Moveout velocity versus stacking velocity
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
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 t_{stk} 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 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:
- 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.
- The difference between the stacking velocity v_{stk} and NMO velocity v_{NMO} 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 v_{stk} and v_{NMO}.
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
References
- ↑ Al-Chalabi, 1973, Al-Chalabi, M., 1973, Series approximations in velocity and traveltime computations: Geophys. Prosp., 21, 783–795.
- ↑ ^{2.0} ^{2.1} Hubral and Krey (1980), Hubral, P. and Krey, T., 1980, Interval velocities from seismic reflection time measurements: Soc. Expl. Geophys.