A transversely isotropic medium with a tilted symmetry axis normal to the reflector |

symmetry axis normal to the reflector

**Tariq Alkhalifah, King Abdulah University of Science and Technology, and
Paul Sava, Center for Wave Phenomena, Colorado School of Mines**

tkhalfah@kacst.edu.sa, psava@mines.edu

The computational tools for imaging in transversely isotropic media
with tilted axes of symmetry (TTI) are complex and in most cases do
not have an explicit closed-form
representation. As discussed in this paper, developing
such tools for a TTI medium with tilt
constrained to be normal to the reflector dip (DTI) reduces their
complexity and allows for closed-form representations. We show that, for the homogeneous case
zero-offset migration in such a medium can be performed using an
isotropic operator scaled by the velocity of the medium in the tilt
direction. We also show that, for the nonzero-offset
case, the reflection angle is always equal to the incidence angle,
and thus, the velocities for the source and receiver waves at the
reflection point are equal and explicitly dependent on the
reflection angle. This fact allows us to develop explicit
representations for angle decomposition as well as moveout formulas
for analysis of extended images obtained by wave-equation
migration. Although setting the tilt normal to the reflector dip may
not be valid everywhere (i.e., salt flanks), it can be used in the
process of velocity model building where such constrains are useful
and typically used.

- Introduction
- Dip-constrained TTI media
- Extended imaging condition
- Moveout analysis
- Angle decomposition
- Downward Continuation
- Domain of applicability
- Conclusions
- Acknowledgments
- Bibliography
- About this document ...

A transversely isotropic medium with a tilted symmetry axis normal to the reflector |

2013-04-02