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

Abstract 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 cross-well 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.