Waveform Inversion Technique for Measuring Elastic Wave Attenuation inCylindrical Bars

摘要

This report presents a new technique for measuring elastic wave attenuation inthe frequency range of 10-150 kHz. The technique consists of measuring low-frequency waveforms using two cylindrical bars of the same material, but different lengths. The attenuation is obtained in two steps. First, the waveform, measured within the shorter bar, is theoretically propagated to the length of the longer bar. The distortion of the waveform due to the dispersion effect of the cylindrical waveguide is corrected for. Second, is the inversion for the attenuation, or Q of the rock, is obtained by minimizing the difference between the propagated waveform and the actual waveform measured within the longer bar. Because the waveform inversion is performed in the time domain, the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (approx 100-1000 kHz). Attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40-140 kHz. The attenuation for the two materials are found to be consistent with other measuring techniques.