A Fast Sweeping Scheme for Calculating P Wave First-Arrival Travel Times in Transversely Isotropic Media with an Irregular Surface

2014 ◽  
Vol 171 (9) ◽  
pp. 2199-2208 ◽  
Author(s):  
Haiqiang Lan ◽  
Jingyi Chen ◽  
Zhongjie Zhang
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Irregular Surface ◽  
Travel Times ◽  
Transversely Isotropic Media ◽  
Fast Sweeping ◽  
First Arrival Travel Times ◽  
Isotropic Media ◽  
First Arrival

scholarly journals The offset-midpoint traveltime pyramid in 3D transversely isotropic media with a horizontal symmetry axis

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. T51-T62 ◽  
Author(s):  
Qi Hao ◽  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Symmetry Axis ◽  
Transversely Isotropic ◽  
P Wave ◽  
Analytic Representation ◽  
Velocity Inversion ◽  
Transversely Isotropic Media ◽  
Horizontal Symmetry ◽  
Time Domains ◽  
Isotropic Media ◽  
Hti Media

Analytic representation of the offset-midpoint traveltime equation for anisotropy is very important for prestack Kirchhoff migration and velocity inversion in anisotropic media. For transversely isotropic media with a vertical symmetry axis, the offset-midpoint traveltime resembles the shape of a Cheops’ pyramid. This is also valid for homogeneous 3D transversely isotropic media with a horizontal symmetry axis (HTI). We extended the offset-midpoint traveltime pyramid to the case of homogeneous 3D HTI. Under the assumption of weak anellipticity of HTI media, we derived an analytic representation of the P-wave traveltime equation and used Shanks transformation to improve the accuracy of horizontal and vertical slownesses. The traveltime pyramid was derived in the depth and time domains. Numerical examples confirmed the accuracy of the proposed approximation for the traveltime function in 3D HTI media.

A fast-marching eikonal solver for tilted transversely isotropic media

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. S385-S393
Author(s):  
Umair bin Waheed
Keyword(s):  
Transversely Isotropic ◽  
Fast Marching Method ◽  
Fast Marching ◽  
P Waves ◽  
Eikonal Equations ◽  
Transversely Isotropic Media ◽  
Fast Sweeping ◽  
Fast Marching Algorithm ◽  
Isotropic Media ◽  
And Migration

Fast and accurate traveltime computation for quasi-P waves in anisotropic media is an essential ingredient of many seismic processing and interpretation applications such as Kirchhoff modeling and migration, microseismic source localization, and traveltime tomography. Fast-sweeping methods are widely used for solving the anisotropic eikonal equation due to their flexibility in solving general equations compared to the fast-marching method. However, it has been observed that fast sweeping can be much less efficient than fast marching for models with curved characteristics and practical grid sizes. By representing a tilted transversely isotropic (TTI) equation as a sequence of elliptically isotropic (EI) eikonal equations, we determine that the fast-marching algorithm can be used to compute fast and accurate traveltimes for TTI media. The tilt angle is absorbed into the description of the effective EI model; therefore, the adopted approach does not compromise on the solution accuracy. Through tests on benchmark synthetic models, we test our fast-marching algorithm and discover considerable improvement in accuracy by using factorization and a second-order finite-difference stencil. The adopted methodology opens the door to the possibility of using the fast-marching algorithm for a wider class of anisotropic eikonal equations.

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