Casing thickness estimation by frequency correlation

A system comprising:

• an ultrasonic logging tool to measure a pulse-echo waveform in a borehole casing;
• and
• circuitry to process the measured pulse-echo waveform by
• extracting, from the measured pulse-echo waveform, a reflection portion corresponding to a reflection off an interface between the borehole casing and a borehole fluid contained within the borehole casing;
• computing, for each of a plurality of casing thicknesses, a synthetic frequency spectrum as a weighted sum of plane-wave echo waveforms simulated for the respective casing thickness across a range of frequencies, using the reflection portion extracted from the measured pulse-echo waveform as a driving pulse to weight the simulated plane-wave echo waveforms;
• correlating a frequency spectrum of the measured pulse-echo waveform with the synthetic frequency spectra computed for the plurality of casing thicknesses to obtain a correlation coefficient as a function of casing thickness;
• and
• determining a thickness of the borehole casing based on a maximum of the correlation coefficient.

A machine-readable medium storing instructions for processing pulse-echo waveforms measured in a borehole casing to determine a thickness of the borehole casing, the instructions, when executed by one or more processors, cause the one or more processors to

• extract, from the measured pulse-echo waveform, a reflection portion corresponding to a reflection off an interface between the borehole casing and a borehole fluid contained within the borehole casing;
• compute, for each of a plurality of casing thicknesses, a synthetic frequency spectrum as a weighted sum of plane-wave echo waveforms simulated for the respective casing thickness across a range of frequencies, using the reflection portion extracted from the measured pulse-echo waveform as a driving pulse to weight the simulated plane-wave echo waveforms;
• correlate a frequency spectrum of the measured pulse-echo waveform with the synthetic frequency spectra computed for the plurality of casing thicknesses to obtain a correlation coefficient as a function of casing thickness;
• and
• determine a thickness of the borehole casing based on a maximum of the correlation coefficient.