Born modeling for heterogeneous media using the Gaussian beam summation based Green's function

Sun

et al. 2020

GEOPHYSICS

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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.

Section: Complex Asymptotic Solutions Using Complex Point Source Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Sun

et al. 2020

GEOPHYSICS

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“…Yuan et al [10] performed a localized waveform inversion time-lapse survey by combining the wavefield injection and extrapolation. Unlike the methods above, we develop a target-oriented waveform inversion scheme based on the distorted Born iterative T-matrix method [24] and Gaussian beam based Green's function [40][41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

“…For our approach, two critical aspects are (1) to calculate the initial local wavefields of the target region and (2) its iterative updating for the local inversion. To this end, we employ two methods, called Gaussian beam based Green's function approach [40,45] and the T-matrix method. These two methods are used to calculate the initial local wavefields of the target region.…”

Section: Introductionmentioning

confidence: 99%

Taming the divergent terms in the scattering series of Born by renormalization

SEG Technical Program Expanded Abstracts 2019

Jakobsen

Wuy

2019

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This research has received support from the Research Council of Norway for the Petromaks II project 267769/E3 (Bayesian inversion of 4D seismic waveform data for quantitative integration with production data).When starting to write my PhD thesis and looking back to the past two and half years of my PhD studies, I realize that it would not have been possible to finish my PhD without the help of many friends and colleagues.Firstly, I would like to express my deepest gratitude to my supervisor Morten Jakobsen, for giving me the opportunity to pursue PhD studies at University of Bergen and collaboration research at University of California, Santa Cruz, and for guiding me throughout the PhD studies. I would say I am lucky to meet such a supervisor. Morten is very clever and nice supervisor, who is not only my supervisor but also my good friend, helping me from work to life. My words cannot express how blessed I am your PhD student.

“…Modelling seismic traveltimes is clearly essential for understanding and quantification of the kinematic properties of the propagating waves in such media. It finds many applications such as velocity analysis, anisotropic parameter estimation (Alkhalifah 2011a), traveltime tomography (Chapman & Pratt 1992;Zelt & Barton 1998;Zhou et al 2008;Bai & Greenhalgh 2005), seismic migration (Huang et al 2016a; and full waveform inversion (Alkhalifah & Choi 2014;Silva et al 2016). The seismic traveltimes can be obtained by solving the nonlinear partial differential equation under the high-frequency assumption; this is referred to as the eikonal equation.…”

Section: Introductionmentioning

confidence: 99%

Traveltime approximation for strongly anisotropic media using the homotopy analysis method

Geophysical Journal International

Greenhalgh

2018

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Traveltime approximation plays an important role in seismic data processing, for example, anisotropic parameter estimation and seismic imaging. By exploiting seismic traveltimes, it is possible to improve the accuracy of anisotropic parameter estimation and the resolution of seismic imaging. Conventionally, the traveltime approximations in anisotropic media are obtained by expanding the anisotropic eikonal equation in terms of the anisotropic parameters and the elliptically anisotropic eikonal equation based on perturbation theory. Such an expansion assumes a small perturbation and weak anisotropy. In a realistic medium, however, the assumption of small perturbation likely breaks down. We present a retrieved zero-order deformation equation that creates a map from the anisotropic eikonal equation to a linearized partial differential equation system based on the homotopy analysis method. By choosing the linear and nonlinear operators in the retrieved zero-order deformation equation, we develop new traveltime approximations that allow us to compute the traveltimes for a medium of arbitrarily strength anisotropy. A comparison of the traveltimes and their errors from the homotopy analysis method and from the perturbation method suggests that the traveltime approximations provide a more reliable result in strongly anisotropic media.