The thickness of borehole casing can be determined by ultrasound logging in conjunction with simulations of ultrasonic plane-wave echo waveforms across a range of frequencies for a plurality of casing thicknesses and correlation of synthetic frequency spectra derived from the simulated plane-wave echo waveforms for the various casing thicknesses against the frequency spectrum of a measured pulse-echo waveform. In accordance with various embodiments, a portion of the measured pulse-echo waveform that corresponds to the first reflection off the interface between the borehole casing and the borehole fluid is used as a driving pulse to weight the simulated plane-wave echo waveforms in the synthetic frequency spectrum.