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.

3D wave-equation interferometric migration of VSP free-surface multiples

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. S195-S203 ◽  
Author(s):  
Ruiqing He ◽  
Brian Hornby ◽  
Gerard Schuster
Keyword(s):  
Wave Equation ◽  
Free Surface ◽  
Signal To Noise Ratio ◽  
Time Lapse ◽  
Seismic Profile ◽  
Velocity Estimation ◽  
Seismic Survey ◽  
3D Surface ◽  
Vsp Data ◽  
Image Volume

Interferometric migration of free-surface multiples in vertical-seismic-profile (VSP) data has two significant advantages over standard VSP imaging: (1) a significantly larger imaging area compared to migrating VSP primaries and (2) less sensitivity to velocity-estimation and static errors than other methods for migration of multiples. In this paper, we present a 3D wave-equation interferometric migration method that efficiently images VSP free-surface multiples. Synthetic and field data results confirm that a reflectivity image volume, comparable in size to a 3D surface seismic survey around the well, can be computed economically. The reflectivity image volume has less fold density and lower signal-to-noise ratio than that obtained by a conventional 3D surface seismic survey because of the relatively weak energy of multiples and the limited number of geophones in the well. However, the efficiency of this method for migrating VSP multiples suggests that it might sometimes be a useful tool for 4D seismic monitoring where reflectivity images can be computed quickly for each time-lapse survey.

Efficient FDTD algorithm for plane-wave simulation for vertically heterogeneous attenuative media

Geophysics ◽  
2007 ◽  
Vol 72 (4) ◽  
pp. H43-H53 ◽  
Author(s):  
Arash JafarGandomi ◽  
Hiroshi Takenaka
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Plane Wave ◽  
Wave Equations ◽  
Plane Waves ◽  
Computation Time ◽  
Staggered Grid ◽  
Seismic Profiles ◽  
Vertical Seismic Profiles ◽  
Incident Waves

We propose an efficient algorithm for modeling seismic plane-wave propagation in vertically heterogeneous viscoelastic media using a finite-difference time-domain (FDTD) technique. In the algorithm, the wave equation is rewritten for plane waves by applying a Radon transform to the 2D general wave equation. Arbitrary values of the quality factor for [Formula: see text]- and [Formula: see text]-waves ([Formula: see text] and [Formula: see text]) are incorporated into the wave equation via a generalized Zener body rheological model. An FDTD staggered-grid technique is used to numerically solve the derived plane-wave equations. The scheme uses a 1D grid that reduces computation time and memory requirements significantly more than corresponding 2D or 3D computations. Comparing the finite-difference solutions to their corresponding analytical results, we find that the methods are sufficiently accurate. The proposed algorithm is able to calculate synthetic waveforms efficiently and represent viscoelastic attenuation even in very attenuative media. The technique is then used to estimate the plane-wave responses of a sedimentary system to normal and inclined incident waves in the Kanto area of Japan via synthetic vertical seismic profiles.

Seismic velocity estimation using time-reversal focusing

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. U43-U50 ◽  
Author(s):  
Ariel Lellouch ◽  
Evgeny Landa
Keyword(s):  
Wave Equation ◽  
Time Reversal ◽  
Seismic Velocity ◽  
Signal To Noise Ratio ◽  
Onset Time ◽  
Velocity Model ◽  
Source Location ◽  
Velocity Estimation ◽  
Adequate Model ◽  
Traveltime Tomography

Seismic velocity estimation is a challenging task, especially when no initial model is present. In most cases, a traveltime tomography approach is used as a significant part of the workflow. However, it requires noise-sensitive, time-consuming picking and uses a ray approximation of the wave equation. Time reversal (TR) is a fundamental physical concept, based on the wave equation’s invariance under TR operation. If the recorded wavefield is reversed and back-propagated into the medium, it will focus at its original source location regardless of the complexity of the medium. We use this property for seismic velocity analysis, formulated as an inversion problem with focusing at the known source location and onset time as the objective function. It is globally solved using competitive particle swarm optimization and an adequate model parameterization. This approach has the advantages of using the wave equation, being picking-free, handling low signal-to-noise ratio and requiring neither information on the source wavelet nor an initial velocity model. Although the method is discussed in the framework of direct source-receiver path acquisition, the foundations for its use with conventional reflection data are laid. We have determined the method’s usefulness and limitations using synthetic and field crosshole acquisition examples. In both cases, inversion results are compared with a standard traveltime tomography approach and illustrate the advantages of using TR focusing.

Datum correction by wave‐equation extrapolation

Geophysics ◽  
1988 ◽  
Vol 53 (10) ◽  
pp. 1311-1322 ◽  
Author(s):  
V. Shtivelman ◽  
A. Canning
Keyword(s):  
Wave Equation ◽  
Synthetic Data ◽  
Real Data ◽  
Static Solution ◽  
Velocity Model ◽  
Lateral Velocity ◽  
Static Correction ◽  
Slow Velocity ◽  
Velocity Variations ◽  
Seismic Sections

Seismic sections are usually datum corrected by static shifting. For small differences in elevation and slow velocity variations between the input datum and the output datum, static shifting is a sufficiently accurate datum correction procedure. However, for significant differences in elevations and a more complicated velocity model, the accuracy of the static solution may prove to be insufficient; and a more exact method should be used. In this paper, we study the limitations of the static method of datum correction and develop simple and effective extrapolation schemes based on the wave equation, schemes which lead to more accurate datum correction. The distortions of seismic events caused by static correction are illustrated by a number of simple examples. To reduce the distortions, we propose a number of extrapolation schemes based on the asymptories of the Kirchhoff integral solution of the 2-D scalar wave equation. Application of the extrapolation algorithms to synthetic data shows that they provide accurate datum corrections even for a nonplanar input datum and vertical and lateral velocity variations. The algorithms have been successfully applied to real data.

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.

scholarly journals Benchmarking wave equation solvers using interface conditions: the case of porous media

2020 ◽  
Vol 224 (1) ◽  
pp. 355-376
Author(s):  
Haorui Peng ◽  
Yanadet Sripanich ◽  
Ivan Vasconcelos ◽  
Jeannot Trampert
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Plane Waves ◽  
Spherical Wave ◽  
Seismic Exploration ◽  
Complex Media ◽  
Two Phase ◽  
Poroelastic Media

SUMMARY The correct implementation of the continuity conditions between different media is fundamental for the accuracy of any wave equation solver used in applications from seismic exploration to global seismology. Ideally, we would like to benchmark a code against an analytical Green’s function. The latter, however, is rarely available for more complex media. Here, we provide a general framework through which wave equation solvers can be benchmarked by comparing plane wave simulations to transmission/reflection (R/T) coefficients from plane-wave analysis with exact boundary conditions (BCs). We show that this works well for a large range of incidence angles, but requires a lot of computational resources to simulate the plane waves. We further show that the accuracy of a numerical Green’s function resulting from a point-source spherical-wave simulation can also be used for benchmarking. The data processing in that case is more involved than for the plane wave simulations and appears to be sufficiently accurate only below critical angles. Our approach applies to any wave equation solver, but we chose the poroelastic wave equation for illustration, mainly due to the difficulty of benchmarking poroelastic solvers, but also due to the growing interest in imaging in poroelastic media. Although we only use 2-D examples, our exact R/T approach can be extended to 3-D and various cases with different interface configurations in arbitrarily complex media, incorporating, for example, anisotropy, viscoelasticity, double porosities, partial saturation, two-phase fluids, the Biot/squirt flow and so on.

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.

Ensemble estimation of polarization ellipse parameters

2007 ◽  
Vol 463 (2088) ◽  
pp. 3375-3394 ◽  
Author(s):  
A.T Walden ◽  
T Medkour
Keyword(s):  
Angular Distribution ◽  
Standard Deviation ◽  
Aspect Ratio ◽  
Plane Wave ◽  
Wave Field ◽  
Covariance Matrix ◽  
Time Instant ◽  
Azimuth Angle ◽  
Ensemble Estimation ◽  
Plane Wave Field

An ellipse describes the polarized part of a partially polarized quasi-monochromatic plane wave field. Its azimuth angle and aspect ratio are functions of the elements of the covariance matrix associated with the polarized part at a particular time instant. Given an ensemble of K independent samples at that time, the distributions of the estimators of these parameters are derived. The estimation is thus based on a sample ensemble at any time, and does not assume temporal stationarity. Additionally, the azimuth angle estimator has an angular distribution so that non-standard statistical methods are needed when deriving its mean and standard deviation.

scholarly journals Interphotoreceptor coupling: an evolutionary perspective

2021 ◽  
Author(s):  
Lorenzo Cangiano ◽  
Sabrina Asteriti
Keyword(s):  
Visual Information ◽  
Signal To Noise Ratio ◽  
Electrical Coupling ◽  
Physiological Role ◽  
Cellular Processes ◽  
Contact Points ◽  
Highly Sensitive ◽  
The Many ◽  
The Impact

AbstractIn the vertebrate retina, signals generated by cones of different spectral preference and by highly sensitive rod photoreceptors interact at various levels to extract salient visual information. The first opportunity for such interaction is offered by electrical coupling of the photoreceptors themselves, which is mediated by gap junctions located at the contact points of specialised cellular processes: synaptic terminals, telodendria and radial fins. Here, we examine the evolutionary pressures for and against interphotoreceptor coupling, which are likely to have shaped how coupling is deployed in different species. The impact of coupling on signal to noise ratio, spatial acuity, contrast sensitivity, absolute and increment threshold, retinal signal flow and colour discrimination is discussed while emphasising available data from a variety of vertebrate models spanning from lampreys to primates. We highlight the many gaps in our knowledge, persisting discrepancies in the literature, as well as some major unanswered questions on the actual extent and physiological role of cone-cone, rod-cone and rod-rod communication. Lastly, we point toward limited but intriguing evidence suggestive of the ancestral form of coupling among ciliary photoreceptors.

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.

Sign in / Sign up

Export Citation Format

Share Document