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Consider a model with a dipping waterbottom in 2D. The raypath of the primary
reflection can be easily computed using the concept of the image source
as illustrated in Figure .
rayprim
Figure 1 Construction of the primary
reflection from a dipping interface.

 
The moveout of the primary reflection in the CMP domain is given by:
 
(1) 
where t_{p} is the time of the primary, is the dip angle of the
reflector, Z_{D} is the
perpendicular distance between the surface and the reflector at the CMP location,
h_{D} is half the sourcereceiver offset, V is the propagation velocity
above the dipping reflector, is the normal moveout velocity
and t_{0} is the traveltime of the zerooffset reflection. This is obviously
the equation of a hyperbola, as illustrated in Figure .
The raypath of the multiple reflection can be considered as a cascaded of two
primary reflections as SRME methods do
(Figure ), but the
traveltime of the multiple, t_{m}, can be computed more easily as the traveltime of
an equivalent primary from a reflector dipping at twice the dip angle of the
actual reflector as illustrated in Figure . That is,
 
(2) 
where is the perpendicular distance between the surface and the
equivalent reflector with twice the dip at the CMP location and
is now . Figure corresponds to a CMP showing
the primary and the multiple reflection. Obviously, they are both hyperbolas
since the multiple has the same kinematics as a primary from a reflector
dipping at twice the dip as indicated above.
raymul1
Figure 2 Decomposition of the waterbottom
multiple as a cascaded of two primary reflections.

 
raymul2
Figure 3 Multiple reflection as a primary
from an equivalent reflector with twice the dip angle.

 
moveouts1
Figure 4 Moveout curves of primary and
waterbottom multiple from a dipping interface on a CMP gather.

 
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Stanford Exploration Project
5/3/2005