sfiwarp performs mapping between different coordinates.

If you have sampled functions $f(x)$ and $y(x)$, sfiwarp with inv=y (the default) finds sampled $f(y)$. If inv=n, sfiwarp takes $f(y)$ and $y(x)$ and finds $f(x)$. In both cases, the sampled $y(x)$ function is supplied in a file specified by warp= parameter. The following example from milano/taupvel/cmp shows a seismic taup-p gather flattening by predictive painting and time warping.

Coordinate mapping is a fundamental data-transformation operation, which finds many applications. The term warping comes from medical imaging. See, for example,

• Wolberg, G., 1990, Digital image warping: IEEE Computer Society Press.
• W. Burnett and S. Fomel, 2009, Moveout analysis by time-warping: 79th Annual International Meeting, SEG, 3710-3714.

The algorithm used in sfiwarp is B-spline interpolation and inverse spline interpolation. If forward warping (inv=n) is ${\mathbf{f}}_x=\mathbf{B}{\mathbf{f}}_y$, then the inverse transformation (inv=y) is given by the regularized least-squares inverse
$${\mathbf{f}}_y={({\mathbf{B}}^T\mathbf{B}+{ϵ}^2\mathbf{D})}^{-1}{\mathbf{B}}^T{\mathbf{f}}_x,$$ where $\mathbf{D}$ is the derivative operator. The $ϵ$ parameter is supplied by eps=. The sampling in $y$ is supplied by n1=, d1=, o1= parameters.

For 2-D and 3-D versions, try sfiwarp2 and sfiwarp3.

10 previous programs of the month

• sfpick
• sffft3
• sfdip
• sfderiv
• sfgrey3
• sfspectra
• sfnoise
• sfgraph
• sfclip
• sfagc