3-D true‐amplitude finite‐offset migration

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1112-1126 ◽  
Author(s):  
Jorg Schleicher ◽  
Martin Tygel ◽  
Peter Hubral
Keyword(s):  
Weight Function ◽  
A Priori ◽  
Three Dimensional ◽  
Reflection Coefficients ◽  
Ray Theory ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Prestack Migration ◽  
The One ◽  
Paraxial Ray

Compressional primary nonzero offset reflections can be imaged into three‐dimensional (3-D) time or depth‐migrated reflections so that the migrated wavefield amplitudes are a measure of angle‐dependent reflection coefficients. Various migration/inversion algorithms involving weighted diffraction stacks recently proposed are based on Born or Kirchhoff approximations. Here a 3-D Kirchhoff‐type prestack migration approach is proposed where the primary reflections of the wavefields to be imaged are a priori described by the zero‐order ray approximation. As a result, the principal issue in the attempt to recover angle‐dependent reflection coefficients becomes the removal of the geometrical spreading factor of the primary reflections. The weight function that achieves this aim is independent of the unknown reflector and correctly accounts for the recovery of the source pulse in the migrated image irrespective of the source‐receiver configurations employed and the caustics occurring in the wavefield. Our weight function, which is computed using paraxial ray theory, is compared with the one of the inversion integral based on the Beylkin determinant. It differs by a factor that can be easily explained.

Controlling amplitudes in 2.5D common‐shot migration to zero offset

Geophysics ◽  
2004 ◽  
Vol 69 (5) ◽  
pp. 1299-1310 ◽  
Author(s):  
Jörg Schleicher ◽  
Claudio Bagaini
Keyword(s):  
Wave Propagation ◽  
Weight Function ◽  
Seismic Data ◽  
Constant Velocity ◽  
A Priori ◽  
Weight Functions ◽  
A Priori Knowledge ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Zero Offset

Configuration transform operations such as dip moveout, migration to zero offset, and shot and offset continuation use seismic data recorded with a certain measurement configuration to simulate data as if recorded with other configurations. Common‐shot migration to zero offset (CS‐MZO), analyzed in this paper, transforms a common‐shot section into a zero‐offset section. It can be realized as a Kirchhoff‐type stacking operation for 3D wave propagation in a 2D laterally inhomogeneous medium. By application of suitable weight functions, amplitudes of the data are either preserved or transformed by replacing the geometrical‐spreading factor of the input reflections by the correct one of the output zero‐offset reflections. The necessary weight function can be computed via 2D dynamic ray tracing in a given macrovelocity model without any a priori knowledge regarding the dip or curvature of the reflectors. We derive the general expression of the weight function in the general 2.5D situation and specify its form for the particular case of constant velocity. A numerical example validates this expression and highlights the differences between amplitude preserving and true‐amplitude CS‐MZO.

Three‐dimensional true‐amplitude zero‐offset migration

Geophysics ◽  
1991 ◽  
Vol 56 (1) ◽  
pp. 18-26 ◽  
Author(s):  
Peter Hubral ◽  
Martin Tygel ◽  
Holger Zien
Keyword(s):  
Time Derivative ◽  
Three Dimensional ◽  
Normal Incidence ◽  
Earth Model ◽  
Ray Theory ◽  
Transmission Losses ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Time Migration ◽  
Zero Offset

The primary zero‐offset reflection of a point source from a smooth reflector within a laterally inhomogeneous velocity earth model is (within the framework of ray theory) defined by parameters pertaining to the normal‐incidence ray. The geometrical‐spreading factor—usually computed along the ray by dynamic‐ray tracing in a forward‐modeling approach—can, in this case, be recovered from traveltime measurements at the surface. As a consequence, zero‐offset reflections can be time migrated such that the geometrical‐spreading factor for the normal‐incidence ray is removed. This leads to a so‐called “true‐amplitude time migration.” In this work, true‐amplitude time‐migrated reflections are obtained by nothing more than a simple diffraction stack essentially followed by a time derivative of the diffraction‐stack traces. For small transmission losses of primary zero‐offset reflections through intermediate‐layer boundaries, the true‐amplitude time‐migrated reflection provides a direct measure of the reflection coefficient at the reflecting lower end of the normal‐incidence ray. The time‐migrated field can be easily transformed into a depth‐migrated field with the help of image rays.

Computing true amplitude reflections in a laterally inhomogeneous earth

Geophysics ◽  
1983 ◽  
Vol 48 (8) ◽  
pp. 1051-1062 ◽  
Author(s):  
Peter Hubral
Keyword(s):  
Three Dimensional ◽  
Physical Experiment ◽  
Reflection Coefficients ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Seismic Section ◽  
Earth Models ◽  
Reflecting Boundaries ◽  
The Common ◽  
Zero Offset

Recently Bortfeld (1982) gave a cursory nonmathematical introduction to a procedure for computing the geometrical spreading factor of a primary zero‐offset reflection from the common datum point traveltime measurements of the event. To underline the significance and consequences of this method, a derivation and discussion of geometrical spreading factors is now given for two‐ and three‐dimensional earth models with curved reflecting boundaries. The spreading factors can be used easily to transform primary reflections in a zero‐offset seismic section to true amplitude reflections. These permit an estimation of interface reflection coefficients, either directly or in connection with a true amplitude migration. A seismic section with true amplitude reflections can be described by one physical experiment: the tuned reflector model. Hence the application of the wave equation (in connection with a migration after stack) is justified on such a seismic section. Also the geometrical spreading factors that are derived can be looked upon as a generalization of a well‐known formula (Newman, 1973), which is commonly used in true amplitude processing and trace inversion in the presence of a vertically inhomogeneous earth.

3-D prestack migration in anisotropic media

Geophysics ◽  
1993 ◽  
Vol 58 (1) ◽  
pp. 79-90 ◽  
Author(s):  
Zhengxin Dong ◽  
George A. McMechan
Keyword(s):  
A Priori ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Anisotropic Media ◽  
P Wave ◽  
Common Source ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Prestack Migration ◽  
Time Migration

A three‐dimensional (3-D) prestack reverse‐time migration algorithm for common‐source P‐wave data from anisotropic media is developed and illustrated by application to synthetic data. Both extrapolation of the data and computation of the excitation‐time imaging condition are implemented using a second‐order finite‐ difference solution of the 3-D anisotropic scalar‐wave equation. Poorly focused, distorted images are obtained if data from anisotropic media are migrated using isotropic extrapolation; well focused, clear images are obtained using anisotropic extrapolation. A priori estimation of the 3-D anisotropic velocity distribution is required. Zones of anomalous, directionally dependent reflectivity associated with anisotropic fracture zones are detectable in both the 3-D common‐ source data and the corresponding migrated images.

Obtaining three‐dimensional velocity information directly from reflection seismic data: An inverse scattering formalism

Geophysics ◽  
1981 ◽  
Vol 46 (8) ◽  
pp. 1116-1120 ◽  
Author(s):  
A. B. Weglein ◽  
W. E. Boyse ◽  
J. E. Anderson
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Inverse Scattering ◽  
Seismic Data ◽  
A Priori ◽  
Three Dimensional ◽  
Quantum Scattering ◽  
Acoustic Wave Equation ◽  
Reflection Seismic ◽  
The One

We present a formalism for obtaining the subsurface velocity configuration directly from reflection seismic data. Our approach is to apply the results obtained for inverse problems in quantum scattering theory to the reflection seismic problem. In particular, we extend the results of Moses (1956) for inverse quantum scattering and Razavy (1975) for the one‐dimensional (1-D) identification of the acoustic wave equation to the problem of identifying the velocity in the three‐dimensional (3-D) acoustic wave equation from boundary value measurements. No a priori knowledge of the subsurface velocity is assumed and all refraction, diffraction, and multiple reflection phenomena are taken into account. In addition, we explain how the idea of slant stack in processing seismic data is an important part of the proposed 3-D inverse scattering formalism.

TRANSPORT EQUATIONS WITH UNBOUNDED FORCE FIELDS AND APPLICATION TO THE VLASOV–POISSON EQUATION

2009 ◽  
Vol 19 (02) ◽  
pp. 199-228 ◽  
Author(s):  
DELPHINE SALORT
Keyword(s):  
Initial Data ◽  
Poisson Equation ◽  
Force Fields ◽  
A Priori ◽  
Kinetic Equations ◽  
Three Dimensional ◽  
Transport Equations ◽  
New Approach ◽  
The One ◽  
The Cost

The aim of this paper is to give new dispersive tools for certain kinetic equations. As an application, we study the three-dimensional Vlasov–Poisson equation for initial data having strictly less than six moments in [Formula: see text] where the nonlinear term E is a priori unbounded. We prove via new dispersive effects that in fact the force field E is smooth in space at the cost of a localization in a ball and an averaging in time. We deduce new conditions to bound the density ρ in L∞ and to have existence and uniqueness of global weak solutions of the Vlasov–Poisson equation with bounded density for initial data strictly less than six moments in [Formula: see text]. The proof is based on a new approach which consists in establishing a priori dispersion estimates (moment effects) on the one hand for linear transport equations with unbounded force fields and on the other hand along the trajectories of the Vlasov–Poisson equation.

Geometrical spreading corrections of offset reflections in a laterally inhomogeneous earth

Geophysics ◽  
1992 ◽  
Vol 57 (8) ◽  
pp. 1054-1063 ◽  
Author(s):  
M. Tygel ◽  
J. Schleicher ◽  
P. Hubral
Keyword(s):  
Three Dimensional ◽  
Velocity Model ◽  
Earth Model ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Depth Migration ◽  
Avo Analysis ◽  
Amplitude Versus Offset ◽  
One Step

Compressional primary seismic nonzero offset reflections are the most essential wavefield attributes used in seismic parameter estimation and imaging. We show how the determination of angle‐dependent reflection coefficients can be addressed from identifying such events for arbitrarily curved three‐dimensional (3-D) subsurface reflectors below a laterally inhomogeneous layered overburden. More explicitly, we show how the geometrical‐spreading factor along a reflected primary ray with offset can be calculated from the identified (i.e., picked) traveltimes of offset primary reflections. Seismic traces in which all primary reflections are corrected with the geometrical‐spreading factor are, as is well‐known, referred to as true‐amplitude traces. They can be constructed without any knowledge of the velocity distribution in the earth model. Apart from possibly finding a direct application in an amplitude‐versus‐offset (AVO) analysis, the theory developed here can be of use to derive true‐amplitude time‐ and depth‐migration methods for various seismic data acquisition configurations, which pursue the aim of performing the wavefield migration (based upon the use of a macro‐velocity model) and the AVO analysis in one step.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Sea Urchins and Circuses: The Modernist Natural Histories of Jean Painlevé and Alexander Calder

2018 ◽  
Vol 13 (2) ◽  
pp. 187-211
Author(s):  
Patricia E. Chu
Keyword(s):  
New Media ◽  
Sea Urchins ◽  
Life Sciences ◽  
Three Dimensional ◽  
Machine Age ◽  
Avant Garde ◽  
History Of ◽  
And Performance ◽  
The One ◽  
Natural Historian

The Paris avant-garde milieu from which both Cirque Calder/Calder's Circus and Painlevé’s early films emerged was a cultural intersection of art and the twentieth-century life sciences. In turning to the style of current scientific journals, the Paris surrealists can be understood as engaging the (life) sciences not simply as a provider of normative categories of materiality to be dismissed, but as a companion in apprehending the “reality” of a world beneath the surface just as real as the one visible to the naked eye. I will focus in this essay on two modernist practices in new media in the context of the history of the life sciences: Jean Painlevé’s (1902–1989) science films and Alexander Calder's (1898–1976) work in three-dimensional moving art and performance—the Circus. In analyzing Painlevé’s work, I discuss it as exemplary of a moment when life sciences and avant-garde technical methods and philosophies created each other rather than being classified as separate categories of epistemological work. In moving from Painlevé’s films to Alexander Calder's Circus, Painlevé’s cinematography remains at the forefront; I use his film of one of Calder's performances of the Circus, a collaboration the men had taken two decades to complete. Painlevé’s depiction allows us to see the elements of Calder's work that mark it as akin to Painlevé’s own interest in a modern experimental organicism as central to the so-called machine-age. Calder's work can be understood as similarly developing an avant-garde practice along the line between the bestiary of the natural historian and the bestiary of the modern life scientist.

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