LOCALIZATION AND BACKSCATTERING SPECTRUM OF SEISMIC-WAVES IN STRATIFIED LITHOLOGY

Using four sonic well logs from diverse geological environments, the statistics of lithological layers relevant to seismic wave propagation are analyzed. The autocorrelation functions are found to be well approximated by exponentials with correlation lengths generally in the 1.5 to 3 m range. Localization theory is used to calculate the apparent attenuation caused by random scattering as a function of frequency. This attentuation has a peak at 50 to 150 Hz with a corresponding localization length of 1.6 to 4.8 km and an apparent Q of 120 to 450. At seismic frequencies (20 Hz) the attenuation is smaller, with localization lengths in the 16 to 32 km range and an apparent Q of 300 to 600. These values of apparent Q are consistent with observations of previous authors who used well-log calculations. Using finite differences, synthetic traces are computed for a 20-Hz pulse with multiple backscattering from the lithology given by each of the well logs. The power spectral density of the trace is computed for different time gates and compared with theoretical predictions. The nonwhite f2 dependence of the spectrum as predicted by theory is confirmed. -from Authors