Although synthetic borehole seismograms routinely can be computed for a widerange of borehole conditions, the physical nature of shear and compressional headwaves in fluid-filled boreholes is poorly understood. This paper presents a series ofnumerical experiments designed to provide insight into the physical mechanismscontrolling head wave propagation in boreholes. These calculations demonstrate theexistence of compressional normal modes equivalent to shear normal modes, orpseudo-Rayleigh waves, with sequential cutoff frequencies spaced between thecutoff frequencies for the shear normal modes. Major contributions to head wavespectra are shown to occur in discrete peaks at frequencies just below mode cutofffor both compressional and shear modes. This result is confirmed by calculations withsynthetic waveforms at frequencies corresponding to mode cutoff, and by branch cutintegrals designed to yield independent spectra for the compressional mode. In thecase of soft formations where shear velocity falls below acoustic velocity in theborehole fluid, leaky compressional normal modes attain properties similar to thoseobserved for shear normal modes in the hard rock case. This result is formally relatedto a fluid-fluid waveguide with undamped compressional normal modes in the limit ofvanishing shear velocity. Synthetic waveforms demonstrate that high amplitudearrivals, traveling at velocities less than the acoustic velocity of the borehole fluid,and at frequencies above a few kilohertz represent the Airy phase of thecompressional mode and not a tube wave. Comparison of synthetic waveforms withwaveforms obtained in soft sea sediments indicates that the predicted Airy phasearrivals are present in the experimental data.
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