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## Limitations of the multiple prediction using real data

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 surface-related multiple modeling equation Verschuur et al. (1992)

 ur = u0 - W-1 um, (18)

where ur is the recorded wavefield at the surface, W the source wavelet, and um the multiple wavefield given by
 (19) (20)
where represents the nonstationary convolution and ui the i-th order multiples. If we use equation (16), replacing u0 by ur, 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 high-order multiples (amplitude wise) but models them with the correct pattern.

Next: Appendix B Up: Surface-related multiple prediction theory Previous: Two-dimensional earth
Stanford Exploration Project
4/29/2001