Techniques involve obtaining acoustic data from an acoustic logging tool, where the acoustic data includes waves reflected from the casing, the annular fill material, the formation, and/or interfaces between any of the casing, the annular fill material, one or more interfaces between any of the mud, the casing, and the annular fill material. Techniques include normalizing the acoustic wave to result in a normalized wave having a comparable spectral shape with a reference wave, and comparing the normalized wave with the reference wave. The reference wave may be generated or modeled or produced from a look-up table or database, and may be estimated based on initial estimates of wellbore parameters. Based on the comparison of the normalized wave with the reference wave, a best-fit reference wave substantially matching the normalized wave may be identified. The best-fit reference wave may correspond with a thickness of the casing, an acoustic impedance of the annular fill material, and an acoustic impedance of mud.