An investigation into the fundamental relationships between attenuation, phase dispersion, and frequency using seismic refraction profiles over sedimentary structures

Despite many attenuation measurements which indicate a linear functional frequency dependence of absorption or constant Q (super -1) in sediments, several theories predict no such linear dependence. The primary justification for rejecting a first-power frequency dependence of attenuation is that it implies that seismic waves cannot propagate causally. Seismic waves must also travel with some velocity dispersion to satisfy causality, yet there is a lack of velocity dispersion measurements in sediments. In-situ attenuation is caused by two distinct mechanisms: anelastic heating, and scattering due to interbed multiples. Apparent, or scattering, attenuation can produce both frequency-dependent and non-frequency-dependent effects. Accurate measurements of attenuation and velocity dispersion are difficult; it is not surprising that a systematic investigation into the frequency dependence of absorption and velocity has not been made.A reinvestigation into two seismic refraction data sets collected over thickly stratified deep-sea fans indicates that Q (super -1) should not be assumed to be independent of frequency. Further, significant frequency-independent absorption is present, indicating a high degree of apparent attenuation. Phase, or velocity, dispersion was also measured, but the results are more ambiguous than those for attenuation, due to inherent limitations of digital signals. Nevertheless, the absorption and velocity dispersion results are largely compatible, suggesting that if apparent attenuation is observed, then the scattered waves propagate causally.