Systems, methods, and devices for evaluating proper cement installation in a well are provided. In one example, a method includes receiving acoustic cement evaluation data having a first parameterization. At least a portion of the entire acoustic cement evaluation data may be corrected to account for errors in the first parameterization, thereby obtaining corrected acoustic cement evaluation data. This corrected acoustic cement evaluation data may be processed with an initial solid-liquid-gas model before performing a posteriori refinement of the initial solid-liquid-gas model, thereby obtaining a refined solid-liquid-gas model. A well log track-indicating whether a material behind the casing is a solid, liquid, or gas—may be generated by processing the corrected acoustic cement evaluation data using the refined solid-liquid-gas model.