An Iterative Method for the Inversion of the Two-Dimensional Wave Equation with a Potential

Zhang, Guanquan

doi:10.1006/jcph.1998.9996

Cited by 2 publications

(2 citation statements)

References 20 publications

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“…The first issue that arises is how to numerically calculate the pseudo-differential operator Λ defined in Eq.(53). In Zhang [29,32,33] , it is shown that Λ can be explicitly expressed as a differential-integral operator…”

Section: True Amplitude Common-shot Migration Based On True Amplitudementioning

confidence: 99%

The Theory of True Amplitude One‐Way Wave Equation Migrations

2006

Chinese J of Geophysics

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In this technical report, we review the recent development of true amplitude one-way wave equation migration and summarize the migrated amplitude performance from different one-way wave equations. To produce correct amplitude from postack phase-shift migration, we have to apply accurate geometrical spreading compensation in preprocessing. Although Dubrulle's common-offset phase-shift migration gives correct imaging position, it is not a true amplitude migration except for zero offset or flat reflectors. We have shown that the conventional common-shot one-way wave equation migration does not produce correct migration amplitude. Based on the true amplitude one-way wave equations and the surface boundary condition corrections, we have developed true amplitude common-shot migration and have proved that it produces an inversion output that agrees asymptotically to Kirchhoff inversion. In the next step, we propose a way to obtain true amplitude common-angle image gathers from both single-square-root and double-square-root wave equation migrations. Our analysis indicates that the pUp * D imaging condition is a good candidate to produce true amplitude angle domain common imaging gathers. Compared to the pU/pD imaging condition which is required for true amplitude common-shot migration, the new approach suggests a more stable way of doing inversion and is more attractive to the real seismic data processing.

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Section: True Amplitude Common-shot Migration Based On True Amplitudementioning

confidence: 99%

The Theory of True Amplitude One‐Way Wave Equation Migrations

2006

Chinese J of Geophysics

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“…For the some numerical aspects of inverse initialboundary value problems for the two and multidimensional wave equations are considered in [16][17][18][19], and [20].…”

Section: Introductionmentioning

confidence: 99%

Zamana bağlı potansiyeli olan dikdörtgen bir zarın zorlanmış çapraz titreşimi için bir ters problem

Tekin¹

2020

Deu Muhendislik Fakultesi Fen Ve Muhendislik

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In this paper, an initial-boundary value problem for a two-dimensional wave equation which arises in the equation of motion for the forced transverse vibration of a rectangular membrane is considered. Giving an additional condition, a time-dependent coefficient is determined and existence and uniqueness theorem for small times is proved. Moreover, characterization of the conditional stability is given and numerical solution of the inverse problem investigated by using finite difference method.

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An Iterative Method for the Inversion of the Two-Dimensional Wave Equation with a Potential

Cited by 2 publications

References 20 publications

The Theory of True Amplitude One‐Way Wave Equation Migrations

The Theory of True Amplitude One‐Way Wave Equation Migrations

Zamana bağlı potansiyeli olan dikdörtgen bir zarın zorlanmış çapraz titreşimi için bir ters problem

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