** Next:** Migration and shot illumination
** Up:** \begin>tex2html_wrap_inline>$V(x,y,z)$\end>tex2html_wrap_inline>\space and non-stationary inverse
** Previous:** Numerical examples

The helical factorization scheme outlined in
Chapter can
be extended to deal with non-stationarity by replacing stationary
convolution and inverse convolution with their non-stationary
counterparts. I factorize non-stationary filters by making an
assumption of local stationarity. Although this is only strictly
valid for smoothly-varying media, is has the advantage that for a
fixed number of filter coefficients the cost remains linear in the
number of grid nodes.
Since I factorize the entire implicit system, it is difficult to
ensure that the extrapolator embedded inside has the non-negative
definite property necessary for unconditional stability.
Unfortunately, this means the helical factorization is not robust to
the presence of strong lateral velocity variations in the model, and
the solution may diverge.

** Next:** Migration and shot illumination
** Up:** \begin>tex2html_wrap_inline>$V(x,y,z)$\end>tex2html_wrap_inline>\space and non-stationary inverse
** Previous:** Numerical examples
Stanford Exploration Project

5/27/2001