Variable velocity

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Seismic Data Analysis
Series Investigations in Geophysics
Author Öz Yilmaz
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store

The preceding discussion was based on a constant-velocity assumption. To be of practical use, DMO must be applicable to data with velocity gradients. Figure 5.1-17 shows the depth model we will use to investigate DMO correction in the case of vertical velocity variation. The depth model consists of three point scatterers buried beneath the center midpoint (CMP 32) in a medium with a horizontally layered velocity-depth model. Mathematical aspects of the variable-velocity DMO theory is quite involved and we shall only refer to the results of the experiments with the synthetic data associated with the depth model in Figure 5.1-17.

Selected common-offset sections and CMP gathers associated with this subsurface model are shown in Figures 5.1-18a and 5.1-18b. The same processing sequence is followed as that used for the constant-velocity model (Figure 5.1-3). The NMO correction (Figure 5.1-18c) before DMO correction is done using the rms velocity function indicated in Figure 5.1-17. Selected moveout-corrected common-offset sections are shown in Figure 5.1-19a. We shall apply both constant-velocity DMO correction and variable-velocity DMO correction [1][2] to these data. The corresponding impulse responses are shown in Figures 5.1-19b,c. Consider the common case of velocities increasing with depth in practice. As noted earlier, the higher the velocity the less the action of the DMO operator. Note that at late times the lateral extent of the impulse response of the variable-velocity DMO operator is less than that of the constant-velocity DMO operator. This is equivalent to modifying the offset value for the common-offset section under consideration — making it smaller than it is so as to decrease the action of the DMO operator.

Results of constant-velocity and variable-velocity DMO corrections are shown in Figures 5.1-20 and 5.1-21, respectively. Events on the selected CMP gathers are better flattened with the variable-velocity DMO correction. The corresponding stacked sections accompanied with the zero-offset conventional stacked sections without DMO correction are shown in Figure 5.1-22. The improvement with the depth-variable velocity also is evident on the stacked section (Figure 5.1-22d). Specifically, note that the flanks of the diffraction events are enhanced with the depth-variable velocity, making it resemble much more closely the zero-offset section (Figure 5.1-22a) as compared to the constant-velocity DMO stack (Figure 5.1-22c).

In practice, constant-velocity DMO correction aften yields acceptable results so long as the vertical velocity gradient is reasonably small and does not change rapidly in depth. The constant-velocity DMO correction also has the bonus effect of attenuating coherent linear noise as demonstrated in the next section.


  1. Hale and Artley (1992), Hale, D. and Artley, C., 1992, Squeezing dip-moveout for depth-variable velocity: Geophysics, 58, 257–264.
  2. Artley and Hale (1994), Artley, C. and Hale, D., 1994, Dip-moveout processing for depth-variable velocity: Geophysics, 59, 610–622.

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Variable velocity
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