Estimation of the formation shear and borehole fluid slownesses using sonic dispersion data in the presence of a drill collar

Abstract

Compressional and shear slownesses are widely used in the mechanical characterizaion and lithological interpretation of formations in the oil and gas industry. A traditional way to estimate the formation shear slowness consists of minimizing differences between a measured and model-based sonic dispersions. However, this procedure requires repeated computations of model-based dispersions or a look-up table of dispersion data. A pre-computed look-up table of dispersion data as a function of system parameters may also have to be interpolated that can introduce additional inversion error. Either of these procedures results in expensive computational costs. To overcome these limitations, we introduce a parametric inversion methodology where the cost function is derived from the corresponding waveguide dispersion model. Hence, the exact solution can be always obtained with noise-free data. Inversion efficiency is also improved by avoiding an explicit computation of wideband dispersion curves. Since the borehole fluid slowness is usually not correctly known, the inversion algorithm has been extended to simultaneously estimate the formation shear and borehole fluid slownesses. We demonstrate validity of the proposed inversion algorithm using synthetic data for modal dispersions for a fluid-filled borehole in the presence of a drill-collar in both the fast and slow formations. Excellent agreement between the input modal dispersion and that computed using the inverted shear slowness confirms the accuracy of the inversion algorithm.