Full-Waveform Inversion Cycle-Skipping Mitigation with Dynamic Time Warping, Part 2: An Intermediate Signal Approach

Abstract This paper presents Part 2 of a study that explores underemployed applications of the Dynamic Time Warping (DTW) method for cycle-skipping mitigation in Full-Waveform Inversion (FWI). To achieve a representative subsurface model, FWI seeks to minimise an objective function that quantifies the difference between modelled and observed seismic data. However, the non-convex nature of the objective function often drives the inversion process to converge to local minima, resulting in cycle-skipping. Mitigating this issue requires the initial and observed signals to differ by no more than half a cycle, requiring an initial model close to the observed. This condition is one of the primary challenges in FWI. In this Part 2 study, we introduce the Dynamic Time Warping Intermediate Signal Approach (DTW-ISA), which generates intermediate signals between the modelled and observed signals. These intermediate signals are placed sufficiently close to the modelled signals to perform as temporary targets, allowing the inversion to advance in steps, gradually taking the results to the observed model and mitigating cycle-skipping. DTW-ISA creates the intermediate signals with two interpolation methods developed in this work: Proportional Interpolation (PI) and Maximum Time Lag Interpolation (MTLI). We compared DTW-ISA with the multiscale approach, and the results demonstrated that DTW-ISA successfully reduced cycle-skipping in all tests, producing better outcomes than those achieved with the multiscale method. These findings suggest that DTW-ISA holds significant potential for mitigating cycle-skipping, especially utilising initial models distant from the observed ones.