Full waveform inversion (FWI) is a machine learning algorithm with the goal to ﬁnd the Earth’s model parameters that minimize the difference of acquired and synthetic shots. We did a simulation of the methodology on 2D data at the Marmousi model. This report is divided in two parts. On the ﬁrst part, we applied a band-limited impedance inversion on the migrated residuals to estimate a gradient cheaper and leading to a with higher resolution at deeper areas and more continuity of the geologic features when compared to previous works. On the second part, we introduce a new interpretation of the gradient as a residual impedance inversion of the acquired data. Its estimation is forward modeling and wavelet free, reducing its costs drastically, as the inverted model was obtained on a personal laptop without parallel processing. The new method was successfully applied on the acoustic Marmousi simulation. The inverted model, when using the same starting point, is comparable to the results of using the migrated residuals. A preliminarily test was done by inversion the order of migration and stack and using a post-stack depth migration to estimate the gradient with promising outputs. In the end, we are proposing a new FWI approximation that is cheap and stable and could be used on real data in the same processing center that has enough computer power to run a PSDM or even just a post-stack depth migration.
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