The traveltime surface of a point diffractor in offset space where raypaths are straight and the source and receiver are not coincident; see Figure D-20b.
Figure
D-20.
DMO. (a) Depth section showing the updip movement of the reflecting point for an offset geophone for constant velocity; Δ=(
h2/
D)cosξsinξ, where ξ is the dip (Levin, 1971)
[1]. To avoid reflection point smearing, an offset trace should be gathered with the updip zero-offset trace at a distance G=(–
h2/
D)sinξ, but such a gather is not hyperbolic; the DMO correction makes this gather hyperbolic.
(b) A diffraction in location-offset space, a
Cheops pyramid, is not a hyperboloid.
(c) Applying NMO changes the Cheops pyramid into a saddle-shaped surface.
(d) Applying DMO along with NMO yields data that can be stacked without reflection-point smear.
(e) NMO corrects for the time delay on an offset trace assuming horizontality, DMO moves the data to the correct zero-offset trace for a dipping reflection, and migration further moves it to its subsurface location. (After Deregowski, 1986)
[2]
If x=midpoint location and y=offset (source-geophone distance), it is the surface t(x,y)
,
where m=inline distance from diffracting point to the midpoint and h its depth. The surface is called a Cheops pyramid (ke’ ops). This equation contrasts with the hyperbolic single-square-root equation for a zero-offset (CMP) section,
.
DMO processing transforms a Cheops pyramid so that a cylindrical hyperbola (see Figure D-20d) is obtained after normal moveout correction with the correct velocity. After a transformation y=Ut that constitutes slicing the pyramid by radial planes containing the x-axis, NMO can be applied correctly.
References
- ↑ Levin, F. K., 1971, Apparent velocity from dipping interface reflections: Geophysics, 36: 510–516.
- ↑ Deregowski, S. M., 1986, What is DMO: First Break, 4, No. 7, 7–24.
External links
find literature about
Double-square-root equation
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