Demigration and migration in isotropic inhomogeneous media

Jaramillo, Herman

doi:10.1190/1.1885748

Cited by 3 publications

(5 citation statements)

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“…Thus, Kirchhoff demigration (8) can be conceived as an (asymptotic) inverse to Kirchhoff migration (4). Motivated by the work of Tygel et al (1996), Jaramillo and Bleistein (1997) show that the Kirchhoff modeling and demigration integrals (1) and (8) are asymptotically equivalent to each other. This means their leading-order, ray-theory contributions coincide.…”

Section: True-amplitude Demigrationmentioning

confidence: 97%

“…Although the two integrals describing Kirchhoff forward modeling and Kirchhoff demigration both appear to be inverses to Kirchhoff migration in an asymptotic sense, they do not exactly coincide. Jaramillo and Bleistein (1997) investigate their relationship. They show that both integrals possess the same stationary points (i.e., specular reflection points) and that their integrands are identical at these points.…”

Section: Introductionmentioning

confidence: 99%

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Seismic modeling by demigration

et al. 2000

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Kirchhoff‐type, isochron‐stack demigration is the natural asymptotic inverse to classical Kirchhoff or diffraction‐stack migration. Both stacking operations can be performed in true amplitude by an appropriate selection of weight functions. Isochron‐stack demigration is closely related to seismic modeling with the Kirchhoff integral. The principal objective of this paper is to show how demigration can be used to compute synthetic seismograms. The idea is to attach to each reflector in the model an appropriately stretched (i.e., frequency‐shifted) spatial wavelet. Its amplitude is proportional to the reflection coefficient, transforming the original reflector model into an artificially constructed true‐amplitude, depth‐migrated section. The seismic modeling is then realized by a true‐amplitude demigration operation applied to this artificially constructed migrated section. A simple but typical synthetic data example indicates that modeling by demigration yields results superior to conventional zero‐order ray theory or classical Kirchhoff modeling.

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Section: True-amplitude Demigrationmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Seismic modeling by demigration

et al. 2000

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“…The research was initially motivated by a need to develop a specific technology and computer software for TZO in a depth‐dependent earth model. The application has been reported on by Jaramillo (1998) and Jaramillo and Bleistein (1998, 1999). It extends the earlier NMO/DMO process in a depth‐dependent background of Hale and Artley (1993) and Artley and Hale (1994) to a true‐amplitude process.…”

Section: Introductionmentioning

confidence: 93%

“…However, we exploit an approximation of the obliquity factor in the Kirchhoff model that allows us to push the transformation process further than the results of the motivating papers. In a companion paper ( Jaramillo and Bleistein 1999), the authors have derived a migration/demigration formalism in the space–time domain, based on the generalized Radon transform inversion technique. Jaramillo (1998) and Jaramillo and Bleistein (1998) extended that work to a data mapping formalism in the space–time domain.…”

Section: Introductionmentioning

confidence: 99%

“…Tygel et al . (1998 ), Jaramillo (1998) and Jaramillo and Bleistein (1998, 1999) carried out this process in the space–time domain, while a space–frequency domain derivation, partially described by Bleistein and Jaramillo (1998), is presented here. An advantage of space–time methods is that the time‐domain integral produces a delta function that essentially reduces the dimension of the space‐domain integration.…”

Section: Introductionmentioning

confidence: 99%

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A platform for Kirchhoff data mapping in scalar models of data acquisition

Bleistein

Jaramillo

2000

Geophysical Prospecting

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Kirchhoff data mapping (KDM) is a procedure for transforming data from a given input source/receiver configuration and background earth model to data corresponding to a different output source/receiver configuration and background model. The generalization of NMO/DMO, datuming and offset continuation are three examples of KDM applications. This paper describes a ‘platform’ for KDM for scalar wavefields. The word, platform, indicates that no calculations are carried out in this paper that would adapt the derived formula to any one of a list of KDMs that are presented in the text. Platform formulae are presented in 3D and in 2.5D. For the latter, the validity of the platform equation is verified — within the constraints of high‐frequency asymptotics — by applying it to a Kirchhoff approximate representation of the upward scattered data from a single reflector and for an arbitrary source/receiver configuration. The KDM formalism is shown to map this Kirchhoff model data in the input source/receiver configuration to Kirchhoff data in the output source/receiver configuration, with one exception. The method does not map the reflection coefficient. Thus, we verify that, asymptotically, the ray theoretical geometrical spreading effects due to propagation and reflection (including reflector curvature) are mapped by this formalism, consistent with the input and output modelling parameters, while the input reflection coefficient is preserved. In this sense, this is a ‘true‐amplitude’ formalism. As with earlier Kirchhoff inversion, a slight modification of the kernel of KDM provides alternative integral operators for estimating the specular reflection angle, both in the input configuration and in the output configuration, thereby providing a basis for amplitude‐versus‐angle analysis of the data.

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2007

Seismic True-Amplitude Imaging

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Demigration and migration in isotropic inhomogeneous media

Abstract: S u m m a r yWe derive inverse migration (demigration) and migration operators from the Kirchhoff modelingformula (Scales, 1995) representation. Using the superposition principle, we obtain two alternative (demigration and migration) operators.

Cited by 3 publications

References 13 publications

Seismic modeling by demigration

Seismic modeling by demigration

A platform for Kirchhoff data mapping in scalar models of data acquisition

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