sfnmo implements normal moveout (NMO) correction, one of the most fundamental operations in seismic reflection data processing.

The following example from jsg/avo/avo shows synthetic data before and after NMO correction.

NMO transforms prestack seismic gathers by stretching each trace according to the equation

$$t = \sqrt{t_0^2 + \frac{x^2}{v^2(t_0)}}\;,$$

where $t$ is time before the correction, $t_0$ is time after the correction, $x$ is offset, and $v(t_0)$ is velocity specified in **velocity=** file. The NMO velocity can be picked (for example, with sfpick) from velocity scans (for example, produced with sfvscan).

If **s=** file is provided, **sfnmo** uses Malovichko’s shifted-hyperbola approximation

$$t \approx \left(1-\frac{1}{s(t_0)}\right) + \frac{1}{s(t_0)}\,\sqrt{t_0^2 + s(t_0)\,\frac{x^2}{v^2(t_0)}}$$

See

- Malovichko, A. A., 1978, A new representation of the traveltime curve of reflected waves in horizontally layered media: Applied Geophysics (in Russian), 91, 47-53
- Sword, C. H., 1987, A Soviet look at datum shift, in SEP-51: Stanford Exploration Project, 313-316.
- de Bazelaire, E., 1988, Normal moveout revisited – Inhomogeneous media and curved interfaces: Geophysics, 53, 143-157.
- Castle, R. J., 1994, Theory of normal moveout: Geophysics, 59, 983-999.

If **a=** file is provided, **sfnmo** uses Taner’s velocity-acceleration approximation

$$t = \sqrt{t_0^2 + \frac{x^2}{v^2(t_0)+a(t_0)\,x^2}}$$

See

- Taner, M. T., S. Treitel, and M. Al-Chalabi, 2005, A new travel time estimation method for horizontal strata: 75th Ann. Internat. Mtg, Soc. of Expl. Geophys., 2273-2276.
- Taner, M. T., S. Treitel, M. Al-Chalabi, and S. Fomel, 2007, An offset dependent NMO velocity model: EAGE 69th Conference and Exhibition, EAGE, P036.

The offset $x$ can be either regular (specified as the second axis in the input file) or irregular (specified in **offset=** file). By default, half-offset is used $h=x/2$. To use full offset, specify **half=n**.

Additionally, it is possible to specify a mask (with **mask=** file containing 1s and 0s) for skipping certain traces during the correction. See the following example from rsf/scons/rsf

The NMO correction is associated with the phenomenon of “NMO stretch”, a non-linear stretching of time at large offsets. The maximum allowed relative stretch is controlled by **str=** parameter. The part of the data that is stretched more than the allowed stretch gets muted. The width of the mute zone is controlled by **mute=** parameter.

NMO with constant velocity can be accomplished with sfnmostretch. For 3-D azimuthally-anisotropic moveout correction, try sfnmo3. For NMO in the tau-p domain, try sftaupmo. For an inverse NMO operation, try sfnimo.

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