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3D hybrid DEPTH MIGRATION AND FOUR-WAY SPLITTING SCHEMES

Journal of Computational Mathematics 2006年第4期24卷 463-474页

作者： Wen-sheng Zhang Guan-quan Zhang LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China

The alternately directional implicit （ADI） scheme is usually used in 3D depth migration. It splits the 3D square-root operator along crossline and inline directions alternately. In this paper, based on the ideal of data line, the four-way splitting schemes and their splitting errors for the finite-difference （FD） method.and the hybrid method.are investigated. The wavefield extrapolation of four-way splitting scheme is accomplished on a data line and is stable unconditionally. Numerical analysis of splitting errors show that the two-way FD migration have visible numerical anisotropic errors, and that four-way FD migration has much less splitting errors than two-way FD migration has. For the hybrid method. the differences of numerical anisotropic errors between two-way scheme and four-way scheme are small in the case of lower lateral velocity variations. The schemes presented in this paper can be used in 3D post-stack or prestack depth migration. Two numerical calculations of 3D depth migration are completed. One is the four-way FD and hybrid 3D post-stack depth migration for an impulse response, which shows that the anisotropic errors can be eliminated effectively in the cases of constant and variable velocity variations. The other is the 3D shot-profile prestack depth migration for SEG/EAEG benchmark model with two-way hybrid splitting scheme, which presents good imaging results. The Message Passing Interface （MPI） programme based on shot number is adopted.

关键词： 3D depth migration Multiway splitting Data line Wavefield computation Finite-difference hybrid method.

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Numerical Study of Singularity Formation in Relativistic Euler Flows

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Communications in Computational Physics 2014年第7期16卷 348-364页

作者： Pierre A.Gremaud Yi Sun Department ofMathematics North Carolina State UniversityRaleighNC27695USA Department of Mathematics University of South CarolinaColumbiaSC 29208USA.

The formation of singularities in relativistic flows is not well *** solutions to the relativistic Euler equations are known to have a finite lifespan;the possible breakdown mechanisms are shock formation,violation of the subluminal conditions andmass *** propose a new hybrid Glimm/centralupwind scheme for relativistic *** scheme is used to numerically investigate,for a family of problems,which of the above mechanisms is involved.

关键词： Relativistic Euler equations singularity formation Glimm scheme central-upwind scheme hybrid method.

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