With the development of the helical coordinate system Claerbout (1998b), recursive inverse filtering is now practical in multi-dimensional space. Non-stationary, or adaptive Widrow and Stearns (1985), recursive filtering is now becoming an important tool for preconditioning a range of geophysical estimation (inversion) problems Clapp et al. (1997); Crawley (1999); Fomel et al. (1997), and enabling 3-D depth migration with a new breed of wavefield extrapolation algorithms Fomel and Claerbout (1997); Rickett et al. (1998); Rickett and Claerbout (1998).

With these applications in mind, it is important to understand fully the properties of non-stationary filtering and inverse-filtering. Of particular concern is the stability of the non-stationary operators.

10/25/1999