FWI with wave equation migration: well validation vs data validation vs well-and-data validation

Sergio J. Romahn, Kristopher A. Innanen

Conventional acoustic full waveform inversion (FWI) involves the crosscorrelation of the back-propagated data residuals with the forward-propagated source to produce the gradient. This process can be seen as the reverse time migration (RTM) of the data residuals. The gradient then is scaled to create a velocity perturbation. This step is achieved by applying a line search of the step length in a typical gradient descent scheme. We used PSPI, a wave equation migration method, to obtain the gradient, and we compared three different ways to produce the velocity perturbation. Firstly, we used a line-search method to scale the gradient, a process called data validation. Secondly, we applied well calibration, a technique that is called well validation. Finally, we used a combination of well and data validation. We applied these techniques to two different models, one with moderate lateral velocity changes, and the other one to the more complex Marmousi model. For a simple geological setting the three techniques provided similar results. Well and data validation produced the best result in the presence of more complex geological settings.