Velocity and Q in transverse isotropic media
, by Martin Karrenbach
Seismic velocity and Q measurements determine elastic and viscoelastic stiffness constants
in a cross-well experiment. The methods described rely on picking direct wave traveltimes
and determination of Q. Measured group velocity is converted to phase velocity, based on the
assumption that wave propagation can be adequatedly described using plane waves. A general
method is developed to invert for elastic and viscoelastic constants in a least-squares fit.
A practical determination scheme fits ellipses to dispersion relations of the medium.
In a small angle approximation, elastic constants are deduced. This paraxial approximation
is useful since it separates v(z) effects from the intrinsic velocity anisotropy. Determined
stiffness constants match model constants well where small angle measurements are used
in a Greenhorn shale example.
STANFORD