1. A method comprising:a) defining, by a processor, Thomsen parameters for each log measurement depth using at least one of one or more formation constituents, one or more predetermined formation constraints, one or more predetermined formation type cut-offs and maximum Thomsen parameters for the formation;
b) correcting, by the processor, shear wave travel time (DTS) and compressional wave travel time (DTC) simultaneously for deviation and dispersion on sonic log measurements of deviated wells using the Thomsen parameters and a non-linear solver;
c) calculating, by the processor, dispersion, shear wave velocity with horizontal polarizations at 90 degrees (VSH90), shear wave velocity with horizontal polarizations at 0 degrees (VSH0), compressional wave velocity at 0 degrees (VP0), compressional wave velocity at 90 degrees (VP90), shear wave velocity at ? degrees (VSV?), and new Thomsen parameters based on the corrected sonic log measurements; and
d) plotting, by the processor, the actual log measurements and the calculated dispersion, VSH90, VSH0, VP0, VP90, VSV?, new Thomsen parameters on separate respective graphs;
e) building, by the processor, a model of the deviated well using the calculated dispersion, VSH90, VSH0, VP0, VP90, VSV?, and new Thomsen parameters.