Method and apparatus for determining a tubular thickness using a pulse echo waveform signal

A method for characterizing a tubular includes obtaining acoustic waveform data in a time domain using an acoustic transducer configured to emit an acoustic signal and receive a return acoustic signal and transforming the acoustic waveform data into a frequency domain to provide frequency domain acoustic waveform data. The method also includes determining a complex group delay function Gk derived from the frequency domain acoustic waveform data to provide a phase delay function as a function of frequency, wherein the complex group delay function Gk represents a first derivative of phase in the frequency domain with respect to frequency. The method further includes determining an imaginary component function of the complex group delay function Gk to provide a phase delay function as a function of frequency and characterizing the tubular using the phase delay function.