There are other ways to achieve a continuous, monotonic flattening result. Smoothing the input dip in depth can achieve similar results. Alternatively, the method that we use to apply the time-shifts can, in principle, be modified so that it is constrained to preserve the relative data order.
The regularized analytical method can be used to find a smooth solution but it cannot fill in missing data. One of the main benefits of regularization is the ability to fill missing data. This requires a weight matrix or mask to discern known data from unknown data. Unfortunately, this weight matrix is singular and the analytical solution would require us to know its inverse. Therefore, in the case of regions of unknown dip, it is necessary to abandon the analytical method and solve the flattening problem in the time domain.