The need for DMO

The need for Dip Moveout appeared from the problem of stacking traces that share the same Common-Mid-Point (CMP). Figure shows the geometry of a CMP section over a flat layer. In a CMP section, traces are sorted so they share the same mid-point for different locations of the source and receiver. In this configuration when only flat layers are present, the reflections come from a single point situated under the CMP.

 

CMPgeonodips Figure 1 Geometry for CMP gather over a flat layer.

Figure depicts the geometry of a CMP section over a dipping layer. In this case the reflections do not come from the same point, but are moving updip as the offset between source and receiver increases.

The CMP Stacking assumes that reflections come from horizontal layers. Under this assumption the Normal Moveout correction (NMO) flattens the hyperbolas in a CMP gather to horizontal lines. After NMO, traces belonging to the same CMP are summed together (stacked) to enhance the reflected signal and to attenuate the noise.

 

CMPgeodips Figure 2 Geometry for CMP gather over a dipping layer.

Problems appear when multiple dipping events are present in a section. If we combine Figures and for multiple CMPs we obtain Figure a. In Figure a we combine the geometry in Figures and for multiple Common-Mid-Points. Each hyperbola corresponds to a CMP section over a dipping layer and a flat layer. As the CMP moves updip, the hyperbolas corresponding to the dipping layer appear closer to the surface while the ones corresponding to the flat layer are unchanged.

A dipping reflector in a CMP section (see Figure a) produces a reflection hyperbola as it will be proven later. The NMO velocity necessary to flatten the hyperbolas originating from reflections on the dipping layer is higher than the real velocity.

Figure a shows several CMP gathers containing reflections from a dipping layer and from a horizontal layer. After NMO with the real velocity the hyperbolas corresponding to the flat layer become straight lines (Figure b) and after stacking (Figure c), the horizontal event is preserved at the expense of the dipping event. In Figure b NMO is performed with a higher velocity which is necessary to flatten the hyperbolas corresponding to the dipping event. After stacking (Figure c) the dipping event is preserved at the expense of the horizontal layer. It is obvious that the NMO correction with a single velocity combined with CMP stacking acts as a dip filter. The result is a degradation of the final image when conflicting dips are present.

 

CMPnmoEx1
Figure 3 The effect of CMP stacking with real velocity on dipping reflectors.
a. Several CMP gathers for a flat layer and a dipping layer.
b. The CMP gathers after NMO with medium velocity (v_real); the hyperbolas from the horizontal event are flattened.
c. Traces after stacking for the same CMP.

 

CMPnmoEx2
Figure 4 The effect of CMP stacking with velocity $(v_{nmo}= {v_{real} / {\cos \theta}})$ on horizontal reflectors.
a. Several CMP gathers for a flat layer and a dipping layer.
b. The CMP gathers after NMO with higher velocity; the hyperbolas from the dipping event are flattened.
c. Traces after stacking for the same CMP.