NUMERICAL COMPUTATION OF INDIVIDUAL FAR-FIELD ARRIVALS EXCITED BY AN ACOUSTIC SOURCE IN A BOREHOLE

The acoustic logging problem is modeled, and individual arrivals at far-field receivers are numerically computed. Following Roever et al. (1974) and others, the full wave field is represented as a sum of contributions from both poles and branch cuts in the complex wavenumber plane. The pole contributions correspond to mode arrivals, while the branch cuts are associated with body waves (i. e. , head waves). Both the pole and branch-cut contributions are computed numerically, and results are presented for the cases of a slow and a fast formation. The shear event in the slow formation is found to be relatively small, consistent with observations in measured data. Contrary to existing knowledge, the shear event in the fast formation is also relatively small. The apparent strong shear arrival in the full waveforms is due primarily to the trapped mode pole in the vicinity of cutoff.