater than 0.98. Comparison of synthetic records calculated for an actual borehole with field records showed qualitative agreement in the major reflections because of the washout zones, but showed some disagreements in the reflections caused by the fractures. Since the synthetic records include only information relating to the borehole geometry and the elastic properties of formation, the reflection caused by the fracture will appear only in the field record. These results suggest the possibility of distinguishing Stoneley‐wave reflections caused by fractures from those caused by borehole irregularities. Further, the fast computational speed of this method—over 300 times faster than either boundary integral or finite‐difference methods—makes it quite suitable for field application.