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## The NMO velocity

Figure shows a dipping reflector and the position of the source, geophone and CMP. The constant-offset traveltime from the source at point A to the receiver at point B is represented by the segments AR+RB. The zero-offset traveltime from the CMP to the reflector and back is given by the segment FG. The dipping reflector serves as the axis of symmetry for the figure.

dmofig1
Figure 3
A dipping reflector in a constant velocity medium. The dipping angle is . The raypath from the source to the receiver is sketched by the segments AR and RB. The zero-offset raypath is equal to the segment FG.

For the geometry in Figure we have

where v is the velocity of the medium and th is the shot-receiver traveltime. The segment FG (which has the length of the zero-offset raypath) is equal to the segment AE. From Figure

From the triangle we have
 (1)
where is the angle of the dipping reflector and 2h is the distance between source and receiver. Finally, by dividing the segments with the velocity we have the zero-offset traveltime from the CMP to the reflector:
 (2)

From equation (2) we easily see that the expression for th is a hyperbola, with the top at t0. The NMO velocity necessary to flatten the hyperbola for a dipping reflector is
 (3)

Next: DMO and NMO Up: Introduction Previous: The need for DMO
Stanford Exploration Project
11/18/1997