Moveout velocity versus stacking velocity

Seismic Data Analysis

Series	Investigations in Geophysics
Author	Öz Yilmaz
DOI	http://dx.doi.org/10.1190/1.9781560801580
ISBN	ISBN 978-1-56080-094-1
Store	SEG Online Store

Table 3-3 summarizes the NMO velocity obtained from various earth models. After making the small-spread and small-dip approximations, moveout is hyperbolic for all cases and is given by

$t^{2}(x)=t^{2}(0)+{\frac {x^{2}}{v_{NMO}^{2}}}.$

(14)

Table 3-3. NMO velocity for various earth models.

Model	NMO Velocity
Single Horizontal Layer	Velocity of the medium above the reflecting interface
Horizontally Stratified Earth	The rms velocity function provided the spread is small
Single Dipping Layer	Medium velocity divided by cosine of the dip angle
Multilayered Earth with Arbitrary Dips	The rms velocity function provided the spread is small and the dips are gentle

The hyperbolic moveout velocity should be distinguished from the stacking velocity that optimally allows stacking of traces in a CMP gather. The hyperbolic form is used to define the best stacking path t_stk as

$t_{stk}^{2}(x)=t_{stk}^{2}(0)+{\frac {x^{2}}{v_{stk}^{2}}},$

(15)

where v_stk is the velocity that allows the best fit of the traveltime trajectory on a CMP gather to a hyperbola within the spread length.

The optimum stacking hyperbola described by equation (15) is not necessarily the small-spread hyperbola given by equation (14). Refer to the travel-times illustrated in Figure 3.1-16 and note the following:

1. The observed two-way zero-offset time OC = t(0) in equation (14) can be different from the twoway zero-offset time OB = t_stk(0) associated with the best-fit hyperbola (equation 15). This occurs, for example, if some heterogeneity exists in the velocity layers above a reflector under consideration.
2. The difference between the stacking velocity v_stk and NMO velocity v_NMO is called spread-length bias ; . From equations (14) and (15), the smaller the spread length, the closer the optimum stacking hyperbola to the small-spread hyperbola, hence the smaller the difference between v_stk and v_NMO.

Figure 3.1-16  The equation for moveout velocity is derived by assuming a small-spread hyperbola (equation 14). On the other hand, stacking velocity is derived from the best-fit hyperbola over the entire spread length (equation 15). Here, (a) is the actual traveltime, (b) is best-fit hyperbola over the offset range OA, and (c) is small-spread hyperbola. Adapted from .

In practice, when we refer to stacking velocity and the zero-offset time associated with the optimum stacking hyperbola described by equation (15), we almost always think of the moveout velocity and the zero-offset time associated with the small-spread hyperbola given by equation (14).

See also

• NMO for a flat reflector
• NMO in a horizontally stratified earth
• Fourth-order moveout
• NMO stretching
• NMO for a dipping reflector
• NMO for several layers with arbitrary dips
• Exercises
• Topics in moveout and statics corrections

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