Plane waves in three dimensions

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.

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.

Plane waves in three dimensions