Generalized nonhyperbolic moveout approximation

Published as Geophysics, 75, no. 2, U9-U18, (2010)

Generalized nonhyperbolic moveout approximation

Sergey Fomeland 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

Abstract:

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.

Generalized nonhyperbolic moveout approximation