Hybrid Fast Sweeping Methods for Anisotropic Eikonal Equation in Two-Dimensional Tilted Transversely Isotropic Media

Huang, Guangnan; Luo, Songting

doi:10.1007/s10915-020-01280-3

Cited by 8 publications

(2 citation statements)

References 69 publications

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“…Zhao (2007) illustrates the first attempt of parallelized Fast Sweeping method and Detrixhe et al (2013) show that the Zhao ( 2007) method cannot be parallelized on large scale, and proposed a better solution that solves the problem efficiently. The Fast Sweeping Method is broadly applied using anisotropic media (Luo and Qian, 2012;Waheed et al, 2015;Waheed and Alkhalifah, 2017;Huang and Luo, 2020) with great feasibility for realistic applications. Focusing on accuracy, Vidale (1988) operator, the precision increase and some operators could be discarded to improve execution time (Noble et al, 2014).…”

Section: Accurate Fast Sweeping Methodsmentioning

confidence: 99%

3D Refraction Travel Time Accuracy Study in High Contrasted Media

Alves,

Santos,

Capuzzo

et al. 2024

Braz J Geophys

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Among all the existing methods to solve the eikonal equation, three methods are chosen to verify accuracy, symmetry, reciprocity and error propagation along large offsets of refracted waves in seismic near surface exploration context. Performance is extremely highlighted nowadays and accuracy is being neglected, then an eikonal solver poorly explored in geoscience is used. A classical solver, the Fast Iterative and the modified Fast Sweeping Method are applied in three modeling schemes: a simple two layers model, a large four layers and a complex benchmark model. The three methods compute the first arrival of refracted waves in high contrast media and the results are compared to the analytical solution. A circular geometry is considered in all experiments to explore the method applicability using full azimuth angles. On the first scheme, the errors in travel time are computed among the three methods using different model sample spacing and we discuss accuracy, symmetry and reciprocity of first arrivals. On the second scheme, three circular receivers are placed in different offsets to check errors along refracted wave propagation. Finally, the third scheme, four shots are strategically positioned over the SEG/EAGE Overthrust model in order to compare the full acoustic wavefield with the eikonal solvers and then check the similarities. Although the focus is on methods accuracy, the algorithm run time is also considered and the comparison shows that the modified Fast Sweeping Method is the most accurate. The most computational efficient eikonal solver is the Fast Iterative Method, but its geoscience applicability needs to be cautious, because of its inaccurate results.

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Section: Accurate Fast Sweeping Methodsmentioning

confidence: 99%

3D Refraction Travel Time Accuracy Study in High Contrasted Media

Alves,

Santos,

Capuzzo

et al. 2024

Braz J Geophys

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show abstract

“…We use a Gauss-Seidel fast-sweep method for Hamilton-Jacobi equations 50 with slight modifications. The main advantages of using a fast-sweep method are its stability against a wide range of Hamilton-Jacobi and related differential equations and its implementability 58,59 A drawback is that there seems to be no theoretical proof of convergence of the iteration procedure. To the best of the authors' knowledge, this numerical method has not been applied to HJB equations of the ergodic controls like ours.…”

Section: Fast-sweep Methodsmentioning

confidence: 99%

Analytical and numerical solutions to ergodic control problems arising in environmental management

Yoshioka

Tsujimura

Yaegashi

2022

Math Methods in App Sciences

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Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated nonlocal Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on sediment storage management as a modern engineering problem, we formulate, analyze, and compute a new ergodic control problem under discrete observations: a simple but non-trivial mathematical problem. We give optimality and comparison results of the corresponding HJB equation having unique non-smoothness and discontinuity. To numerically compute HJB equations, we propose a new fast-sweep method resorting to neither pseudo-time integration nor vanishing discount. The optimal policy and the effective Hamiltonian are then computed simultaneously. Convergence rate of numerical solutions is computationally analyzed. An advanced robust control counterpart where the dynamics involve uncertainties is also numerically considered.

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High Order Absolutely Convergent Fast Sweeping Methods with Multi-resolution WENO Local Solvers for Eikonal and Factored Eikonal Equations

Hu,

Zhang

2024

J Sci Comput

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Hybrid Fast Sweeping Methods for Anisotropic Eikonal Equation in Two-Dimensional Tilted Transversely Isotropic Media

Cited by 8 publications

References 69 publications

3D Refraction Travel Time Accuracy Study in High Contrasted Media

3D Refraction Travel Time Accuracy Study in High Contrasted Media

Analytical and numerical solutions to ergodic control problems arising in environmental management

High Order Absolutely Convergent Fast Sweeping Methods with Multi-resolution WENO Local Solvers for Eikonal and Factored Eikonal Equations

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