Anisotropic Crosshole+VSP Traveltime Tomography Through Triangular Cell Model with a Normalized Jacobian Matrix and Multistage Inversion Strategy

He, Leiyu; Bai, Chao-ying; Wang, Di

doi:10.1007/s00024-018-1953-3

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Pure Appl. Geophys.

2018

DOI: 10.1007/s00024-018-1953-3

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Anisotropic Crosshole+VSP Traveltime Tomography Through Triangular Cell Model with a Normalized Jacobian Matrix and Multistage Inversion Strategy

Leiyu He

Chao-ying Bai

Di Wang

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Cited by 2 publications

References 35 publications

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Analytic formula for the group velocity and its derivatives with respect to elastic moduli for a general anisotropic medium

Wang

Bai

et al. 2023

GEOPHYSICS

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Studying the anisotropy of seismic wave velocity can provide a theoretical basis for understanding the characteristics of seismic wave propagation in anisotropic media, such as forward modeling of seismic wavefield and simultaneous inversion of anisotropic parameters. It is an important work to calculate the group velocities of three kinds of seismic waves (qP, qS1, and qS2) and the analytical expressions of the partial derivatives of the group velocities with respect to 21 elastic parameters in general anisotropic media. Therefore, a new relationship between the phase and group velocity in general anisotropic medium is introduced first, and then the analytical expressions of the group velocity of three kinds of waves are deduced. Then the analytical formulas of partial derivatives of group (or phase) velocity with respect to 21 elastic parameters are derived. Finally, the distribution of partial derivatives of group slowness with respect to 21 elastic parameters with varied ray angles is analyzed and discussed. The final analytical expressions of group velocity and its partial derivatives are relatively concise and can deal with the singular points and multivalued problems of qS waves. By comparing with the numerical solution of the eigenvector method, the accuracy of the analytical formula of group velocity and its partial derivatives with respect to elastic parameters are verified. The numerical simulation results show that the algorithm can accurately obtain the partial derivatives of group slowness with respect to 21 elastic parameters, and would provide a theoretical basis for seismic ray tracing and traveltime inversion in general anisotropic media.

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Analytic formula for the group velocity and its derivatives with respect to elastic moduli for a general anisotropic medium

Wang

Bai

et al. 2023

GEOPHYSICS

View full text Add to dashboard Cite

show abstract

Detect Multiple-Set Fractures by Crosshole Seismic Tomography for use in Environmental and Engineering Geophysics

Chang,

Tong

2024

JEEG

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Crosshole seismic tomography (CST) could be used to reconstruct the velocity section of media between two holes. One commonly used attribute of fractures reflected in seismic waves is the anisotropy of velocity. Therefore, in this study, the multiple symmetry axes of anisotropic media are utilized to simulate the multiple-set fractures in strata. The anisotropic algebraic reconstruction technique (AART) and anisotropic simultaneous iterative reconstruction technique (ASIRT), extensions of isotropic ART and SIRT, are developed to detect the medium with multiple symmetry axes and strong anisotropy. Full coverage of ray paths in azimuth is needed for these techniques. The performances of these techniques are tested by numerical and physical modeling. Testing results show that the proposed AART and ASIRT methods can successfully detect the multiple-set fractures when the observed data exceeds the estimated parameters. However, in complexly anisotropic and heterogeneous media, the estimation error will significantly increase when using these techniques if the number of estimated parameters is equal to or greater than the number of observed data.

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Anisotropic Crosshole+VSP Traveltime Tomography Through Triangular Cell Model with a Normalized Jacobian Matrix and Multistage Inversion Strategy

Cited by 2 publications

References 35 publications

Analytic formula for the group velocity and its derivatives with respect to elastic moduli for a general anisotropic medium

Analytic formula for the group velocity and its derivatives with respect to elastic moduli for a general anisotropic medium

Detect Multiple-Set Fractures by Crosshole Seismic Tomography for use in Environmental and Engineering Geophysics

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