Deep-learning-based time shift estimation for Full Waveform Inversion

SUMMARY

Full Waveform Inversion (FWI) is a technique that leverages the discrepancy between modelled and observed seismic data to estimate a potentially high-resolution velocity model of the subsurface. However, due to the highly oscillatory nature of seismic waveforms, point-wise discrepancy measures are susceptible to cycle-skipping, particularly when starting from a poor initial velocity model.

Over the years, various alternative misfit functions have been proposed, each with its own advantages and limitations. Dynamic Time Warping (DTW) is a widely used technique in signal processing for aligning two time series. Although a differentiable version of DTW has been recently developed, its application in gradient-based optimization faces challenges, including the presence of high-frequency artifacts in the adjoint source and the significant computational cost of gradient computation.

In this work, we propose using a neural network to learn the time shift required to align a pair of time series in a supervised manner. The trained network is subsequently employed to compare traces from the observed and modelled data in FWI, offering a more computationally-efficient alternative to DTW. Moreover, as neural networks are inherently differentiable via back-propagation, the trained network can be seamlessly integrated into the misfit function of an FWI framework. We demonstrate the feasibility of this approach on the Chevron blind test dataset.