How DMO works

The goal of the $NMO \cdot DMO$ processing step is to transform a constant-offset section into a zero-offset section. We can conceive any structure (or depth model) as composed of independent diffractors. This is the commonplace assumption for Kirchhoff migration. By summing the contributions from all the diffractors we can obtain our constant-offset section. Following this hypothesis it is interesting to examine the behavior of a single diffraction curve in constant-offset. Figure shows a constant-offset diffraction curve together with a zero-offset diffraction curve which is actually a hyperbola. The aim of the $NMO \cdot DMO$ step is to transform the former into the latter.

 

cozo Figure 6 Zero-offset hyperbola and the constant-offset diffraction curve.

Figure shows the kinematics of the $DMO \cdot NMO$operator; each point along the constant-offset diffraction curve is spread along an operator similar to the one shown in Figure and using equation (8). The result of this operation is displayed on the right side in Figure . The artifacts at the top of the figure are due to the constant amplitude assigned along the DMO curve. In reality the amplitude along the DMO curve is tapered toward the end of the operator, as will be shown in the next chapters.

 

codmo
Figure 7 $NMO \cdot DMO$ transforms a constant-offset diffraction curve to a zero-offset hyperbola.
(LEFT) $NMO \cdot DMO$ kinematics; each point on the constant-offset diffraction curve is spread along the DMO curve and shifted with the NMO correction.
(RIGHT) The result of applying $NMO \cdot DMO$ to the constant-offset hyperbola. The artifacts are due to using a constant amplitude along the DMO curve.