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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 5 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 *t*_{h} 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
2*h* 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 *t*_{h} is a hyperbola, with the
top at *t*_{0}. 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

11/17/1997