A method of processing waveforms (e.g. dispersive waveforms from a monopole Stonley mode, dipole, quadrupole or higher order mode) includes: (a) transforming at least a portion of the waveforms to produce frequency domain signals 223; (b) obtaining a model dispersion curve 225 based on a borehole-formation model 226 having a set of borehole-formation parameters (e.g. shear slowness, compressional slowness, mud slowness, formation density, mud density, borehole diameter, signal time support window, signal frequency range); (c) adjusting phases of the frequency domain signals according to the model dispersion curve to produce back-propagated signals 224; (d) computing coherence of the back propagated signals 228; (e) repeating steps (b) to (d) varying values of the set of borehole-formation parameters until the coherence reaches a selected criterion; and (f) outputting 240 at least a portion of the set of borehole-formation parameters (e.g. formation shear slowness). Also disclosed is a method of determining formation anisotropy by determining elastic shear constants from acoustic waveforms corresponding to the monopole Stoneley mode and the dipole or quadrupole mode.
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