On the Inverse Problem of Seismic Imaging: A Mathematical View on Full Waveform Inversion

Time-domain full waveform inversion (FWI) is the up-to-date geophysical imaging technique being capable to exploit the full information content of recorded seismic waves which have been excited locally by controlled sources or globally by earthquakes. Mathematically, FWI entails a parameter identification task for the underlying wave propagation model.
 
In this talk I will first model wave propagation in dispersive media by the viscoelastic wave equation and introduce the resulting nonlinear and ill-posed inverse problem. Further, I will shortly present some of the research on the Mathematics of FWI done within our Collaborative Research Center “Wave Phenomena”. In the second part of the talk we will have a closer look to FWI in the acoustic regime. Here, we validate the tangential cone condition (TCC) for the corresponding parameter-to-state map in a semi-discrete setting where the searched-for parameters are restricted to a finite dimensional space. The TCC is an important ingredient in the convergence analysis of a variety of inversion algorithms for nonlinear ill-posed problems, such as FWI.