A potential application for single-well acoustic imaging is the detection of an existing cased borehole in the vicinity of the well being drilled, which is important for drilling toward (when drilling a relief well), or away from (collision prevention), the existing borehole. To fulfill this application in the unconsolidated formation of shallow sediments, we propose a detection method using the low-frequency compressional waves from dipole acoustic logging. For this application, we perform theoretical analyses on elastic wave scattering from the cased borehole and derive the analytical expressions for the scattered wavefield for the incidence of compressional and shear waves from a borehole dipole source. The analytical solution, in conjunction with the elastic reciprocity theorem, provides a fast algorithm for modeling the whole process of wave radiation, scattering, and reception for the borehole acoustic detection problem. The analytical results agree well with those from 3D finite-difference simulations. The results show that compressional waves, instead of shear waves as commonly used for dipole acoustic imaging, are particularly advantageous for the borehole detection in the unconsolidated formation. Field data examples are used to demonstrate the application in a shallow marine environment, where dipole-compressional wave data in the measurement well successfully delineate a nearby cased borehole, validating our analysis results and application.
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