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

An apparatus for characterizing a tubular disposed in a borehole penetrating a subsurface formation, the apparatus comprising:

• an acoustic transducer configured to emit and receive an acoustic signal to provide to provide acoustic waveform data in a time domain;
• and
• a processor configured to:
• transform the acoustic waveform data in the time domain into a frequency domain using a frequency domain transform to provide frequency domain acoustic waveform data;
• determine 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;
• determine an imaginary component function of the complex group delay function Gk to provide a phase delay function as a function of frequency;
• and
• characterize the tubular using the phase delay function.