Linearized Extended Waveform Inversion

The extended model concept links migration velocity analysis and waveform inversion. This abstract presents a method to solve a partially linearized version of the full waveform inversion problem with model extension. Linearization separates the model of the earth into the smooth long scale background model and the short scale model. Extended waveform inversion allows the short scale model to depend on an extra parameter, for example the shot coordinates. The objective function is the least squares misfit function of Born modeling, plus a differential semblance term. Minimization over the short scale model (a quadratic problem) by an iterative method results in a smooth objective function over the background model. Computation of objective values from Marmousi model with acoustic constant density modeling illustrate the smoothness and unimodality of the objective, for proper choice of parameters.