Fold preconditioning

To accelerate the convergence of the iterative solution, we precondition the inversion by the binning fold of the data Chemingui and Biondi (1996b). This is equivalent to a post-multiplication of the matrix L by a diagonal matrix C^-1.

The preconditioning operator introduces a new model x given by

$$x = C m \EQNLABEL{prec}$$ (7)

By the preconditioning transformation, we have recast the original inversion relation equ1 into

$$d = LC^{-1}x \EQNLABEL{prec}$$ (8)

The fold normalization is an approximate solution to the column-scaling preconditioning Ronen (1994), which is a normalization by the coverage after AMO.