Present know-how and difficulties in elastic nonlinear inversion of seismograms

The simplest formulation of the seismic inverse problem is to find the Earth and source models predicting the best synthetic seismograms. This problem has to be solved iteratively, each iteration reducing the residual seismograms. The physical properties of the subsurface that are most significant for interpreting seismic data are the background velocities and the impedance contrasts. They can be inferred in different wavelength bands (long wavelengths of velocities, short wavelengths of impedances) with almost no overlapping. • A proper formulation of the inverse problem allows a much better understanding of the problem of interpretation of seismograms, and naturally allows, in particular, extracting amplitude versus offset information. But inverse theory has not lead to the discovery of any new algorithm: inversion algorithms are closely related to migration or velocity analysis algorithms. • Nonlinear inversion has built-in capability of interpreting all sort of waves: direct, reflected, refracted, multiply reflected,... But as our present know-how in forward modeling is not good enough to model all those waves accurately, we still need to "mute" some of them. • As the inverse problem is strongly nonlinear, estimation of uncertainties in the solution could only be made using Monte Carlo techniques, but this exceeds present-day computer hardware capabilities. In spite of this difficulties, the results so far obtained show that full waveform inversion is no more a laboratory curiosity. In our talk we will try to make a fair comparison between cost and quality of results obtained from inversion and from more conventional "migration" techniques.