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Regularization of the Least-Squares Problem

In this section, three discriminants between crosstalk and signal are exploited to devise model regularization operators which ``guide'' the final model toward the one with the peglegs best separated from the data.
1.
Inconsistency with multiple order - After imaging, corresponding crosstalk events on two model panels have different residual moveout, e.g. residual first-order multiples on $\bold m_0$ and residual second-order multiples on $\bold m_{1,k}$. The moveout difference is negligible at near offsets, but larger than the Fresnel Zone (half a wavelength) at long offsets. Conversely, actual signal events are flat on all the $\bold m_{i,k}$. Conclusion: For fixed (t,x), the difference between one model panel and another will be relatively small where there is signal, but large where there is crosstalk noise, especially at far offsets.
2.
Curvature with offset - After imaging, signal events are flat, while crosstalk events have at least some residual curvature, especially at far offsets and in regions with a strong velocity gradient. Conclusion: Provided that the AVO response of the signal changes slowly with offset, the difference (in x) between adjacent samples of any $\bold m_{i,k}$ will be relatively small where there is signal, but large where there is crosstalk noise.
3.
Predictability of ``pre-seabed multiple'' events - The third discriminant exploits the inherent predictability of crosstalk to suppress it. Between the seabed reflection and the onset of its first multiple, the recorded data contains only primaries (inter-bed multiples and locally-converted shear waves are generally weak); these strong events spawn the (usually) most troublesome crosstalk events. Fortunately, the pre-seabed-mutiple primaries can be used to directly construct a prior model of the crosstalk noise, valid even at near offsets. Conclusion: Given an accurate kinematic model of crosstalk noise, a corresponding set of model-space weights used in a model regularization term penalizes crosstalk events but not signal.


 
next up previous print clean
Next: Model Regularization 1: Differencing Up: Brown: LSJIMP field data Previous: Consistency of the Data
Stanford Exploration Project
7/8/2003