Generalized nonhyperbolic moveout approximation |

Equations 1-2 reduce to some well-known approximations with special choices of parameters.

- If , the proposed approximation reduces to
the classic hyperbolic form

which is a two-parameter approximation. - The choice of parameters ; ; reduces the proposed
approximation to the shifted hyperbola (Malovichko, 1978; de Bazelaire, 1988; Castle, 1994), which is the following three-parameter
approximation:

- The choice of parameters ;
;
reduces approximation 2 to the form
proposed by Alkhalifah and Tsvankin (1995) for VTI media, which is the following
three-parameter approximation:

- The choice of parameters
; ; reduces approximation 2 to the following
three-parameter approximation suggested by Blias (2007) and
reminiscent of the ``velocity acceleration'' equation proposed by
Taner et al. (2005,2007):

- The choice of parameters ; ; reduces the proposed approximation to the following
three-parameter approximation suggested by Blias (2009):

- The choice of parameters ; reduces the proposed approximation to the following
three-parameter approximation also suggested by Blias (2009):

- The choice of parameters
,
,
reduces the proposed
approximation to the double-square-root expression

where , , and . Equation 17 describes moveout precisely for the case of a diffraction point in a constant velocity medium.

Thus, the proposed approximation encompasses some other known forms but introduces more degrees of freedom for optimal fitting.

Generalized nonhyperbolic moveout approximation |

2013-07-26