Crosshole seismic tomography including the anisotropy effect

Rao, Ying; Wang, Yanghua

doi:10.1088/1742-2132/8/2/016

Cited by 12 publications

(4 citation statements)

References 15 publications

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“…Zhou et al (2008) use a nonlinear inversion method for Thomsen's anisotropic parameters from the traveltime inversion. Rao and Wang (2011) demonstrate that the anisotropic traveltime tomography results in a much better match in the first-arrival times between the synthetic and observed data, particularly at far offsets.…”

Section: Introductionmentioning

confidence: 80%

Crosshole seismic tomography with cross-firing geometry

et al. 2016

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We have developed a case study of crosshole seismic tomography with a cross-firing geometry in which seismic sources were placed in two vertical boreholes alternatingly and receiver arrays were placed in another vertical borehole. There are two crosshole seismic data sets in a conventional sense. These two data sets are used jointly in seismic tomography. Because the local sediment is dominated by periodic, flat, thin layers, there is seismic anisotropy with different velocities in the vertical and horizontal directions. The vertical transverse isotropy anisotropic effect is taken into account in inversion processing, which consists of three stages in sequence. First, isotropic traveltime tomography is used for estimating the maximum horizontal velocity. Then, anisotropic traveltime tomography is used to invert for the anisotropic parameter, which is the normalized difference between the maximum horizontal velocity and the maximum vertical velocity. Finally, anisotropic waveform tomography is implemented to refine the maximum horizontal velocity. The cross-firing acquisition geometry significantly improves the ray coverage and results in a relatively even distribution of the ray density in the study area between two boreholes. Consequently, joint inversion of two crosshole seismic data sets improves the resolution and increases the reliability of the velocity model reconstructed by tomography.

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Section: Introductionmentioning

confidence: 80%

Crosshole seismic tomography with cross-firing geometry

et al. 2016

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“…Figure 4 is an actual anisotropic velocity model, V h ðx; zÞ and γðx; zÞ, reconstructed from seismic tomography of a field crosshole seismic data set (Rao and Wang, 2011). For ray tracing in such com- Seismic ray tracing in anisotropic media T5 plicated anisotropic media, when using the minimum-time constraint in step length (AEc β ) selection, a low time limit is also needed, to ensure that the update is not too far away from the current position and thus to secure a steady convergence for such a high nonlinear problem.…”

Section: Ray Tracing In Anisotropic Modelsmentioning

confidence: 99%

Seismic ray tracing in anisotropic media: A modified Newton algorithm for solving highly nonlinear systems

Wang

2014

GEOPHYSICS

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Seismic ray tracing with a path-bending method leads to a nonlinear system that has much stronger nonlinearity in anisotropic media than the counterpart in isotropic media. Any path perturbation causes changes to directional velocities, which depend not only upon the spatial position but also upon the local propagation direction in anisotropic media. To combat the high nonlinearity of the problem, the Newton-type iterative algorithm is modified by enforcing Fermat's minimum-time principle as a constraint for the solution update, instead of conventional error minimization in the nonlinear system. As the algebraic problem is incorporated with the physical principle, it is able to stabilize the solution for such a highly nonlinear problem as ray tracing in realistically complicated anisotropic media. With this modified algorithm, two ray-tracing schemes are presented. The first scheme involves newly derived raypath equations, which are approximate for anisotropic media but the minimum-time constraint will ensure that the solution steadily converges to the true solution. The second scheme is based on the minimal variation principle. It is more efficient than the first one as it solves a tridiagonal system and does not need to compute the Jacobian and its inverse in each iteration. Even in this second scheme, Fermat's minimum-time constraint is employed for the solution update, so as to guarantee a robust convergence of the iterative solution in anisotropic media.

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“…6(b) is γ (x, z), the anisotropy parameter. This anisotropic velocity model is constructed from crosshole seismic waveform tomography (Rao & Wang 2011). Slowness paths and wave fronts of two shots at depths 100 m from the top and the bottom of the model (as shown in Fig.…”

Section: Wav E F Ro N T Ta N G E N T I a L Smentioning

confidence: 99%

Simultaneous computation of seismic slowness paths and the traveltime field in anisotropic media

Wang¹

2013

Geophysical Journal International

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This paper presents a novel system for computing seismic slowness paths and the traveltime field simultaneously in anisotropic media, in which the ray path concept is replaced with the concept of slowness paths. Like ray paths in isotropic media, slowness paths are orthogonal to the wave fronts in anisotropic media. The novelty of the proposed system relies on the explicit normal constraint that slowness vectors are perpendicular to wave fronts. While the system finds the positions of sequential wave fronts with a constant time interval, samples of consecutive wave fronts represent slowness paths which are normal to wave fronts and follow phase velocities in anisotropic media. The simultaneous calculation can remove any shadow zones where paths might fail to emerge by path-tracing and meanwhile avoid the instability problem in conventional eikonal-equation solution for traveltimes. While any differential discontinuity (such as cusps in a wave front) causes numerical instability, it is dealt with by a least-squares smoothing strategy along the wave front. The feasibility is demonstrated using numerical examples from simple to realistic anisotropic models.

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Crosshole seismic tomography including the anisotropy effect

Cited by 12 publications

References 15 publications

Crosshole seismic tomography with cross-firing geometry

Crosshole seismic tomography with cross-firing geometry

Seismic ray tracing in anisotropic media: A modified Newton algorithm for solving highly nonlinear systems

Simultaneous computation of seismic slowness paths and the traveltime field in anisotropic media

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