Vector wavefield separation

Let us assume now that the propagation of seismic waves in the earth can be described by the vector wave equation which, according to (13.35), can be written in the frequency domain as 

We represent the distribution of velocity in the model in the same way as we did for the acoustic wave equation  

Similar to the acoustic field, the total vector wavefield in the model described above can be represented as a sum of two parts, the incident (background) field u (r, w) and the scattered (anomalous) field u (r,C( ), 

The incident field u (r,w) is the solution of the Helmholtz equation with the background velocity distribution  

Both the incident and the scattered fields satisfy the corresponding radiation conditions at infinity. 

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I For conciseness, the sccilar acoustic and vector wavefield equations have been combined into single equations in this summary, with alternative subscripts a and v to distinguish them it is understood, of course, that d , A , and Rv n (but not the adjoint operator F. ), would be printed in boldface in separate vector wavefield equations since they refer to 3-D vector elements in... 

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