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.

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.

Transformation to zero offset for mode‐converted waves

Geophysics ◽  
1992 ◽  
Vol 57 (3) ◽  
pp. 474-477 ◽  
Author(s):  
Mohammed Alfaraj ◽  
Ken Larner
Keyword(s):  
Seismic Data ◽  
Constant Velocity ◽  
Reflection Point ◽  
P Waves ◽  
S Waves ◽  
Nmo Correction ◽  
Converted Waves ◽  
Zero Offset ◽  
Correct Data

The transformation to zero offset (TZO) of prestack seismic data for a constant‐velocity medium is well understood and is readily implemented when dealing with either P‐waves or S‐waves. TZO is achieved by inserting a dip moveout (DMO) process to correct data for the influence of dip, either before or after normal moveout (NMO) correction (Hale, 1984; Forel and Gardner, 1988). The TZO process transforms prestack seismic data in such a way that common‐midpoint (CMP) gathers are closer to being common reflection point gathers after the transformation.

scholarly journals Subglacial seismic reflection strategies when source amplitude and medium attenuation are poorly known

2009 ◽  
Vol 55 (193) ◽  
pp. 931-937 ◽  
Author(s):  
Charles W. Holland ◽  
Sridhar Anandakrishnan
Keyword(s):  
Reflection Coefficient ◽  
Physical Properties ◽  
Seismic Data ◽  
Seismic Reflection ◽  
A Priori ◽  
Normal Incidence ◽  
A Priori Knowledge ◽  
New Methods ◽  
Attenuation Profile ◽  
Lack Of Knowledge

AbstractSeismic reflection techniques are a powerful way to probe physical properties of subglacial strata. Inversion of seismic data for physical properties may be hampered, however, by lack of knowledge of the source amplitude as well as lack of knowledge of the compressional and shear attenuation in the ice. New methods are described to measure the source signature that require no a priori knowledge of the ice attenuation profile. Another new method is described to obtain the angular dependence of the subglacial bed reflection coefficient that is relatively insensitive to knowledge of the ice attenuation. Finally, a correction is provided to a long-standing error in the literature regarding measurement of the bed normal incidence reflection coefficient.

2.5-D true‐amplitude Kirchhoff migration to zero offset in laterally inhomogeneous media

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 557-573 ◽  
Author(s):  
Martin Tygel ◽  
Jörg Schleicher ◽  
Peter Hubral ◽  
Lúcio T. Santos
Keyword(s):  
Seismic Source ◽  
Velocity Model ◽  
Dynamic Effects ◽  
Geometrical Spreading ◽  
Spreading Factor ◽  
Seismic Section ◽  
Kirchhoff Migration ◽  
Reflection Angle ◽  
Earth Models ◽  
Zero Offset

The proposed new Kirchhoff‐type true‐amplitude migration to zero offset (MZO) for 2.5-D common‐offset reflections in 2-D laterally inhomogeneous layered isotropic earth models does not depend on the reflector curvature. It provides a transformation of a common‐offset seismic section to a simulated zero‐offset section in which both the kinematic and main dynamic effects are accounted for correctly. The process transforms primary common‐offset reflections from arbitrary curved interfaces into their corresponding zero‐offset reflections automatically replacing the geometrical‐spreading factor. In analogy to a weighted Kirchhoff migration scheme, the stacking curve and weight function can be computed by dynamic ray tracing in the macro‐velocity model that is supposed to be available. In addition, we show that an MZO stretches the seismic source pulse by the cosine of the reflection angle of the original offset reflections. The proposed approach quantitatively extends the previous MZO or dip moveout (DMO) schemes to the 2.5-D situation.

A procedure for multidimensional inversion of seismic data

Geophysics ◽  
1982 ◽  
Vol 47 (10) ◽  
pp. 1422-1430 ◽  
Author(s):  
S. Raz
Keyword(s):  
Seismic Data ◽  
A Priori ◽  
Three Dimensional ◽  
One Dimensional ◽  
Born Model ◽  
Inversion Procedure ◽  
Error Accumulation ◽  
New Space ◽  
Zero Offset ◽  
Reduced Forms

A new space‐time approach to inverting multidimensional seismic data is formulated. This work constitutes a natural, but assuredly nontrivial, extension of a previously reported one‐dimensional (1-D) Bremmer inversion procedure. In its most general format, the scheme applies to the three‐dimensional (3-D) inversion problem; however, appropriately reduced forms applicable to two‐dimensional (2-D) as well as 1-D configurations are also presented. The basic scheme and all its variants utilize exclusively zero‐offset data. Although interpretable in terms of a distorted wave Born model, the inversion procedure and subsequent algorithms differ substantially from their Born‐based predecessors. Here, the background is not only inhomogeneous but is not known a priori. The choice of a uniquely defined “phase‐corrected” background is cardinal to the proposed reconstruction scheme. The improvement in the inversion accuracy is considerable. Comparatively large discontinuities can be handled, and the phenomenon of error accumulation with depth is overcome.

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.

Seeing, Knowing, and Doing

2020 ◽  
Author(s):  
Robert Audi
Keyword(s):  
Practical Reasoning ◽  
Practical Knowledge ◽  
A Priori ◽  
Human Action ◽  
A Priori Knowledge ◽  
Rational Action ◽  
Reasons For Action ◽  
Discriminative Response ◽  
Rich Information ◽  
Priori Knowledge

This book provides an overall theory of perception and an account of knowledge and justification concerning the physical, the abstract, and the normative. It has the rigor appropriate for professionals but explains its main points using concrete examples. It accounts for two important aspects of perception on which philosophers have said too little: its relevance to a priori knowledge—traditionally conceived as independent of perception—and its role in human action. Overall, the book provides a full-scale account of perception, presents a theory of the a priori, and explains how perception guides action. It also clarifies the relation between action and practical reasoning; the notion of rational action; and the relation between propositional and practical knowledge. Part One develops a theory of perception as experiential, representational, and causally connected with its objects: as a discriminative response to those objects, embodying phenomenally distinctive elements; and as yielding rich information that underlies human knowledge. Part Two presents a theory of self-evidence and the a priori. The theory is perceptualist in explicating the apprehension of a priori truths by articulating its parallels to perception. The theory unifies empirical and a priori knowledge by clarifying their reliable connections with their objects—connections many have thought impossible for a priori knowledge as about the abstract. Part Three explores how perception guides action; the relation between knowing how and knowing that; the nature of reasons for action; the role of inference in determining action; and the overall conditions for rational action.

How Reality is Reasonable

2018 ◽  
Author(s):  
Donald C. Williams
Keyword(s):  
A Priori ◽  
A Priori Knowledge ◽  
Dimensional Manifold ◽  
The World ◽  
Being There ◽  
Ways Of Being ◽  
Fundamental Entity ◽  
Spatiotemporal Relations ◽  
Priori Knowledge

This chapter begins with a systematic presentation of the doctrine of actualism. According to actualism, all that exists is actual, determinate, and of one way of being. There are no possible objects, nor is there any indeterminacy in the world. In addition, there are no ways of being. It is proposed that actual entities stand in three fundamental relations: mereological, spatiotemporal, and resemblance relations. These relations govern the fundamental entities. Each fundamental entity stands in parthood relations, spatiotemporal relations, and resemblance relations to other entities. The resulting picture is one that represents the world as a four-dimensional manifold of actual ‘qualitied contents’—upon which all else supervenes. It is then explained how actualism accounts for classes, quantity, number, causation, laws, a priori knowledge, necessity, and induction.

How Do We Know that We’re Not Brains in Vats?

2018 ◽  
Author(s):  
Keith DeRose
Keyword(s):  
Epistemic Justification ◽  
A Priori ◽  
A Priori Knowledge ◽  
Conservative Approach ◽  
Contingent Fact ◽  
Brains In Vats ◽  
Priori Knowledge

In this chapter the contextualist Moorean account of how we know by ordinary standards that we are not brains in vats (BIVs) utilized in Chapter 1 is developed and defended, and the picture of knowledge and justification that emerges is explained. The account (a) is based on a double-safety picture of knowledge; (b) has it that our knowledge that we’re not BIVs is in an important way a priori; and (c) is knowledge that is easily obtained, without any need for fancy philosophical arguments to the effect that we’re not BIVs; and the account is one that (d) utilizes a conservative approach to epistemic justification. Special attention is devoted to defending the claim that we have a priori knowledge of the deeply contingent fact that we’re not BIVs, and to distinguishing this a prioritist account of this knowledge from the kind of “dogmatist” account prominently championed by James Pryor.

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