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A complex point-source solution of the acoustic eikonal equation for Gaussian beams in transversely isotropic media

Xingguo Huang, Sun Hui, Sun Zhangqing and Nuno Vieira da Silva
A complex point-source solution of the acoustic eikonal equation for Gaussian beams in transversely isotropic media
Geophysics (April 2020) 85 (3): T191-T207

Abstract

The complex traveltime solutions of the complex eikonal equation are the basis of inhomogeneous plane-wave seismic imaging methods, such as Gaussian beam migration and tomography. We have developed analytic approximations for the complex traveltime in transversely isotropic media with a titled symmetry axis, which is defined by a Taylor series expansion over the anisotropy parameters. The formulation for the complex traveltime is developed using perturbation theory and the complex point-source method. The real part of the complex traveltime describes the wavefront, and the imaginary part of the complex traveltime describes the decay of the amplitude of waves away from the central ray. We derive the linearized ordinary differential equations for the coefficients of the Taylor-series expansion using perturbation theory. The analytical solutions for the complex traveltimes are determined by applying the complex point-source method to the background traveltime formula and subsequently obtaining the coefficients from the linearized ordinary differential equations. We investigate the influence of the anisotropy parameters and of the initial width of the ray tube on the accuracy of the computed traveltimes. The analytical formulas, as outlined, are efficient methods for the computation of complex traveltimes from the complex eikonal equation. In addition, those formulas are also effective methods for benchmarking approximated solutions.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 85
Serial Issue: 3
Title: A complex point-source solution of the acoustic eikonal equation for Gaussian beams in transversely isotropic media
Affiliation: University of Bergen, Department of Earth Science, Bergen, Norway
Pages: T191-T207
Published: 20200414
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 55
Accession Number: 2020-041683
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Annotation: Includes appendices
Illustration Description: illus.
Secondary Affiliation: Southwest Jiaotong University, CHN, ChinaJilin University, CHN, ChinaTotal E&P UK, GBR, United Kingdom
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2020, American Geosciences Institute. Reference includes data from GeoScienceWorld, Alexandria, VA, United States. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 2020
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