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Consistency of the Data and the Crosstalk Problem

Our hope is that, after solving equation (3) for the unknown model, $\bold m_0$ contains only primaries (and other non-pegleg events) and the $\bold m_{i,k}$ contain only peglegs. Unfortunately, simple least-squares minimization of the data residual (4) proves insufficient to properly segregate the various modes. Nemeth et al. (1999) pins the problem on operator ``overlap'', or coincident operator range. In this application, operator overlap is most troublesome at near offsets, where primaries and multiples are both flat. If (for instance) $\bold m_0$ contains residual first-order pegleg multiple energy, equation (1) will map this energy back into data space, at the position of a first-order multiple at near offsets. The residual multiple energy is called ``crosstalk'' Claerbout (1992). Luckily, Nemeth et al. show that that properly designed model regularization operators can at least partially mitigate the crosstalk problem.
next up previous print clean
Next: Regularization of the Least-Squares Up: Least-Squares Joint Imaging of Previous: Nemeth Forward Model
Stanford Exploration Project
7/8/2003