Moveout velocity versus stacking velocity
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Series | Investigations in Geophysics |
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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
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle t^2(x)=t^2(0)+\frac{x^2}{v^2_{NMO}}.} ( )
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 tstk as
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle t^2_{stk}(x)=t^2_{stk}(0)+\frac{x^2}{v^2_{stk}},} ( )
where vstk 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:
- The observed two-way zero-offset time OC = t(0) in equation (14) can be different from the twoway zero-offset time OB = tstk(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.
- The difference between the stacking velocity vstk and NMO velocity vNMO is called spread-length bias [1]; [2]. 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 vstk and vNMO.

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
- main page: Reflection_moveout
- 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