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Plane waves in three dimensions

Jon Claerbout


In this chapter we seek a deeper understanding of plane waves in three dimensions, where the examples and theory typically refer to functions of time $ t$ and two space coordinates $ (x,y)$ , or to 3-D migration images where the $ t$ coordinate is depth or traveltime depth. As in Chapter [*], we need to decompose data volumes into subcubes, shown in Figure 1.

rayab3D
Figure 1.
Left is space of inputs and outputs. Right is their separation during analysis.
rayab3D
[pdf] [png] [xfig]

In this chapter we will see that the wave model implies the 3-D whitener is not a cube filter but two planar filters. The wave model allows us to determine the scale factor of a signal, even where signals fluctuate in strength because of interference. Finally, we examine the local-monoplane concept that uses the superposition principle to distinguish a sedimentary model cube from a data cube.




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Next: THE LEVELER: A VOLUME Up: Reproducible Documents

2013-07-27