Wave-equation tomography with surface offset gathers by plane-wave encoding

2017 ◽  
Author(s):  
Yujin Liu ◽  
Yan Wu ◽  
Xiongwen Wang ◽  
Tong Fei ◽  
Yi Luo
Keyword(s):  
Wave Equation ◽  
Plane Wave

Maxwell fields satisfying Huygens's principle

1968 ◽  
Vol 64 (3) ◽  
pp. 779-785 ◽  
Author(s):  
H. P. Künzle
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Maxwell Fields ◽  
Wave Space

AbstractIt is shown that Huygens's principle holds for the solutions of Maxwell's equations for p-forms of all degrees in a gravitational plane wave space, while the solutions of the wave equation for 1, 2, and 3-forms, however, may have tails.

Joint PP and PS plane-wave wave-equation migration-velocity analysis

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. R507-R525 ◽  
Author(s):  
Zongcai Feng ◽  
Bowen Guo ◽  
Lianjie Huang
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Wave Velocity ◽  
Migration Velocity ◽  
Relative Depth ◽  
Velocity Analysis ◽  
Analysis Method ◽  
S Wave ◽  
Velocity Models ◽  
Migration Velocity Analysis

Conventional joint PP and PS velocity analysis is based on ray tomography. We develop a joint PP and PS wave-equation migration-velocity-analysis method using plane-wave common-image gathers (CIGs) to produce accurate P- and S-wave velocity models. The objective function of our new method consists of three terms: The first and second terms penalize the moveout residuals computed from PP and PS plane-wave CIGs, respectively, and the third term constrains the nonzero relative depth shifts between the PP and PS migration images. The moveout of plane-wave CIGs is automatically picked using a semblance analysis method, and the relative depth shifts between the PP and PS images are automatically computed using dynamic warping or manually picking the depths of certain primary reflectors. The moveout residuals and the relative depth shifts are transformed into weighted image perturbations, and they are then projected into the velocity models to update the P- and S-wave velocity models using the scalar-wave equations and their linearized forms. Numerical tests with synthetic and multicomponent field data demonstrate that our method can simultaneously invert for accurate P- and S-wave velocity models for elastic migration.

scholarly journals A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation

1989 ◽  
Vol 30 (6) ◽  
pp. 1254-1269 ◽  
Author(s):  
Ioannis M. Besieris ◽  
Amr M. Shaarawi ◽  
Richard W. Ziolkowski
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Exact Solutions ◽  
Scalar Wave ◽  
Scalar Wave Equation

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.

scholarly journals Expansions in terms of Parabolic Cylinder Functions

1948 ◽  
Vol 8 (2) ◽  
pp. 50-65 ◽  
Author(s):  
T. M. Cherry
Keyword(s):  
Wave Equation ◽  
Positive Integer ◽  
Plane Wave ◽  
Arbitrary Function ◽  
Hermite Polynomials ◽  
Parabolic Cylinder ◽  
Parabolic Cylinder Functions ◽  
Image Position

When the plane wave equation is expressed in terms of parabolic co-ordinates x, y, the variables are separable, and the elementary solutions have the formwhere x, y, μ are real. In this context, therefore, the functions Dν (z) which are directly significant are those where amp z = ± π/4 and ν + ½ is purely imaginary, rather than those where z is real and ν is a positive integer. The expansion of an arbitrary function in terms of the latter sort of D-function (substantially, in terms of Hermite polynomials) is well known. This paper is concerned with the expansion in terms of the former sort of D-function.

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.

scholarly journals THE WAVE EQUATION AND GENERAL PLANE WAVE SOLUTIONS IN FRACTIONAL SPACE

2010 ◽  
Vol 19 ◽  
pp. 137-146 ◽  
Author(s):  
Muhammad Zubair ◽  
Muhammad Junaid Mughal ◽  
Qaisar Abbas Naqvi
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Wave Solutions ◽  
General Plane ◽  
Fractional Space ◽  
General Plane Wave

Efficient 3D velocity modeling building using joint inline and crossline plane-wave wave-equation migration velocity analyses

2020 ◽  
Author(s):  
Xuejian Liu ◽  
Lianjie Huang ◽  
Zongcai Feng ◽  
George El-kaseeh ◽  
Robert Will ◽  
...  
Keyword(s):  
Wave Equation ◽  
Plane Wave ◽  
Model Building ◽  
Velocity Model ◽  
Migration Velocity ◽  
Inversion Method ◽  
Data Interpolation ◽  
Image Domain ◽  
Velocity Model Building ◽  
3D Velocity Model

Summary Wave-equation migration velocity analysis (WEMVA) is an image-domain inversion method for velocity model building. Automatic plane-wave WEMVA (PWEMVA) calculates the moveouts of plane-wave common-image gathers (CIGs) by searching a best-fitting parabola with semblance analysis and back-projects residual CIG moveouts into wavefield wavepaths with a reflection tomographic kernel. However, 3D PWEMVA is very computationally expensive because 3D reflection tomographic inversion requires at least five 3D reverse-time migrations per iteration and stores two types of source wavefields at model boundaries. We develop a joint inline and crossline PWEMVA method for efficient 3D velocity model building. We alternatively implement the inline and crossline PWEMVAs with a constraint for each other, in which we iteratively construct the 3D velocity model update through 1D spline interpolation of 2D gradients. The inline and crossline joint inversion is practical since PWEMVA only inverts for low-wavenumber velocity perturbations along wavepaths, and the method can take less than one per cent of the computational cost of full 3D PWEMVA. To construct unaliased plane-waves for our joint inline and crossline PWEMVA, we develop a 3D data interpolation method in the frequency-wavenumber (FK) domain to recover regularly and randomly missing traces. The method minimizes the misfit on sufficiently localized data subsets with iterative optimal step-lengths and a gradient preconditioner that iteratively selects dominant dips along different azimuths. In numerical experiments, we use a 3D synthetic seismic dataset and a land 3D field seismic dataset acquired at the Farnsworth CO2-EOR [Enhanced Oil Recovery] field to demonstrate the efficacy of our velocity model building and data interpolation methods.

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