A method, comprising: obtaining a waveform from a sonic borehole device in a formation; processing the obtained waveform to obtain at least one of a Stoneley, flexural, quadrupole and Pseudo-Rayleigh dispersion; at least one of performing a computation and obtaining a library computation for interpolated theoretical dispersions of the Stoneley, flexural, quadrupole and Pseudo-Rayleigh dispersions; performing an initial estimate of mud slowness using both the processing of the obtained waveform and the interpolating the theoretical dispersions; calculating a first mismatch between the processed waveform obtaining the at least one Stoneley, flexural, quadrupole and Pseudo-Rayleigh dispersion and the theoretical dispersions of the Stoneley, flexural, quadrupole and Pseudo-Rayleigh dispersions; estimating at least one DTmud value as a vertical depth profile; characterized by calculating a second mismatch between the theoretical dispersion and the processed waveform using the at least one estimated DTmud value; estimating at least one anisotropic parameter by minimizing the second mismatch; using regression, calculating the at least one anisotropic parameter over multiple depths; updating values for the at least one anisotropic parameter based upon the regression; calculating a third mismatch between the theoretical and measured dispersions by the sonic borehole device based upon the updated values for the at least one parameter based upon the regression; estimating a final value of the at least one anisotropic parameter by minimizing a mismatch between the theoretical and the measured dispersions; and using the final value to build a more accurate mechanical earth model, MEM, for geomechanical analysis. obtaining a waveform from a sonic borehole device in a formation; processing the obtained waveform to obtain at least one of a Stoneley, flexural, quadrupole and Pseudo-Rayleigh dispersion; at least one of performing a computation and obtaining a library computation for interpolated theoretical dispersions of the Stoneley, flexural, quadrupole and Pseudo-Rayleigh dispersions; performing an initial estimate of mud slowness using both the processing of the obtained waveform and the interpolating the theoretical dispersions; calculating a first mismatch between the processed waveform obtaining the at least one Stoneley, flexural, quadrupole and Pseudo-Rayleigh dispersion and the theoretical dispersions of the Stoneley, flexural, quadrupole and Pseudo-Rayleigh dispersions; estimating at least one DTmud value as a vertical depth profile; calculating a second mismatch between the theoretical dispersion and the processed waveform using the at least one estimated DTmud value; estimating at least one anisotropic parameter by minimizing the second mismatch; using regression, calculating the at least one anisotropic parameter over multiple depths; updating values for the at least one anisotropic parameter based upon the regression; calculating a third mismatch between the theoretical and measured dispersions by the sonic borehole device based upon the updated values for the at least one parameter based upon the regression; estimating a final value of the at least one anisotropic parameter by minimizing a mismatch between the theoretical and the measured dispersions; and using the final value to build a more accurate mechanical earth model, MEM, for geomechanical analysis.