Concepts in the Direct Waveform Inversion (DWI) Using Explicit Time-Space Causality

The Direct Waveform Inversion (DWI) is a recently proposed waveform inversion idea that has the potential to simultaneously address several existing challenges in many full waveform inversion (FWI) schemes. A key ingredient in DWI is the explicit use of the time-space causality property of the wavefield in the inversion which allows us to convert the global nonlinear optimization problem in FWI, without information loss, into local linear inversions that can be readily solved. DWI is a recursive scheme which sequentially inverts for the subsurface model in a shallow-to-deep fashion. Therefore, there is no need for a global initial velocity model to implement DWI. DWI is unconditionally convergent when the reflection traveltime from the boundary of inverted model is beyond the finite recording time in seismic data. In order for DWI to work, DWI must use the full seismic wavefield including interbed and free surface multiples and it combines seismic migration and velocity model inversion into one process. We illustrate the concepts in DWI using 1D and 2D models.