Toward a unified analysis for source plane-wave migration

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. S129-S139 ◽  
Author(s):  
Faqi Liu ◽  
Douglas W. Hanson ◽  
Norman D. Whitmore ◽  
Richard S. Day ◽  
Robert H. Stolt
Keyword(s):  
Plane Wave ◽  
Plane Waves ◽  
Computational Cost ◽  
Cylindrical Wave ◽  
Ray Theory ◽  
Source Plane ◽  
Lateral Velocity ◽  
Theoretical Justification ◽  
Wave Migration ◽  
Better Than

In complex areas with large lateral velocity variations, wave-equation-based source plane-wave migration can produce images comparable to those from shot-profile migration, with less computational cost. Image quality can be better than in ray-theory-based Kirchhoff-type methods. This method requires the composition of plane-wave sections from all shot gathers. We provide a general framework to evaluate plane-wave composition in prestack source plane-wave migration. Our analysis shows that a plane-wave section can be treated as encoded shot gathers. This study provides the theoretical justification for applying plane-wave migration algorithms to sparsely sampled shot gathers with irregularly distributed receivers and limited offset. In addition, we discuss cylindrical-wave migration, which is 3D migration of 2D-constructed plane waves along the inline direction. We mathematically prove the equivalence of shot and plane-wave migration, and their equivalence to cylindrical wave migration in 3D cases when the sail lines are straight. Examples (including the Sigsbee 2A model) demonstrate the theory.

The impact of reciprocity on prestack source plane wave migration

2004 ◽  
Author(s):  
Faqi Liu ◽  
Dan N. Whitmore ◽  
Douglas W. Hanson ◽  
Richard S. Day ◽  
Chuck C. Mosher
Keyword(s):  
Plane Wave ◽  
Source Plane ◽  
Wave Migration ◽  
The Impact

Plane-wave depth migration

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. S261-S272 ◽  
Author(s):  
Paul L. Stoffa ◽  
Mrinal K. Sen ◽  
Roustam K. Seifoullaev ◽  
Reynam C. Pestana ◽  
Jacob T. Fokkema
Keyword(s):  
Phase Space ◽  
Plane Wave ◽  
Plane Waves ◽  
Computation Time ◽  
Depth Migration ◽  
Velocity Modeling ◽  
Natural Domain ◽  
Data Volume ◽  
Wave Migration ◽  
Slant Stacking

We present fast and efficient plane-wave migration methods for densely sampled seismic data in both the source and receiver domains. The methods are based on slant stacking over both shot and receiver positions (or offsets) for all the recorded data. If the data-acquisition geometry permits, both inline and crossline source and receiver positions can be incorporated into a multidimensional phase-velocity space, which is regular even for randomly positioned input data. By noting the maximum time dips present in the shot and receiver gathers and constant-offset sections, the number of plane waves required can be estimated, and this generally results in a reduction of the data volume used for migration. The required traveltime computations for depth imaging are independent for each particular plane-wave component. It thus can be used for either the source or the receiver plane waves during extrapolation in phase space, reducing considerably the computational burden. Since only vertical delay times are required, many traveltime techniques can be employed, and the problems with multipathing and first arrivals are either reduced or eliminated. Further, the plane-wave integrals can be pruned to concentrate the image on selected targets. In this way, the computation time can be further reduced, and the technique lends itself naturally to a velocity-modeling scheme where, for example, horizontal and then steeply dipping events are gradually introduced into the velocity analysis. The migration method also lends itself to imaging in anisotropic media because phase space is the natural domain for such an analysis.

scholarly journals Wave-equation migration velocity analysis using plane-wave common-image gathers

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. S327-S340 ◽  
Author(s):  
Bowen Guo ◽  
Gerard T. Schuster
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Computational Cost ◽  
Migration Velocity ◽  
Memory Storage ◽  
Velocity Analysis ◽  
Data Set ◽  
Image Domain ◽  
Migration Velocity Analysis ◽  
Wave Migration

Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain, or time-lag common-image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, we have developed a WEMVA method using plane-wave CIGs. Plane-wave CIGs reduce computational cost and memory storage because they are directly calculated from prestack plane-wave migration and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on two synthetic data sets and a field data set validate the efficiency and effectiveness of this method.

Reciprocity and double plane-wave migration

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. S453-S466 ◽  
Author(s):  
Zeyu Zhao ◽  
Mrinal K. Sen ◽  
Paul L. Stoffa
Keyword(s):  
Plane Wave ◽  
Computational Cost ◽  
Seismic Energy ◽  
Data Sets ◽  
Reciprocity Principle ◽  
Data Set ◽  
Wave Data ◽  
Double Plane ◽  
Wave Migration ◽  
Ray Parameter

In plane-wave migration techniques, plane-wave data sets with seismic energy in both positive and negative ray-parameter sections are more desirable than those with seismic energy only in either positive or negative ray-parameter sections. Such plane-wave data sets are often referred to as optimal plane-wave data sets because they can be used to illuminate the subsurface from both sides of the targets and, therefore, can produce sharp images. Traditionally, to obtain optimal plane-wave data sets from one-sided gathers generated by marine seismic acquisition geometry, one needs to invoke the reciprocity principle to sort split-spread gathers prior to implementing plane-wave decomposition. We have investigated the applicability of the reciprocity principle in the double plane-wave (DPW) domain. We have developed an easy and efficient merging method that generates optimal plane-wave data sets in the DPW domain using one-sided shot gathers. We call this resultant plane-wave data set the “optimal DPW data set.” We find that an optimal DPW data set transformed from one-sided gathers is a good approximation to a DPW data set transformed from split-spread gathers with the same maximum offset as that of the one-sided gathers. We find that ray-parameter common-image gathers with continuous events in both positive and negative ray-parameter sections can be generated by migrating optimal DPW data sets. This helps migration velocity analysis and improves the subsurface illumination. In addition, we show that the computational cost of DPW migration methods could be reduced with the help of the reciprocity principle. We test our proposed method using a synthetic model to demonstrate its effectiveness.

VELOCITY ESTIMATION AND DOWNWARD CONTINUATION BY WAVEFRONT SYNTHESIS

Geophysics ◽  
1978 ◽  
Vol 43 (4) ◽  
pp. 691-714 ◽  
Author(s):  
Philip S. Schultz ◽  
Jon F. Claerbout
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Wave Field ◽  
Signal To Noise Ratio ◽  
Plane Waves ◽  
Velocity Estimation ◽  
Lateral Velocity ◽  
The Common ◽  
Seismic Sections ◽  
The Many

A “wave stack” is any stack over a common shot or geophone gather in which the moveout is independent of time. It synthesizes a particular wavefront by superposition of the many spherical wavefronts of raw data. Unlike the common midpoint stack, wave stacks retain the important property of being the sampling of a wave field and, as such, permit wave‐equation treatment of formerly difficult or impossible problems. Seismic sections of field data generated by wave stacks that synthesized slanted downgoing plane waves showed a similarity in appearance to the common midpoint stacks. In signal‐to‐noise ratio they lay between the single offset section and the midpoint stack. The angle selectivity of the slanted plane‐wave stacks permitted detection of a reflector that was not visible on either the midpoint stack or the raw gathers. Simple velocity estimation in slant frame coordinates differs only in detail from standard frame coordinates. Because of the wave field character of data that have been slant plane‐wave stacked, wave‐equation techniques can be used to generalize migration and velocity estimation to regions in which exist a strong lateral velocity inhomogeneity within the distance of a cable spread.

Electromagnetic waves

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Plane Wave ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Plane Waves ◽  
Geometrical Optics ◽  
Particle Detection ◽  
Spatial Coordinates ◽  
A Charge

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.

scholarly journals Ultrasonic Scattered Field Distribution of One and Two Cylindrical Solids with Phased Array Technique

2019 ◽  
Vol 32 (1) ◽  
Author(s):  
Xiaozhou Liu ◽  
Jian Ma ◽  
Haibin Wang ◽  
Sha Gao ◽  
Yifeng Li ◽  
...  
Keyword(s):  
Plane Wave ◽  
Field Distribution ◽  
Scattered Field ◽  
Phased Array ◽  
Simulation Analysis ◽  
Plane Waves ◽  
Theoretical Solution ◽  
Steel Matrix ◽  
Field Distributions ◽  
Scattered Fields

AbstractThe scattered fields of plane waves in a solid from a cylinder or sphere are critical in determining its acoustic characteristics as well as in engineering applications. This paper investigates the scattered field distributions of different incident waves created by elastic cylinders embedded in an elastic isotropic medium. Scattered waves, including longitudinal and transverse waves both inside and outside the cylinder, are described with specific modalities under an incident plane wave. A model with a scatterer embedded in a structural steel matrix and filled with aluminum is developed for comparison with the theoretical solution. The frequency of the plane wave ranged from 235 kHz to 2348 kHz, which corresponds to scaling factors from 0.5 to 5. Scattered field distributions in matrix materials blocked by an elastic cylindrical solid have been obtained by simulation or calculated using existing parameters. The simulation results are in good agreement with the theoretical solution, which supports the correctness of the simulation analysis. Furthermore, ultrasonic phased arrays are used to study scattered fields by changing the characteristics of the incident wave. On this foundation, a partial preliminary study of the scattered field distribution of double cylinders in a solid has been carried out, and the scattered field distribution at a given distance has been found to exhibit particular behaviors at different moments. Further studies on directivities and scattered fields are expected to improve the quantification of scattered images in isotropic solid materials by the phased array technique.

Surface and interfacial anti-plane waves in micropolar solids with surface energy

2020 ◽  
pp. 108128652096564
Author(s):  
Mriganka Shekhar Chaki ◽  
Victor A Eremeyev ◽  
Abhishek K Singh
Keyword(s):  
Surface Wave ◽  
Plane Wave ◽  
Numerical Study ◽  
Plane Waves ◽  
Angular Frequency ◽  
Elastic Half Space ◽  
Surface Strain ◽  
Theoretical Frameworks ◽  
Algebraic Form ◽  
New Type

In this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for surface and interfacial elasticity. Dispersion equations for both models have been obtained in algebraic form for two types of anti-plane wave, i.e. a Love-type wave and a new type of surface wave (due to micropolarity). The angular frequency and phase velocity of anti-plane waves have been analysed through a numerical study within cut-off frequencies. The obtained results may find suitable applications in thin film technology, non-destructive analysis or biomechanics, where the models discussed here may serve as theoretical frameworks for similar types of phenomena.

Study of wave attenuation in concrete

1993 ◽  
Vol 8 (9) ◽  
pp. 2344-2353 ◽  
Author(s):  
J-M. Berthelot ◽  
Souda M. Ben ◽  
J.L. Robert
Keyword(s):  
Experimental Study ◽  
Plane Wave ◽  
Wave Attenuation ◽  
Plane Waves ◽  
Propagation Distance ◽  
Experimental Results ◽  
The Other ◽  
Wave Frequency ◽  
Concrete Composition ◽  
Analytical Expression

The experimental study of wave attenuation in concrete has been achieved in the case of the propagation of plane waves in concrete rods. Different mortars and concretes have been investigated. A transmitter transducer coupled to one of the ends of the concrete rod generates the propagation of a plane wave in the rod. The receiver transducer, similar to the previous one, is coupled to the other end of the rod. The experimental results lead to an analytical expression for wave attenuation as function of the concrete composition, the propagation distance, and the wave frequency.

A method for the exact solution of a class of two-dimensional diffraction problems

1951 ◽  
Vol 205 (1081) ◽  
pp. 286-308 ◽  
Keyword(s):  
Integral Equation ◽  
Plane Wave ◽  
Integral Equations ◽  
Scattered Field ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Diffraction Theory ◽  
General Interest ◽  
Two Dimensional ◽  
Dual Integral Equations

In the last few years Copson, Schwinger and others have obtained exact solutions of a number of diffraction problems by expressing these problems in terms of an integral equation which can be solved by the method of Wiener and Hopf. A simpler approach is given, based on a representation of the scattered field as an angular spectrum of plane waves, such a representation leading directly to a pair of ‘dual’ integral equations, which replaces the single integral equation of Schwinger’s method. The unknown function in each of these dual integral equations is that defining the angular spectrum, and when this function is known the scattered field is presented in the form of a definite integral. As far as the ‘radiation’ field is concerned, this integral is of the type which may be approximately evaluated by the method of steepest descents, though it is necessary to generalize the usual procedure in certain circumstances. The method is appropriate to two-dimensional problems in which a plane wave (of arbitrary polarization) is incident on plane, perfectly conducting structures, and for certain configurations the dual integral equations can be solved by the application of Cauchy’s residue theorem. The technique was originally developed in connexion with the theory of radio propagation over a non-homogeneous earth, but this aspect is not discussed. The three problems considered are those for which the diffracting plates, situated in free space, are, respectively, a half-plane, two parallel half-planes and an infinite set of parallel half-planes; the second of these is illustrated by a numerical example. Several points of general interest in diffraction theory are discussed, including the question of the nature of the singularity at a sharp edge, and it is shown that the solution for an arbitrary (three-dimensional) incident field can be derived from the corresponding solution for a two-dimensional incident plane wave.

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