Resonance-based inversion of acoustic impedance of annulus behind casing

A non-transitory computer-readable medium storing computer-executable instructions, that when executed by at least one processor, causes the at least one processor to perform the following:

• inputting, from an acoustic tool deployed in a wellbore comprising mud, casing, and annular fill, an acoustic waveform comprising one or more reflected acoustic waves, wherein the acoustic tool is a pulse-echo tool acoustic;
• normalizing the acoustic waveform using a normalization workflow, resulting in a normalized wave, wherein normalizing the acoustic waveform comprises:
• transforming the acoustic waveform to frequency domain, resulting in a wave spectrum;
• estimating a specular wave spectrum from the wave spectrum;
• normalizing the wave spectrum with the specular wave spectrum, resulting in a normalized spectrum;
• renormalizing the normalized spectrum with a shaping spectrum, resulting in a shaped waveform;
• and
• transforming the shaped waveform to time domain, resulting in the normalized wave;
• producing a reference wave based on an initially estimated thickness of the casing, modeling of wellbore parameters, or combinations thereof;
• comparing the normalized wave with the reference wave;
• iteratively producing a new reference wave, if the normalized wave does not substantially match the reference wave;
• iteratively comparing the normalized wave with the new reference wave, until the normalized wave substantially matches a matching reference wave;
• and
• estimating an acoustic impedance of the annular fill, and an acoustic impedance of mud between the casing and the acoustic tool based on the matching reference wave.