An upwind fast sweeping scheme for calculating seismic wave first‐arrival travel times for models with an irregular free surface

Lan, Haiqiang; Chen, Ling

doi:10.1111/1365-2478.12513

Cited by 9 publications

(3 citation statements)

References 67 publications

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“…Later, the post sweeping is applied to address the causality issue caused by the expanding square formalism (Hole & Zelt 1995), and the accuracy and stability are enhanced by using the essentially non-oscillatory (ENO) scheme (Shu & Osher 1988;Kim & Cook 1999). More recently, the fast sweeping method uses monotone numerical Hamiltonian for numerical discretization and solves the resulting system using the Gauss-Seidel iterations with alternative sweeping order, which becomes one of the most effective algorithms to solve eikonal equations (Tsai et al 2003;Kao et al 2004;Zhao 2005;Qian et al 2007;Luo & Qian 2012;Waheed et al 2015;Lan & Chen 2018;Zhang et al 2021;Cui et al 2021;Guo et al 2022). Importantly, this method is highly feasible for parallel computation (Zhao 2007;Detrixhe et al 2013;Detrixhe & Gibou 2016).…”

Section: Model Parametrization and Optimization Algorithmmentioning

confidence: 99%

Adjoint-state traveltime tomography for azimuthally anisotropic media in spherical coordinates

Chen

Nagaso

et al. 2023

Geophysical Journal International

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Summary Tong (2021) has proposed an adjoint-state traveltime tomography method to determine velocity heterogeneity and azimuthal anisotropy. This method, however, ignores the Earth’s curvature when deriving the eikonal equation for azimuthally anisotropic media. Thus, further coordinate transformation or approximation is required to ensure the accuracy of traveltime prediction in large-scale tomography. To address this problem, we derive the eikonal equation for azimuthally anisotropic media in spherical coordinates, which naturally considers the Earth’s curvature. Another key ingredient is the forward modeling algorithm, whose accuracy and efficiency dominate the numerical error and computational cost of the inversion. In this study, we apply a modified fast sweeping method to solve the eikonal equation in spherical coordinates. Two approaches, including the third-order weighted essentially nonoscillatory approximation and multiplicative factorization technique, are applied to improve the accuracy. According to the numerical experiments, this new eikonal solver achieves a second-order accuracy and is about two orders of magnitude more accurate than the commonly used first-order fast sweeping method with similar runtime. Taking advantage of the two improvements, we develop a novel eikonal equation-based adjoint-state traveltime tomography method for azimuthally anisotropic media in spherical coordinates. This method is applicable for large-scale tomography, and its performance is verified by a synthetic checkerboard test and a practical seismic tomographic inversion in central California near Parkfield.

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Section: Model Parametrization and Optimization Algorithmmentioning

confidence: 99%

Adjoint-state traveltime tomography for azimuthally anisotropic media in spherical coordinates

Chen

Nagaso

et al. 2023

Geophysical Journal International

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“…Ma and Alkhalifah (2013) developed a fixed-point iteration method to solve the eikonal equations for 2D VTI media on a rectangular grid. Lan et al (2014) proposed a topographydependent P wave eikonal equation for TI media in the curvilinear coordinate system, and used a high-order FSM to calculate the traveltime of qP wave. and proposed to decompose the traveltime solution of qP wave into elliptic and non-elliptic terms.…”

Section: Introductionmentioning

confidence: 99%

“…The numerical tests validate the accuracy and efficiency of the proposed method for 3D general TTI media. Chen, J.,& Zhang, Z. (2014).…”

mentioning

confidence: 99%

Traveltime calculations for qP, qSV, and qSH waves in 3D tilted transversely isotropic media using fast sweeping method with a Newton method local solver

Zhang

2023

Preprint

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Efficient and accurate traveltime calculations of seismic waves have important applications in tomography, prestack migration, earthquake location, etc. Anisotropy significantly affects the traveltimes of seismic wave. For high-resolution imaging and inversion, it is necessary to consider anisotropy in the traveltime calculations. The fast sweeping method (FSM) does not need to track and store the minimum traveltime point of wavefront, which has important applications in computing the anisotropic first-arrival traveltime. The conventional method that solves a transformed traveltime quartic equation combined with FSM is suitable for general anisotropic media. However, this method involves finding the intervals of roots and solving the quartic equations using bisection algorithm at each iteration, leading to high computational cost and instability for the 3D problems. In our previous work, for the vertical transversely isotropic (VTI) case, we developed an FSM to compute the qP-wave first-arrival traveltimes by analytically solving the simplified quadratic slowness equation in a specific triangular-pyramid stencil. This method greatly improves the computational efficiency. However, for the qP and qSV waves, analytically solving the slowness equation cannot be extended to tilted transversely isotropic (TTI) media. To address this problem, we introduced the Newton method in the triangular-pyramid local solver to quickly solve the TTI slowness equation. For the qSH wave, its slowness equation is quadratic and simple to solve. The proposed method provides an efficient procedure for the traveltime calculations of qP, qSV, and qSH waves in 3D general TTI media. Numerical examples have verified the efficiency and accuracy of the proposed method.

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A hybrid method for calculating seismic wave first-arrival traveltimes in two-dimensional models with an irregular surface

Lan

Chen

Badal

2018

Journal of Applied Geophysics

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An upwind fast sweeping scheme for calculating seismic wave first‐arrival travel times for models with an irregular free surface

Cited by 9 publications

References 67 publications

Adjoint-state traveltime tomography for azimuthally anisotropic media in spherical coordinates

Adjoint-state traveltime tomography for azimuthally anisotropic media in spherical coordinates

Traveltime calculations for qP, qSV, and qSH waves in 3D tilted transversely isotropic media using fast sweeping method with a Newton method local solver

A hybrid method for calculating seismic wave first-arrival traveltimes in two-dimensional models with an irregular surface

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