Influences of Anisotropic Stretching of Boundary Conforming Grid on Traveltime Computation by Topography‐Dependent Eikonal Equation

Lan, Haiqiang; Zhang, Zhi; Xu, Tao; Bai, Zhiming

doi:10.1002/cjg2.1750

Cited by 2 publications

(1 citation statement)

References 46 publications

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“…Most modern tomographic techniques addressing an irregular surface are based on unstructured grids, which is computationally inefficient in model parameterization and traveltime calculation (Kimmel and Sethian, 1998; Sethian, 1999; Sethian and Vladimirsky, 2000; Rawlinson and Sambridge, 2004a, b; Qian JL et al 2007a, b; Kao CY et al, 2008; Lelièvre et al, 2011). Unlike these techniques, the structured grid‐based schemes usually handle irregular surfaces by using model expansion (Vidale, 1988; Reshef, 1991; Hole, 1992; Ma T and Zhang Z, 2014a, b, 2015) or irregular surface flattening (Haines, 1988; Lan HQ and Zhang ZJ, 2011a, b, 2013a, b; Lan HQ et al, 2012). The former scheme usually employs a stair‐step approximation of the irregular surface or a flat low‐velocity layer covering the surface, which may cause accuracy loss and even distorted images.…”

Section: Introductionmentioning

confidence: 99%

Joint tomographic inversion of first-arrival and reflection traveltimes for recovering 2-D seismic velocity structure with an irregular free surface

Zhang

Bai

et al. 2018

Earth and Planetary Physics

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Irregular surface flattening, which is based on a boundary conforming grid and the transformation between curvilinear and Cartesian coordinate systems, is a mathematical method that can elegantly handle irregular surfaces, but has been limited to obtaining first arrivals only. By combining a multistage scheme with the fast‐sweeping method (FSM, the method to obtain first‐arrival traveltime in curvilinear coordinates), the reflected waves from a crustal interface can be traced in a topographic model, in which the reflected wave‐front is obtained by reinitializing traveltimes in the interface for upwind branches. A local triangulation is applied to make a connection between velocity and interface nodes. Then a joint inversion of first‐arrival and reflection traveltimes for imaging seismic velocity structures in complex terrains is presented. Numerical examples all perform well with different seismic velocity models. The increasing topographic complexity and even use of a high curvature reflector in these models demonstrate the reliability, accuracy and robustness of the new working scheme; checkerboard testing illustrates the method's high resolution. Noise tolerance testing indicates the method's ability to yield practical traveltime tomography. Further development of the multistage scheme will allow other later arrivals to be traced and used in the traveltime inversion.

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Section: Introductionmentioning

confidence: 99%

Joint tomographic inversion of first-arrival and reflection traveltimes for recovering 2-D seismic velocity structure with an irregular free surface

Zhang

Bai

et al. 2018

Earth and Planetary Physics

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A topography-dependent eikonal solver for accurate and efficient computation of traveltimes and their derivatives in 3D heterogeneous media

et al. 2023

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Accurate and efficient computation of traveltimes and their spatial gradients for 3D heterogeneous media are essential in many areas of seismology, such as traveltime/slope tomography and quantitative migration. A popular method of obtaining this information is to solve the eikonal equation using the finite difference (FD) scheme. However, the complex surface of the Earth causes numerical complications when applying FD methods based on rectangular grids. To overcome this problem taking into account the topographic effect, we make use of the 3D topography-dependent eikonal equation (TDEE) from the idea of a 3D surface-flattening scheme with curvilinear grid-based FD methods, which could transform irregular surfaces in the physical domain into regular surfaces in the computational domain. Unfortunately, solving the TDEE in 3D starting from the initial point-source condition needs to overcome the point-source singularity, we formulate the 3D factored TDEE based on the factoring principle. Furthermore, to numerically solve the 3D original TDEE, as well as the factored TDEE, we introduce a lock sweeping method, which avoids the problem of repetitive computation in the fast sweeping method. Several numerical examples demonstrate the efficiency of the new lock scheme in terms of computation time and gain in the accuracy of the 3D factored TDEE solver for the calculation of traveltimes and their derivatives. This provides a good choice for the calculation of traveltimes and their spatial derivatives using models with irregular surfaces, which means greater potential for seismic data processing under complex topographical conditions.

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Influences of Anisotropic Stretching of Boundary Conforming Grid on Traveltime Computation by Topography‐Dependent Eikonal Equation

Cited by 2 publications

References 46 publications

Joint tomographic inversion of first-arrival and reflection traveltimes for recovering 2-D seismic velocity structure with an irregular free surface

Joint tomographic inversion of first-arrival and reflection traveltimes for recovering 2-D seismic velocity structure with an irregular free surface

A topography-dependent eikonal solver for accurate and efficient computation of traveltimes and their derivatives in 3D heterogeneous media

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