A unified approach to acoustical reflection imaging. II: The inverse problem

1993 ◽  
Vol 93 (4) ◽  
pp. 2017-2023 ◽  
Author(s):  
A. J. Berkhout ◽  
C. P. A. Wapenaar
Keyword(s):  
Inverse Problem ◽  
Unified Approach ◽  
Reflection Imaging

A Unified approach to seismic reflection imaging

1994 ◽  
Author(s):  
M. Tygel ◽  
P. Hubral ◽  
J. Schleicher
Keyword(s):  
Seismic Reflection ◽  
Unified Approach ◽  
Reflection Imaging

scholarly journals Approximate Image Reconstruction in Landscape Reflection Imaging

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Rémi Régnier ◽  
Gaël Rigaud ◽  
Maï K. Nguyen
Keyword(s):  
Inverse Problem ◽  
Image Reconstruction ◽  
Inversion Formula ◽  
Imaging Modality ◽  
Reconstruction Algorithm ◽  
Reflectivity Function ◽  
Reconstruction Kernel ◽  
Simulation Results ◽  
Reflection Imaging ◽  
Present Simulation

Simple reflection imaging of landscape (scenery or extended objects) poses the inverse problem of reconstructing the landscape reflectivity function from its integrals on some particular family of spheres. Such data acquisition is encoded in the framework of a Radon transform on this family of spheres. In spite of the existence of an exact inversion formula, the numerical landscape reflectivity function reconstitution is best obtained with an approximate but judiciously chosen reconstruction kernel. We describe the working of this reflection imaging modality and its theoretical handling, introduce an efficient and stable image reconstruction algorithm, and present simulation results to prove the validity of this choice as well as to demonstrate the feasibility of this imaging process.

A Unified Approach to Seismic Reflection Imaging

1995 ◽  
Author(s):  
M. Tygel ◽  
P. Hubral ◽  
J. Schleicher
Keyword(s):  
Seismic Reflection ◽  
Unified Approach ◽  
Reflection Imaging

To: “A unified approach to 3-D seismic reflection imaging, Part II: Theory” (M. Tygel, J. Schleicher, and P. Hubral, GEOPHYSICS, 61, 759–775)

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 670-673 ◽  
Author(s):  
Herman Jaramillo ◽  
Jörg Schleicher ◽  
Martin Tygel
Keyword(s):  
Seismic Reflection ◽  
Projection Matrix ◽  
Unified Approach ◽  
The Subject ◽  
Reflection Imaging

It came to our attention that in the paper of Tygel et al. (1996), formula (A-5) is incorrect. First, it is different from the cited equation (17) of Tygel et al. (1995). Second, the derivation of formula (17) in Appendix A of Tygel et al. (1995) is invalid for the purposes of Tygel et al., (1996) because in the 1995 paper, a rotation is treated, whereas in Tygel et al. (1996), a projection matrix is needed. Further investigation of the subject was needed to resolve these inconsistencies.

scholarly journals A unified approach to acoustical reflection imaging

1992 ◽  
Vol 92 (4) ◽  
pp. 2446-2446 ◽  
Author(s):  
A. J. Berkhout
Keyword(s):  
Unified Approach ◽  
Reflection Imaging

Inverse problem on a tree-shaped network: unified approach for uniqueness

2014 ◽  
Vol 94 (11) ◽  
pp. 2370-2395 ◽  
Author(s):  
Lucie Baudouin ◽  
Masahiro Yamamoto
Keyword(s):  
Inverse Problem ◽  
Unified Approach

A unified approach to 3-D seismic reflection imaging, Part II: Theory

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 759-775 ◽  
Author(s):  
Martin Tygel ◽  
Jörg Schleicher ◽  
Peter Hubral
Keyword(s):  
Seismic Reflection ◽  
Seismic Imaging ◽  
Velocity Model ◽  
Image Transformation ◽  
Unified Approach ◽  
Imaging Theory ◽  
Reflection Imaging ◽  
Transformation Problems

Diffraction‐stack and isochrone‐stack integrals are quantitatively described and employed. They constitute an asymptotic transform pair. Both integrals are the key tools of a unified approach to seismic reflection imaging that can be used to solve a multitude of amplitude‐preserving, target‐oriented seismic imaging (or image‐transformation) problems. These include, for instance, the generalizations of the kinematic map‐transformation examples discussed in Part I. All image‐transformation problems can be addressed by applying both stacking integrals in sequence, whereby the macro‐velocity model, the measurement configuration, or the ray‐code of the considered elementary reflections may change from step to step. This leads to weighted (Kirchhoff‐ or generalized‐Radon‐type) summations along certain stacking surfaces (or inplanats) for which true‐amplitude (TA) weights are provided. To demonstrate the value of the proposed imaging theory (which is based on analytically chaining the two stacking integrals and using certain inherent dualities), we examine in detail the amplitude‐preserving configuration transform and remigration for the case of a 3-D laterally inhomogeneous velocity medium.

A unified approach to 3-D seismic reflection imaging, Part I: Basic concepts

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 742-758 ◽  
Author(s):  
Peter Hubral ◽  
Jörg Schleicher ◽  
Martin Tygel
Keyword(s):  
Time Domain ◽  
Seismic Reflection ◽  
Velocity Model ◽  
Unified Approach ◽  
Seismic Record ◽  
Kirchhoff Type ◽  
Velocity Models ◽  
Reflection Imaging ◽  
The Time Domain ◽  
Image Transformations

Given a 3-D seismic record for an arbitrary measurement configuration and assuming a laterally and vertically inhomogeneous, isotropic macro‐velocity model, a unified approach to amplitude‐preserving seismic reflection imaging is provided. This approach is composed of (1) a weighted Kirchhoff‐type diffraction‐stack integral to transform (migrate) seismic reflection data from the measurement time domain into the model depth domain, and of (2) a weighted Kirchhoff‐type isochrone‐stack integral to transform (demigrate) the migrated seismic image from the depth domain back into the time domain. Both the diffraction‐stack and isochrone‐stack integrals can be applied in sequence (i.e., they can be chained) for different measurement configurations or different velocity models to permit two principally different amplitude‐preserving image transformations. These are (1) the amplitude‐preserving transformation (directly in the time domain) of one 3-D seismic record section into another one pertaining to a different measurement configuration and (2) the transformation (directly in the depth domain) of a 3-D depth‐migrated image into another one for a different (improved) macro‐velocity model. The first transformation is referred to here as a “configuration transform” and the second as a “remigration.” Additional image transformations arise when other parameters, e.g., the ray code of the elementary wave to be imaged, are different in migration and demigration. The diffraction‐ and isochrone‐stack integrals incorporate a fundamental duality that involves the relationship between reflectors and the corresponding reflection‐time surfaces. By analytically chaining these integrals, each of the resulting image transformations can be achieved with only one single weighted stack. In this way, generalized‐Radon‐transform‐type stacking operators can be designed in a straightforward way for many useful image transformations. In this Part I, the common geometrical concepts of the proposed unified approach to seismic imaging are presented in simple pictorial, nonmathematical form. The more thorough, quantitative description is left to Part II.

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