Adjoint Kirchhoff operator

For practical realization of this iterative inversion scheme we have to find the explicit expressions for the adjoint Kirchhoff operator K according to formula... 

From the last formula we conclude that the adjoint KirchhofF operator K is given by the formula... 

Therefore, the auxiliary field (r,f ) is the back-propagated field, and the adjoint Kirchhoff operator K for a residual field can be calculated by back propagation of the residual field. We will show in the next sections that this procedure is similar to Stolt s Fourier-based migration transformation. Thus, this result demonstrates that migration is similar to applying an adjoint Kirchhoff operator to observed scattered wavefield data. 

In the general case of an iterative inversion scheme (15.135), we should apply the adjoint Kirchhoff operator K to the residual field Rn = K(A ) — da computed on each iteration. Each of these applications is equivalent to the standard migration of the residual field. Thus, iterative Kirchhoff inversion can be treated as an iterative migration algorithm,... 

In the section of this chapter describing the Kirchhoff inversion method and general non-linear inversion techniques, we have demonstrated that the calculation of the Kirchhoff adjoint operator (15.142) and the adjoint Frechet derivative operator... 

---

See also in sourсe #XX -- [ ]

---