A data reconstruction inversion approach to extended FWI

Abstract

Full waveform inversion (FWI) is a constrained optimization problem that draw inferences about high resolution subsurface parameters by matching the recorded and the simulated seismograms, the latter being obtained by solving the wave equation. The difference between the two sets of seismograms (data residuals) is minimized in a least-squares sense to update the model for an improved match. However, the update will be in a right way only if the predicted data are no more than half a cycle away from the recorded data; otherwise, the update moves away from the desired model due to cycle skipping. The extended FWI called wavefield reconstruction inversion (WRI) has been proposed to mitigate the cycle skipping issue. Wavefields are first extrapolated with the background velocity model from the recorded data collected at the surface to all points in the subsurface. Then, the model parameters are updated by minimizing the source residuals (or source extension) generated by the extrapolation of the data with inaccurate background model. The extrapolation step is however computation and memory intensive in the time domain formulation of WRI. We present a reformulation of time domain extended FWI, which works with reconstructed data rather than reconstructed wavefields. The objective function of the data reconstruction inversion contains two terms: the first replaces the recorded data in the classical FWI misfit function with a suitably defined surrogate data, which are between the recorded and the simulated seismograms, whereby cycle skipping is reduced. The second term is the weighted least-squares distance between the recorded and the surrogate data. The surrogate data are then forced to iteratively converge toward both the recorded and the simulated data by updating the subsurface parameters.