• Geophysics and Geophysical Exploration
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• v.1 no.2
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• pp.116-126
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• 1998

I present a datuming scheme for poststack data that uses wavefield depth extrapolation. The method I have developed allows the use of any depth extrapolation technique, such as phase-shift, split-step, and finite-difference extrapolation. I derive the datuming algorithms by transposing and taking the complex conjugate (i.e. taking adjoint) of the corresponding forward modeling operator, which does upward extrapolation from a flat surface to an irregular surface. The exact adjoint relation between the forward modeling operator and the datuming operator is demonstrated algebraically. Testing the poststack datuming algorithms with synthetic data, using several depth extrapolation algorithms, has shown that the method works well.

• Geophysics and Geophysical Exploration
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• v.2 no.1
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• pp.54-62
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• 1999

This paper describes a datuming scheme for a prestack dataset which uses wavefield depth extrapolation. The formulation of the prestack datuming algorithm is performed by finding the adjoint operator to the corresponding forward prestack wavefield extrapolation from a flat surface to an irregular surface. Here I used double-square-root (DSR) equation to extrapolate wavefield in prestack sense. This correspond to the forward model of the well known `survey sinking` prestack imaging algorithm.

• The Korean Journal of Petroleum Geology
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• v.1 no.1 s.1
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• pp.47-52
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• 1993

A method and results of computations are presented for the 2-D seismic migration process in the frequency-wavenumber domain for the laterally and vertically inhomogeneous medium. In order to take the intrinsic attenuation effect into account in the migration process the complex-valued wave velocity is used in the wavefield extrapolation operator, improving the generalized frequency-wavenumber migration technique. The imaginary part of the complex-valued wave velocity includes the seismic quality factor Q value. In derivation of the solution of the wave equation for the medium of inhomogeneous wave velocity and anelasticity, the inhomogeneous medium is mathematically converted to an equivalent system which consists of a homogeneous medium of averaged slowness and an inhomogeneous distribution of hypothetical wave source. The strength of the hypothetical wave source depends on the deviation of squared slowness from the averaged value of the medium. Results of numerical computation using the technique show more distinct geologic images than those using the convensional generalized frequency-wavenumber migration. Especially, the obscured images due to the wave attenuation by anelasticity are restored to show sharp boundaries of structures. The method will be useful in the imaging of the reflection data obtained in the regions of possible petroleum or natural gas reservoir and of fractured zone.

• Geophysics and Geophysical Exploration
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• v.10 no.2
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• pp.111-123
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• 2007

Unlike the conventional reverse time migration method which is implemented by simply extrapolating wavefield in reverse time, this paper presents a derivation of another reverse time migration operator as the exact adjoint of the presumed forward wavefield extrapolation operator. The adjoint operator is obtained by formulating the forward time extrapolation operator in an explicit matrix equation form and then taking the adjoint to this matrix equation followed by determining the corresponding operator. The reverse time migration operator as the exact adjoint to the implied forward operator can be used not only as a migration algorithm but also as an adjoint operator which is required in the imaging through an inversion such as least-squares migration.

• Geophysics and Geophysical Exploration
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• v.3 no.2
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• pp.70-75
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• 2000

In the seismic migration, Kirchhoff and reverse time migration are used in general. In the reverse time migration using wave equation, two-way and one-way wave equation are applied. The approach of one-way wave equation uses approximately computed downward continuation extrapolator, it need tess amounts of calculations and core memory in compared to that of two-way wave equation. In this paper, we applied one-way wave equation to pre-stack reverse time migration. In the frequency-space domain, forward propagation of source wavefield and back propagration of measured wavefield were executed by using monochromatic one-way wave equation, and zero-lag cross correlation of two wavefield resulted in the image of subsurface. We had implemented prestack migration on a massively parallel processors (MPP) CRAYT3E, and knew the algorithm studied here is efficiently applied to the prestck migration due to its suitability for parallelization.