(1) There exists a paradox: linearized migration/inversion requires that the background velocity is as close as possible to the true velocity distribution; however the Born approximation needs a very smooth background velocity, so that the incident wavefield only includes downward propagating waves. The Born approximation is not a good linearization method and it should be replaced by more accurate approximations, such as De Wolf approximation.

(2) In essence, non-iterative linearized migration/inversion, iterative linearized migration/inversion, and nonlinear waveform inversion, are all inverse scattering imaging methods.

(3) Relative true-amplitude imaging is possible, the condition is that the distribution of the Fourier transform of the object function on is even, and the range of the distribution is the same at every imaging point (or scattering point).

(4) The Hessian matrix is band-limited and its inverse is also band-limited, its inner structure has close relation with the complexity of the velocity and the acquisition geometry. It reflects the energy illuminating imaging points.

11/1/2005