Regularization of the LSJIMP Problem  

In Sections -, I exploit three discriminants between crosstalk and signal to devise model regularization operators. The raw LSJIMP minimization [equation (5)] suffers from non-uniqueness. The model regularization operators choose the particular set of primary and multiple images which are optimally free of crosstalk, from an infinite number of possible combinations. Moreover, these operators exploit signal multiplicity-within and between images-to increase signal fidelity and fill illumination gaps/missing traces. Some existing regularized least-squares prestack migration schemes exploit signal multiplicity across reflection angle (, , ). LSJIMP's additional use of multiples to regularize the least-squares imaging problem is novel.

As mentioned in the previous section, my particular implementation of LSJIMP processes each CMP location independently. Therefore, without loss of generality, the regularization terms described in the following sections assume that the prestack multiple images, $\bold m_{i,k,m}$, are functions of zero-offset traveltime ($\tau$) and offset (x), but not of midpoint. The same logic applies to an image parameterized by depth and reflection angle.