The feasibility of multidimensional deconvolution, proven by the helix transform, allows us to revisit the problem of implicit wavefield extrapolation in three dimensions. The attraction of implicit finite-difference methods lies in their unconditional stability, a property invaluable for practical applications.
We have shown that at least in the constant coefficient case (that is, laterally invariant velocity), it is possible to implement an extremely efficient implicit extrapolation by a recursive inverse filtering in the helix-transformed computational model. Unfortunately, the case of lateral velocity variations still presents a difficult problem that may not have an exact solution. We are currently exploring different roads to that goal.