Ernani Vitillo Volpe

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.

Full-waveform inversion (FWI) is a high-resolution numerical technique for seismic waves used to estimate the physical characteristics of a subsurface region. The continuous problem involves solving an inverse problem on an infinite domain, which is impractical from a computational perspective. In limited area models, absorbing boundary conditions (ABCs) are usually imposed to avoid wave reflections. Several relevant ABCs have been proposed, with extensive literature on their effectiveness on the direct wave problem. Here, we investigate and compare the theoretical and computational characteristics of several ABCs in the full inverse problem. After a brief review of the most widely used ABCs, we derive their formulations in their respective adjoint problems. The different ABCs are implemented in a highly optimized domain-specific language (DSL) computational framework, Devito, which is primarily used for seismic modelling problems. We evaluate the effectiveness, computational efficiency, and memory requirements of the ABC methods, considering from simple models to realistic ones. Our findings reveal that, even though the popular perfectly matching layers (PMLs) are effective at avoiding wave reflections at the boundaries, they can be computationally more demanding than less used hybrid ABCs. We show here that a proposed hybrid ABC formulation, with nested Higdon's boundary conditions, is the most cost-effective method among the methods considered here, for being as effective as or more effective than PML and other schemes but also for being computationally more efficient.

Full-Waveform Inversion (FWI) is a high-resolution numerical technique for seismic waves used to estimate the physical characteristics of a subsurface region. The continuous problem involves solving an inverse problem on an infinite domain, which is impractical from a computational perspective. In limited area models, absorbing boundaries conditions (ABCs) are usually imposed, to avoid wave reflections. Several relevant ABCs have been proposed, with extensive literature on their effectiveness on the direct wave problem. Here, we investigate and compare the theoretical and computational characteristics of several ABCs in the full inverse problem. After a brief review of the most widely used ABCs, we derive their formulations in their respective adjoint problems. The different ABCs are implemented in a highly optimized domain-specific language (DLS) computational framework, Devito, which targets seismic modeling problems. We evaluate the effectiveness, computational efficiency, and memory requirements of the ABC methods, considering from simple models to realistic ones. Our findings reveal that, even though the popular Perfectly Matching Layers (PMLs) are effective in avoiding wave reflections on the boundaries, they can be computationally more demanding than less used Hybrid ABCs. We show here that a proposed Hybrid ABC formulation, with nested Higdon's boundary conditions, is the most cost-effective method among the methods considered here, being as effective, or more, as PML and other schemes, but being computationally more efficient.

A simple way to decrease the drag and oscillating lift forces in the flow around a circular cylinder consists of positioning a splitter plate in the wake, parallel to the flow. In this paper, the effect of the splitter plate on the wake dynamics, more specifically on the wake transition, is described in detail. First, two-dimensional and three-dimensional direct numerical simulations (DNS) using the spectral element method were used to observe the behaviour of the wake in the presence of the splitter plate. Then, a linear stability analysis based on the Floquet theory was performed in order to obtain information on how the splitter plate changes the instabilities that lead to wake transition. Simulations were carried out for several gaps between the splitter plate and the cylinder, with the Reynolds number varying in the range between 100 and 350, which corresponds to the wake transition in the flow around a circular cylinder. The results of the simulations showed a discontinuity in the Strouhal number curve that is consistent with the results available in the literature. The stability analysis showed how the splitter plate modifies the transition of the flow to a three-dimensional configuration. The splitter plate has a stabilizing effect on the flow for small gaps, delaying the appearance of three-dimensional structures to higher Reynolds numbers. Mode A and a quasi-periodic (QP) mode are observed for such small gaps. As the gap is increased the discontinuity in the Strouhal number curve also caused a clear change in the characteristics of the neutral stability curve, and the existence of an unstable period-doubling mode was observed. The onset characteristics of the unstable modes are analysed and discussed in depth.