Generalized nonhyperbolic moveout approximation |

**Sergey Fomel ^{}and Alexey Stovas^{}**

^{}Bureau of Economic Geology,

John A. and Katherine G. Jackson School of Geosciences

The University of Texas at Austin

University Station, Box X

Austin, TX 78713-8972

USA

sergey.fomel@beg.utexas.edu
^{}Department of Petroleum Engineering and
Applied Geophysics

Norwegian University of Science and Technology (NTNU)

S.P. Andersenvei 15A

7491 Trondheim

Norway

alexey.stovas@ntnu.no

Reflection moveout approximations are commonly used for velocity
analysis, stacking, and time migration. We introduce a novel
functional form for approximating the moveout of reflection
traveltimes at large offsets. While the classic hyperbolic
approximation uses only two parameters (the zero-offset time and the
moveout velocity), our form involves five parameters, which can be
determined, in a known medium, from zero-offset computations and
from tracing one non-zero-offset ray. We call it a generalized
approximation because it reduces to some known three-parameter forms
(the shifted hyperbola of Malovichko, de Baziliere, and Castle; the
Padé approximation of Alkhalifah and Tsvankin; and others) with
a particular choice of coefficients. By testing the accuracy of the
proposed approximation with analytical and numerical examples, we
show that it can bring several-orders-of-magnitude improvement in
accuracy at large offsets compared to known analytical
approximations, which makes it as good as exact for many practical
purposes.

- INTRODUCTION
- NONHYPERBOLIC MOVEOUT APPROXIMATION

- ACCURACY TESTS

- Discussion
- CONCLUSIONS
- ACKNOWLEDGMENTS
- Appendix A: LINEAR VELOCITY MODEL
- Appendix B: LINEAR SLOTH MODEL
- Appendix C: REFLECTION FROM A HYPERBOLIC REFLECTOR IN A HOMOGENEOUS VELOCITY MODEL
- Appendix D: REFLECTION FROM A CIRCULAR REFLECTOR IN A HOMOGENEOUS VELOCITY MODEL
- Appendix E: HOMOGENEOUS VTI MODEL
- Bibliography
- About this document ...

Generalized nonhyperbolic moveout approximation |

2013-07-26