Improved Spectral Estimates for Attenuation Studies

Abstract

We analyse the suitability for measuring attenuation of four different spectral decomposition techniques (Stockwell transform, Short-time Fourier Transform, STFT, Wigner-Ville distribution, WVD, and Reduced Interference Distribution, RID), through synthetic wave-localisation and surface seismic reflection experiments based upon 280m of a p-wave velocity, s-wave velocity and density log of a well which covers a target interval and shows random fluctuations in the p-wave velocity log. One aim of this study is to determine if one spectral decomposition technique alone consistently provides results which are closer to the theoretically expected results, with a caveat that the test setup favours quadratic time-frequency distributions, such as WVD and RID by minimizing cross-term interference present in the instantaneous autocorrelation function. Omitting the WVD, the Stockwell transform had the lowest misfit in the wave-localisation experiment whilst the RID is best at deriving the expected inverse Q of 0.02 in the surface seismic reflection experiment with a mean derived inverse Q value of 0.02 /-0.01. Further tests are desired (a) to highlight the effects of the vulnerability to interference inherent in quadratic time-frequency distributions, and (b) to evaluate whether refining RID/STFT parameters, such as applied window size, will further optimise the decomposition and produce more accurate attenuation results.