The inversion of shear wave slowness's radial variations based on the dipole flexural mode dispersion

The effect of shear wave slowness's radial heterogeneities on dipole flexural mode dispersions is analyzed for shear wave slowness's radially layered model. Perturbation method and Backus-Gilbert(BG) theory are used for the inversion of shear wave slowness radial variations based on the difference of flexural wave dispersions between radially heterogeneous and homogeneous formations. When there is no noise and error of other parameters, the radial variations of the inverted shear wave slowness agree very well with the assumed radial profile. When the choice of slowness for the borehole fluid or formation compressional wave has a deviation from the true value within 10 percent, the inverted radial variations of shear wave slowness almost remains unchanged. When there exists noise with SNR (Signal Noise Ratio) of 20 dB or 10 dB, the relative error of the inversion results is within 10 percent, which means the impact of noise on the inversion results is little. From the inversion results described above, the technique which combines perturbation method and BG theory for the inversion of shear wave slowness's radial variations is robust, and can be utilized for understanding formation properties around borehole wall on the spot.