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The travel time computation of microseismic waves in different directions (particularly, the diagonal direction) in three-dimensional space has been found to be inaccurate, which seriously affects the localization accuracy of three-dimensional microseismic sources. In order to solve this problem, this research study developed a method of calculating the P-wave travel time based on a 3D high-order fast marching method (3D_H_FMM). This study focused on designing a high-order finite-difference operator in order to realize the accurate calculation of the P-wave travel time in three-dimensional space. The method was validated using homogeneous velocity models and inhomogeneous layered media velocity models of different scales. The results showed that the overall mean absolute error (MAE) of the two homogenous models using 3D_H_FMM had been reduced by 88.335%, and 90.593% compared with the traditional 3D_FMM. On that basis, the three-dimensional localization of microseismic sources was carried out using a particle swarm optimization algorithm. The developed 3D_H_FMM was used to calculate the travel time, then to conduct the localization of the microseismic source in inhomogeneous models. The mean error of the localization results of the different positions in the three-dimensional space was determined to be 1.901 m, and the localization accuracy was found to be superior to that of the traditional 3D_FMM method (mean absolute localization error: 3.447 m) with the small-scaled inhomogeneous model.

Jack-up Rigs (JuRs) are integral to offshore resource extraction, mainly due to their need for robust structural stability in challenging marine environments. This study introduces a Multi-Cascade Neural Network (MCNN) framework designed to evaluate the structural integrity of JuRs. We implement a Fast-Marching Algorithm (FMA) to process the vibration data obtained from a Multi-Sensor Network (MSN) strategically installed at critical locations on the rig. The FMA facilitates the construction of an overall state ridge from the vibration datasets, which, over time, informs the MCNNbased assessment model. During an 8-week evaluation period, the assessment model was rigorously tested, resulting in a structural state classification value, which effectively encapsulated the rig's overall condition. The application of our proposed methodology in various test scenarios demonstrated promising outcomes, validating the efficacy of our approach in structural assessment for JuRs.

A global path planning algorithm for unmanned surface vehicles (USVs) with short time requirements in large-scale and complex multi-island marine environments is proposed. The fast marching method-based path planning for USVs is performed on grid maps, resulting in a decrease in computer efficiency for larger maps. This can be mitigated by improving the algorithm process. In the proposed algorithm, path planning is performed twice in maps with different spatial resolution (SR) grids. The first path planning is performed in a low SR grid map to determine effective regions, and the second is executed in a high SR grid map to rapidly acquire the final high precision global path. In each path planning process, a modified inshore-distance-constraint fast marching square (IDC-FM 2 ) method is applied. Based on this method, the path portions around an obstacle can be constrained within a region determined by two inshore-distance parameters. The path planning results show that the proposed algorithm can generate smooth and safe global paths wherein the portions that bypass obstacles can be flexibly modified. Compared with the path planning based on the IDC-FM 2 method applied to a single grid map, this algorithm can significantly improve the calculation efficiency while maintaining the precision of the planned path.

First-arrival traveltime computation for quasi-P waves in transversely isotropic (TI) media is the key component of tomography and depth migration. It is appealing to use the fast marching method in isotropic media as it efficiently computes traveltime along an expanding wavefront. It uses the finite difference method to solve the eikonal equation. However, applying the fast marching method in anisotropic media faces challenges because the anisotropy introduces additional nonlinearity in the eikonal equation and solving this nonlinear eikonal equation with the finite difference method is challenging. To address this problem, we present a Fermat's principle-based fast marching method to compute traveltime in two-dimensional TI media. This method is applicable in both vertical and tilted TI (VTI and TTI) media. It computes traveltime along an expanding wavefront using Fermat's principle instead of the eikonal equation. Thus, it does not suffer from the nonlinearity of the eikonal equation in TI media. To compute traveltime using Fermat's principle, the explicit expression of group velocity in TI media is required to describe the ray propagation. The moveout approximation is adopted to obtain the explicit expression of group velocity. Numerical examples on both VTI and TTI models show that the traveltime contour obtained by the proposed method matches well with the wavefront from the wave equation. This shows that the proposed method could be used in depth migration and tomography.

Coverage path planning (CPP) is a field of study which objective is to find a path that covers every point of a certain area of interest. Recently, the use of Unmanned Aerial Vehicles (UAVs) has become more proficient in various applications such as surveillance, terrain coverage, mapping, natural disaster tracking, transport, and others. The aim of this paper is to design efficient coverage path planning collision-avoidance capable algorithms for single or multi UAV systems in cluttered urban environments. Two algorithms are developed and explored: one of them plans paths to cover a target zone delimited by a given perimeter with predefined coverage height and bandwidth, using a boustrophedon flight pattern, while the other proposed algorithm follows a set of predefined viewpoints, calculating a smooth path that ensures that the UAVs pass over the objectives. Both algorithms have been developed for a scalable number of UAVs, which fly in a triangular deformable leader-follower formation with the leader at its front. In the case of an even number of UAVs, there is no leader at the front of the formation and a virtual leader is used to plan the paths of the followers. The presented algorithms also have collision avoidance capabilities, powered by the Fast Marching Square algorithm. These algorithms are tested in various simulated urban and cluttered environments, and they prove capable of providing safe and smooth paths for the UAV formation in urban environments.

When dealing with computed tomography volume data, the accurate segmentation of lung nodules is of great importance to lung cancer analysis and diagnosis, being a vital part of computer-aided diagnosis systems. However, due to the variety of lung nodules and the similarity of visual characteristics for nodules and their surroundings, robust segmentation of nodules becomes a challenging problem. A segmentation algorithm based on the fast marching method is proposed that separates the image into regions with similar features, which are then merged by combining regions growing with k-means. An evaluation was performed with two distinct methods (objective and subjective) that were applied on two different datasets, containing simulation data generated for this study and real patient data, respectively. The objective experimental results show that the proposed technique can accurately segment nodules, especially in solid cases, given the mean Dice scores of 0.933 and 0.901 for round and irregular nodules. For non-solid and cavitary nodules the performance dropped—0.799 and 0.614 mean Dice scores, respectively. The proposed method was compared to active contour models and to two modern deep learning networks. It reached better overall accuracy than active contour models, having comparable results to DBResNet but lesser accuracy than 3D-UNet. The results show promise for the proposed method in computer-aided diagnosis applications.

Multi-UAV systems are attracting, especially in the last decade, the attention of researchers and companies of very different fields due to the great interest in developing systems capable of operating in a coordinated manner in complex scenarios and to cover and speed up applications that can be dangerous or tedious for people: search and rescue tasks, inspection of facilities, delivery of goods, surveillance, etc. Inspired by these needs, this work aims to design, implement and analyze a trajectory planning and collision avoidance strategy for multi-UAV systems in 3D environments. For this purpose, a study of the existing techniques for both problems is carried out and an innovative strategy based on Fast Marching Square—for the planning phase—and a simple priority-based speed control—as the method for conflict resolution—is proposed, together with prevention measures designed to try to limit and reduce the greatest number of conflicting situations that may occur between vehicles while they carry out their missions in a simulated 3D urban environment. The performance of the algorithm is evaluated successfully on the basis of certain conveniently chosen statistical measures that are collected throughout the simulation runs.

We address the numerical computation of distance maps with respect to Riemannian metrics of strong anisotropy. For that purpose we solve generalized eikonal equations, discretized using adaptive upwind finite differences on a Cartesian grid, in a single pass over the domain using a variant of the fast-marching algorithm. The key ingredient of our PDE numerical scheme is Voronoi's first reduction, a tool from discrete geometry which characterizes the interaction of a quadratic form with an additive lattice. This technique, never used in this context, which is simple and cheap to implement, allows us to efficiently handle Riemannian metrics of eigenvalue ratio 10² and more. Two variants of the introduced scheme are also presented, adapted to sub-Riemannian and to Ränder metrics, which can be regarded as degenerate Riemannian metrics and as Riemannian metrics perturbed with a drift term, respectively. We establish the convergence of the proposed scheme and of its variants, with convergence rates. Numerical experiments illustrate the effectiveness of our approach in various contexts, in dimension up to five, including an original sub-Riemannian model related to the penalization of path torsion.

Accurate determination of earthquake parameters is vital task for seismologists due to their potential hazards and the importance of risk mitigation. Hypocenter is one of the paramaters which is critical for tomography and inversion processing. This study introduces a novel approach for hypocenter localization based on the Reciprocal Method of Fast Marching Wavefront Modeling (RFMW). This method models seismic wavefronts by solving the eikonal equation through the Fast Marching Method (FMM). We evaluate the effectiveness of RFMW in locating hypocenters in highly heterogeneous subsurface media and in addressing the nonlinear aspects of wave propagation. Additionally, we investigate how hypocenter accuracy is affected by the spatial configuration and distribution of seismograph stations. The RFMW approach was applied to determine several hypocenters beneath Lake Toba in the North Sumatra. The results reveal the strong correlation between the seismograph network configuration—particularly station spacing and distribution—and the accuracy of hypocenter localization. Interestingly, increasing the number of seismographs did not significantly enhance the accuracy of hypocenter determination, highlighting the importance of optimal station placement position.