Plane waves in three dimensions

  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.