Tomographic reconstruction of near‐borehole slowness using refracted borehole sonic arrivals

Two‐dimensional (2-D) reconstructions of the near‐borehole slowness field are computed using arrival times of refracted borehole sonic arrivals. First‐arrival traveltimes, derived from both computer simulations and field data from full‐waveform sonic tools, were inverted for the near‐borehole formation slowness both axially along the borehole and radially away from the borehole. The inversion is nonlinear; the solution is obtained by means of a series of linear inversions followed by provisional ray tracings. Each iteration involves the application of a tomographic reconstruction algorithm similar to those used in seismic crosswell tomography or medical imaging applications. The technique was demonstrated using ray‐theoretic examples to simulate radial variations in slowness. In addition, full‐waveforms were generated using two‐and‐a‐half‐dimensional (2.5-D) FDM computer models. The finite‐difference method (FDM) computer models were used to test the validity of the ray‐theoretic approximation used in the inversion scheme and to simulate the full‐waveform sonic tool response for both radial and axial changes in formation properties. Field data examples highlighted radial changes in formation slowness caused by two separate mechanisms: water take up by swelling shales and the mechanical breakdown of the near‐borehole rock resulting from stress relief caused by the drilling process. Finally, refracted sonic arrivals from near‐borehole bed boundaries were identified in a horizontal well setting. Using refractions arriving beyond the headwave, a 2-D map of formation slowness was computed in the reservoir away from the borehole. Interpretation of the slowness map resulted in an estimation of the stand‐off of the horizontal borehole from the reservoir boundary.