Anisotropic scalar imaging
using the double elliptic approximation

Martin Karrenbach

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ABSTRACT

The double elliptic approximation to the transverse isotropic dispersion relation can be used to image a subsurface scalar eigenfield. The rationale behind the double elliptic approximation is the use of only four parameters for 2D data. These parameters are found by conventional velocity analysis after a vector wavefield is converted to its scalar eigenfields. The dispersion relation is parameterized by horizontal and vertical direct-wave velocities and horizontal and vertical normal-moveout velocities. Estimation of those four parameters typically requires a combination of surface seismic data and cross-well or VSP data. If the algorithm is implemented in the phase domain, existing scalar imaging techniques are easily extended to anisotropy As an example a transverse isotropic medium (Greenhorn shale) is modeled and migrated using both the exact anisotropic dispersion relation and its double elliptic approximation. The approximation works very well paraxially, but it fails in areas of triplication.