FWI in extended domain using time-warping

Abstract

The automation of model building using Full Waveform Inversion (FWI) depends on the lowest frequencies available in the data and an accurate initial model to avoid cycle-skipping. To overcome the cycle-skipping, a new class of FWI approaches extend the solution search in one or more dimensions. We present a new method that uses the time-warping function as the extension in the data space. This function dynamically transports the recorded data to the synthetic data and is imposed to represent the actual physical time. The resulting FWI objective function enables the solution of two parameters, velocity model and time-warping extension, in a single optimization problem, which is solved by the Alternate Direction Method (ADM). The mapping function is found by Dynamic Time Warping (DTW) with an augmented cost function provided by the time-warping extension. The novel FWI objective function, allows automatic transition from a pure time-shift problem to a conventional FWI. We apply the new FWI method to both synthetic and field data to demonstrate its effectiveness starting from inaccurate initial models. Results show that the new FWI approach is able to build high-resolution models from very simple initial velocity models.