Testing VSP-based Q-estimation with spherical wave models

Arnim B. Haase, Robert R. Stewart

Q-estimation with VSP data from Alberta and Saskatchewan led to the conclusion that stratigraphic effects are a significant part of those estimates. As a first step toward a better understanding of stratigraphic attenuation, we investigate the response to spherical waves of a simple density step model. The Sommerfeld integral is utilized to compute synthetic VSP down-going waves by numerical integration. Q-factors are estimated from these down-going wave fields by applying the spectral ratio method, the analytical signal method, a misfit minimization method adapted from Toverud and Ursin (2005) as well as a modification of the spectral ratio method introduced by Taner and Treitel (2003). We find that at larger depths, away from density steps, all methods recover the model Q factor quite well. A departure of recovered Q from model Q at shallow depths is noticeable for all methods and is thought to be caused by near-field effects. Q-estimation errors for some methods are found to be considerable in the vicinity of single interfaces investigated. Q-estimates obtained by methods based on spectral ratios appear to be least sensitive to step changes in density values, at least in noise-free situations.