Many times we simply deform or stretch a wave field or a map.
A curious mapping I once made was a transformation of world topography
(including ocean depth).
**Great circles**
play an important role in global surface-wave propagation
because waves travel on the great circles.
In my transformed map, the great circle from Stanford University to the east
is plotted as an equator on a Mercator projection.
North at Stanford is plotted vertically as usual.
Figure 2 shows it.

Figure 2

Deformations can either stretch or shrink or both, and different practical problems arise in each of these cases.

- Nearest-neighbor interpolation
- A family of nearest-neighbor interpolations
- Formal inversion
- Nearest-neighbor NMO
- Stack
- Pseudoinverse to nearest-neighbor NMO
- Null space and inconsistency
- NMO with linear interpolation

10/21/1998