Time‐domain apparent‐attenuation operators for compressional and shear waves: Experiment versus single‐scattering theory

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Abstract
We derive time‐domain apparent‐attenuation operators from both laboratory data and a single‐scattering theory. The scattering medium consists of a homogeneous elastic block containing parallel cylindrical voids, with volume fractions in the range from 0.66% to 3.75%. The attenuation operators were computed by first measuring (or theoretically predicting) the attenuation of spectral amplitude and then constructing a causal seismogram using the Kramers‐Kronig (KK) relation. Theory and experiment broadly agree, with the following exceptions: theory underestimated the overall level of attenuation, compressional wave attenuation is more poorly predicted than shear wave attenuation, and the theoretical attenuation operators tend to be larger in amplitude and less oscillatory than is observed. The KK attenuation operators are compared with attenuation operators derived from a least squares deconvolution (LSD) of the attenuated and unattenuated time series. The KK and LSD attenuation operators are superficially very different, reflecting different limitations in the methods. The LSD attenuation operators tend to be narrower than the KK attenuation operators and should not be used to measure pulse width.