The Kirchhoff approximation provides a representation of seismic data as a
summation of imaged data along isochron surfaces (demigration). The asympto
tic inversion of this representation provides a migration as a summation of
seismic data along diffraction surfaces. We replace Born inversion techniq
ues with Kirchhoff inversion techniques and further show the link between t
he Kirchhoff and Born representations after the Born linearized reflection
coefficient is replaced by the Kirchhoff reflection coefficient.