Fast Model Based Inversion of Acoustic Impedance of Annulus Behind Casing

A method comprising:

• measuring an acoustic waveform at an acoustic transducer in a wellbore comprising casing and annular material, wherein the measured acoustic waveform is a reflection from the wellbore;
• computing a crude casing thickness by processing the acoustic waveform;
• determining an initial mud acoustic impedance of mud between the acoustic transducer and the casing and an initial annular acoustic impedance of the annular material;
• using the estimated crude casing thickness, the initial mud acoustic impedance, and the initial annular acoustic impedance in a forward modeling to calculate a model spectra;
• using the model spectra to calculate a specular signal;
• using the model spectra and the specular signal to calculate a calibrated model signal;
• using the model spectra and the calibrated model signal to compute a misfit of the calibrated model signal;
• using the misfit to compute an update to one or more of the estimated casing thickness, the initial mud acoustic impedance, and the initial annular acoustic impedance;
• and
• outputting one or more of a thickness of the casing, an apparent acoustic impedance of the annular fill material, and the acoustic impedance of mud once the computed update is below a threshold.

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 casing and annular fill, a measured waveform comprising one or more reflected acoustic waves;
• estimating, using the measured waveform, a crude thickness of the casing and a positioning of the acoustic tool;
• estimating an initial mud impedance of mud between the acoustic tool and the casing and an initial annular fill acoustic impedance;
• using forward modeling to estimate, based on the crude thickness of the casing and the positioning of the acoustic tool, an estimated casing thickness, an estimated annular fill acoustic impedance, and an estimated mud acoustic impedance;
• modeling a modeled spectra based on the estimated casing thickness, the estimated annular fill acoustic impedance, and the estimated mud acoustic impedance;
• computing a specular signal based on the modeled spectra and estimated casing thickness;
• computing a misfit of the specular signal using a reconstruction operator on the modeled spectra;
• computing an update to the estimated casing thickness based on the computed misfit;
• update the casing thickness;
• and
• output one or more of a calibrated casing thickness, an apparent acoustic impedance of the annular fill material, and the acoustic impedance of mud.