Full-Waveform Inversion Cycle-Skipping Mitigation with Dynamic Time Warping, Part 1: A Method for a Proximity Analysis Between the Current and the Observed Data

Abstract Full-Waveform Inversion (FWI) is a seismic imaging technique employed to achieve detailed subsurface representations by leveraging seismic data. The method solves an optimisation problem to minimise discrepancies between modelled and observed data. However, FWI poses inherent challenges due to the complexity of its non-linear optimisation process and the non-convex nature of the objective function. Typically, gradient-based optimisation algorithms, such as L-BFGS-B, are used to search for the global minimum. Nevertheless, there exists no guarantee of convergence to the global minimum, potentially yielding inaccurate results. To circumvent the risk of converging to local minima, either an initial model closely resembling the true solution must be provided, or strategies to prevent cycle skipping should be employed. This paper is Part 1 of a study that explores the potential of using the Dynamic Time Warping (DTW) methodology to address cycle-skipping with a focus on underinvestigated approaches. We introduce the Dynamic Time Warping Proximity Analysis (DTW-PA), a procedure designed to provide a qualitative estimation of the current model’s suitability for FWI, while in Part 2, we present a method for mitigating cycle-skipping itself. Here, a time-domain multiscale strategy was employed to tackle cycle-skipping challenges. Our results indicate that DTW-PA offers low qualitative insights into the adequacy of the initial model for running FWI without cycle-skipping. However, it facilitates informed decision-making regarding the application of frequency filters for multiscale step building, reducing the number of steps needed and minimising time and computational costs.