Effect of anelastic patchy saturated sand layers on the reflection and transmission responses of a periodically layered medium
B. Dupuy and A. Stovas
Journal name: Geophysical Prospecting
Issue: Vol 64, No 2, March 2016 pp. 299 - 319
Info: Article, PDF ( 3.55Mb )
Based on analytic relations, we compute the reflection and transmission responses of a periodically layered medium with a stack of elastic shales and partially saturated sands. The sand layers are considered anelastic (using patchy saturation theory) or elastic (with effective velocity). Using the patchy saturation theory, we introduce a velocity dispersion due to mesoscale attenuation in the sand layer. This intrinsic anelasticity is creating frequency dependence, which is added to the one coming from the layering (macroscale). We choose several configurations of the periodically layered medium to enhance more or less the effect of anelasticity. The worst case to see the effect of intrinsic anelasticity is obtained with low dispersion in the sand layer, strong contrast between shales and sands, and a low value of the net-togross ratio (sand proportion divided by the sand + shale proportion), whereas the best case is constituted by high dispersion, weak contrast, and high net-to-gross ratio. We then compare the results to show which dispersion effect is dominating in reflection and transmission responses. In frequency domain, the influence of the intrinsic anelasticity is not negligible compared with the layering effect. Even if the main resonance patterns are the same, the resonance peaks for anelastic cases are shifted towards high frequencies and have a slightly lower amplitude than for elastic cases. These observations are more emphasized when we combine all effects and when the net-to-gross ratio increases, whereas the differences between anelastic and elastic results are less affected by the level of intrinsic dispersion and by the contrast between the layers. In the time domain, the amplitude of the responses is significantly lower when we consider intrinsic anelastic layers. Even if the phase response has the same features for elastic and anelastic cases, the anelastic model responses are clearly more attenuated than the elastic ones. We conclude that the frequency dependence due to the layering is not always dominating the responses. The frequency dependence coming from intrinsic visco-elastic phenomena affects the amplitude of the responses in the frequency and time domains. Considering intrinsic attenuation and velocity dispersion of some layers should be analyzed while looking at seismic and log data in thin layered reservoirs.