The theory of wave extrapolation is based on the square‐root equation or one‐way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square‐root equation represents waves propagating in one direction only.

A 3D inversion based Least-Squares Reverse Time Migration (LSRTM) technique was developed. The algorithm uses the RTM as the forward modeling and inversion engine to minimize the amplitude differences between the observed data and the synthetic modeled data. In turn, the final LSRTM will deliver the reflectivity model that will generate the true corresponding amplitude; the migration artifacts are suppressed as well since they are not contained in the observed field data. Compared with the initial RTM image, the LSRTM images from the synthetic data and field data examples show the improved amplitude response and higher resolution gained by suppressing migration artifacts and sharpening the subsurface reflectors' reflectivity.

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In this abstract, we describe how to improve time domain full waveform inversion using source wavelet convolution, windowed back propagation and source side illumination. Instead of estimating the source wavelet from field data, a user defined source wavelet can be convolved to field data. This convolution makes waveform matching between modeled and field data easier. Increasing time window applied to residual enables top down velocity update and reduces the possibility of being stuck at a local minimum. The balance of gradient value can be improved by the illumination compensation using the square of source side wavefield. Well balanced gradient helps FWI restore the absolute value of velocity. We apply this method to estimate migration velocities using 2D and 3D synthetic and real data examples.