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In this Appendix I derive equations 3945.
mul_sktch9
Figure 21 Sketch to show the computation
of t_{s1} and t_{s2} for a nondiffracted multiple from a dipping
waterbottom.

 
From triangle ABC in Figure
we immediately get
 
(57) 
and applying the law of sines to triangle ACD we get
 
(58) 
mul_sktch10
Figure 22 Sketch to show the computation
of t_{r2} and t_{r1} for a nondiffracted multiple from a dipping
waterbottom.

 
Similarly, repeated application of the law of sines to triangles CDE and DEF
in Figure gives
 
(59) 
 (60) 
mul_sktch11
Figure 23 Sketch to show the computation
of in equation 61.

 
These equations are in terms of , which is not known. However,
from Figure we see that
 
(61) 
and can be computed from the traveltime of the zero
surfaceoffset trace, since, according to Figure
 
(62) 
from which it follows immediately that
 
(63) 
mul_sktch12
Figure 24 Sketch to show the computation
of in equation 63.

 
Finally, we need to compute . Applying the law of sines to
triangle ABC in Figure we get
 
(64) 
from which we get
 
(65) 
mul_sktch16
Figure 25 Sketch to compute
the takeoff angle of the source ray from a nondiffracted multiple
from a dipping waterbottom.

 
D
Next: From dip to no
Up: Alvarez: Multiples in image
Previous: Computation of Image Depth
Stanford Exploration Project
11/1/2005