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In the real life, the source is not impulsive.
In addition, multiples are computed directly from the
data and not from the primary wavefield. Hence, the relative amplitude
of first order multiples with respect to higher order multiples is not
preserved. To illustrate this last point, consider the surfacerelated multiple
modeling equation Verschuur et al. (1992)

u_{r} = u_{0}  W^{1} u_{m},

(18) 
where u_{r} is the recorded wavefield at the surface,
W the source wavelet, and u_{m} the multiple wavefield given by
 
(19) 
 
 (20) 
where represents the nonstationary convolution and u_{i} the ith
order multiples. If we use equation (16), replacing
u_{0} by u_{r}, we obtain for the approximated multiple field
 
(21) 
Comparing equation (33) and equation (34), we
notice that higher order multiples in equation (34) are multiplied by
a coefficient that is difficult to correct for. Therefore higher order
multiples have the correct kinematics, but the wrong
amplitudes. Hence, our modeling scheme explicitely overpredict highorder
multiples (amplitude wise) but models them with the correct pattern.
Next: Appendix B
Up: Surfacerelated multiple prediction theory
Previous: Twodimensional earth
Stanford Exploration Project
4/29/2001