Sommerfeld integral based spherical wave field computation applied to multi-interface VSP models for stratigraphic Q investigations
Arnim B. Haase
A method developed from the Ewing algorithm for point sources in layered media is employed to compute the complete spherical wave field for synthetic zero- offset VSPs. For the elastic case of six embedded Class 1 reservoir layers, the transmitted wave spectrum below the stack of layers shows a clear trend of amplitude decay with frequency which the spectral ratio method of Q-estimation interprets as a finite Q-factor; because of the purely elastic model this represents stratigraphic attenuation.
For a more realistic multi-layer situation Ross Lake well-logs are introduced. The depth dependent Q-factor estimated from a synthetic Ross Lake VSP modelled with a constant intrinsic Q of 100 resembles Q(z) estimated from actual Ross Lake VSP-data. This observation suggests a dominant role of stratigraphic attenuation in the Ross Lake area. When implementing a first-order estimation- error reduction by spectral normalization, model Q recovery is improved but still unsatisfactory.