The offset‐midpoint travel‐time pyramid for P‐wave in 2D transversely isotropic media with a tilted symmetry axis

Hao, Qi; Stovas, Alexey

doi:10.1111/1365-2478.12201

Cited by 7 publications

(2 citation statements)

References 20 publications

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“…It should be noted that this equation can also be obtained directly from the eikonal equation of Alkhalifah (2000), Stovas and Alkhalifah (2013) and Hao and Stovas (2015). The transport equation is obtained by setting Q 3 = 0.…”

Section: Non-trivial Solutions For Equation (4) Exist Ifmentioning

confidence: 99%

Travel time computations using a compact eikonal equation for vertical transverse isotropic media

Moghaddam

Khajavi

Keers

2018

Geophysical Prospecting

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Eikonal solvers often have stability problems if the velocity model is mildly heterogeneous. We derive a stable and compact form of the eikonal equation for P‐wave propagation in vertical transverse isotropic media. The obtained formulation is more compact than other formulations and therefore computationally attractive. We implemented ray shooting for this new equation through a Hamiltonian formalism. Ray tracing based on this new equation is tested on both simple as well as more realistic mildly heterogeneous velocity models. We show through examples that the new equation gives travel times that coincide with the travel time picks from wave equation modelling for anisotropic wave propagation.

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Section: Non-trivial Solutions For Equation (4) Exist Ifmentioning

confidence: 99%

Travel time computations using a compact eikonal equation for vertical transverse isotropic media

Moghaddam

Khajavi

Keers

2018

Geophysical Prospecting

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“…In this paper, we adopt the monolithic approach to simulate the wavefield of an acoustic-elastic coupled TTI media. We start from the 2D first-order VTI acoustic-elastic coupled equation (Yu & Geng, 2019) and extend it through the Bond matrix coordinate transformation (Hao & Stovas, 2015). The main purpose of this paper is to construct the 3D first-order TTI acoustic-elastic coupled equation and analyzes the characteristics of Scholte waves in snapshots.…”

Section: Introductionmentioning

confidence: 99%

Numerical modeling of Scholte wave propagation in acoustic-elastic coupled anisotropic media

Chen,

Wang,

Hao

et al. 2023

Preprint

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Numerical modeling of Scholte wave propagation is helpful for seismic exploration in deepwater environment. Scholte waves, which are generated at seafloor, exhibit distinctly different propagation behaviors than body waves in ocean-bottom seismograms. We present a staggered-grid finite-difference method of modeling Scholte wave propagation in the interface between fluid and transversely isotropic media, where the interface does not need to consider the boundary condition. We also derive the stability condition of the proposed method. Numerical examples are used to analyze the wavefield and traveltime of Scholte waves. Numerical results show that the velocity of the Scholte wave is positively correlated with ε and negatively correlated with δ. And the curve of the arrival time of the Scholte wave as a whole is sinusoidal and has no symmetry in inclination. The velocity of the Scholte wave in azimuth is positively related to the polar angle. The energy of the Scholte wave is negatively correlated with the distance from the source to the fluid-solid interface.

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3D P‐wave traveltime computation in transversely isotropic media using layer‐by‐layer wavefront marching

Cao

Wang

et al. 2018

Geophysical Prospecting

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Subsurface rocks (e.g. shale) may induce seismic anisotropy, such as transverse isotropy. Traveltime computation is an essential component of depth imaging and tomography in transversely isotropic media. It is natural to compute the traveltime using the wavefront marching method. However, tracking the 3D wavefront is expensive, especially in anisotropic media. Besides, the wavefront marching method usually computes the traveltime using the eikonal equation. However, the anisotropic eikonal equation is highly non‐linear and it is challenging to solve. To address these issues, we present a layer‐by‐layer wavefront marching method to compute the P‐wave traveltime in 3D transversely isotropic media. To simplify the wavefront tracking, it uses the traveltime of the previous depth as the boundary condition to compute that of the next depth based on the wavefront marching. A strategy of traveltime computation is designed to guarantee the causality of wave propagation. To avoid solving the non‐linear eikonal equation, it updates traveltime along the expanding wavefront by Fermat's principle. To compute the traveltime using Fermat's principle, an approximate group velocity with high accuracy in transversely isotropic media is adopted to describe the ray propagation. Numerical examples on 3D vertical transverse isotropy and tilted transverse isotropy models show that the proposed method computes the traveltime with high accuracy. It can find applications in modelling and depth migration.

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The offset‐midpoint travel‐time pyramid for P‐wave in 2D transversely isotropic media with a tilted symmetry axis

Cited by 7 publications

References 20 publications

Travel time computations using a compact eikonal equation for vertical transverse isotropic media

Travel time computations using a compact eikonal equation for vertical transverse isotropic media

Numerical modeling of Scholte wave propagation in acoustic-elastic coupled anisotropic media

3D P‐wave traveltime computation in transversely isotropic media using layer‐by‐layer wavefront marching

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