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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. In that, a model of the
multiples is obtained by convolving the recorded data with primaries
and multiples as opposed to the primaries only. 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},

(151) 
where u_{r} is the recorded wavefield at the surface with primaries
and surfacerelated multiples, W the source wavelet, and
u_{m} the surfacerelated multiple wavefield given by
 
(152) 
 
 (153) 
where represents the nonstationary convolution and u_{i} the ith
order multiples. If we use equation (), replacing
u_{0} by u_{r}, we obtain for the approximated multiple field
 
(154) 
Comparing equation () and equation (), we
notice that higher order multiples in equation () are multiplied by
a coefficient that is difficult to correct for. Therefore higher order
multiples have the correct kinematics, but the wrong
amplitudes Hugonnet (2002); Wang and Levin (1994).
Hence, the modeling scheme that consists in convolving the shot
gathers only once explicitely overpredict highorder
multiples (amplitude wise) but models them with the correct
pattern. As shown by Berkhout and Verschuur (1997) and Verschuur and Berkhout (1997), this
single convolution can be interpreted as a first iteration of the recursive formulation
of SRME.
Next: REFERENCES
Up: A surfacerelated multiple prediction
Previous: 2 and 3D earth
Stanford Exploration Project
5/5/2005