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Log-validated waveform inversion of reflection seismic data with wavelet phase and amplitude updating

We have formulated an inversion approach for near-offset seismic reflection data based on full-waveform inversion (FWI) workflows, in which an element of standard seismic processing takes the place of each of the fundamental components of FWI. A motivation for using reflections in FWI is trying to update the model in deep zones in which the diving waves could not penetrate due to the large-offset limitation. The workflow is an iterative cycle of simulation, depth migration, and impedance inversion, and it is an outgrowth of an approach referred to as iterative modeling, migration, and inversion. Two-way wave operators (similar to those used in reverse time migration), which are part of the gradient calculation, are replaced with one-way wave operators; pseudo-Hessian preconditioning of the gradient is replaced with a deconvolution imaging condition; and well-log information to calibrate the update direction (i.e., model validation) replaces the standard line search (i.e., data validation). For land data applications, variations in the source wavelet are anticipated to be a large issue. To address this, we update the amplitude and phase of the simulated source wavelet during the inversion. The alternative workflow is referred to as log-validated waveform inversion (LVWI). The stabilization of LVWI is analyzed in a synthetic environment in which we examine the sensitivity to geologic complexity, well location, and log interval, each of which can impact the usefulness of local well-log information. Data from the Hussar experiment, a 2D land survey carried out in 2011 specifically to test waveform inversion procedures, are used to validate the approach. The Hussar data set is the framework for several experiments designed to analyze the effect of the wavelet update and the well-log calibration procedures. The results suggest that the implementation of wavelet updates and well calibration may provide an opportunity to mitigate cycle skipping and overcome potential local minima.