Waveform inversion

Direct waveform Inversion

Our group have come up with a new method for waveform inversion. We call it Direct Waveform Inversion (DWI). The 'Direct' means that it is not 'iterative' scheme based on perturbation theory. See our 2015 SEG paper: Direct waveform inversion (DWI) by Liu and Zheng. Some unique features about the algorithm is: unconditionally convergent; no local-minima issue; recursive; weak initial model dependence. Let me know if you want to collaborate on this method.

Summation of divergent series

In traditional seismic waveform inversion, people use Frechet derivative (1st order functional derivative of the data change wrt the model change) and sometimes include the 2nd term, the Hessian. We showed in a GJI paper that n-th order Frechet derivative one-to-one corresponds to n-th order scattering. If we ignore all higher order terms in the inversion, that is to say we ignore all (2nd, 3rd, 4th, ...) scattering terms. We are developing new inversion algorithm which uses all terms. One significant challenge we have is that when the initial model is far from the true model, adding more terms can lead to divergence in the summation. We have found a new way to 'tame' this divergence issue and we are able to make the divergent series into a convergent one, which also converges to the correct value. Stay tuned for our publication on this matter !