Comparison of seismic attenuation models using zero-offset vertical seismic profiling (VSP) data

Abstract

For seismic frequencies it is common to use an empirical equation to model attenuation. Usually the attenuation coefficient is modeled with linear frequency dependence, a model referred to as the Kolsky-Futterman model. Other models have been suggested in the geophysical literature. We compare eight of these models on a zero-offset vertical seismic profiling (VSP) data set: the Kolsky-Futterman, the power law, the Kjartansson, the Müller, the Azimi second, the Azimi third, the Cole-Cole, and the standard linear solid (SLS) models. For three separate depth zones we estimate velocities and Q-values for all eight models. A least-squares model-fitting algorithm gives almost the same normalized misfit for all models. Thus, none of the models can be preferred or rejected based on the given data set. Slightly better overall results are obtained for the Kolsky-Futterman model; for one depth zone, the SLS model gave the best result.