Numerical dispersion analysis for three-dimensional Laplace-Fourier-domain scalar wave equation

2016 ◽  
Vol 47 (2) ◽  
pp. 158-167
Author(s):  
Jing-Bo Chen
Keyword(s):  
Wave Equation ◽  
Three Dimensional ◽  
Dispersion Analysis ◽  
Numerical Dispersion ◽  
Fourier Domain ◽  
Scalar Wave ◽  
Scalar Wave Equation

Wave‐equation migration in the presence of lateral velocity variations

Geophysics ◽  
1982 ◽  
Vol 47 (7) ◽  
pp. 1001-1011 ◽  
Author(s):  
Richard Jay Castle
Keyword(s):  
Wave Equation ◽  
Three Dimensional ◽  
Scalar Wave ◽  
Lateral Velocity ◽  
Scalar Wave Equation ◽  
Common Depth Point ◽  
Velocity Gradients ◽  
Velocity Variations ◽  
Integral Solutions ◽  
Dimensional Wave

An algorithm for three‐dimensional wave equation migration in the presence of lateral velocity gradients is developed. The algorithm is based geophysically on the exploding reflector model and mathematically on integral solutions to the scalar wave equation. In addition, the velocity is assumed to vary slowly over a seismic wavelength. The primary application of the algorithm is to stacked sections. However, if the velocity is a function of depth only, the algorithm may be used to migrate and/or image common‐depth‐point gathers.

Consistent Infinitesimal Finite Element Cell Method: Three-Dimensional Scalar Wave Equation

1996 ◽  
Vol 63 (3) ◽  
pp. 650-654 ◽  
Author(s):  
J. P. Wolf ◽  
Chongmin Song
Keyword(s):  
Finite Element ◽  
Wave Equation ◽  
Three Dimensional ◽  
Time Domain Analysis ◽  
Spatial Dimension ◽  
Element Formulation ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Cell Method ◽  
Unbounded Medium

To calculate the unit-impulse response matrix of an unbounded medium governed by the scalar wave equation for use in a time-domain analysis of unbounded medium-structure interaction, the consistent infinitesimal finite element cell method is developed for the three-dimensional case. Its derivation is based on the finite element formulation and on similarity. The discretization is only performed on the structure-medium interface, yielding a reduction of the spatial dimension by 1. The procedure is exact in the radial direction and converges to the exact solution in the finite element sense in the circumferential directions.

Seismic scalar wave equation with variable coefficients modeling by a new convolutional differentiator

2010 ◽  
Vol 181 (11) ◽  
pp. 1850-1858 ◽  
Author(s):  
Xiaofan Li ◽  
Tong Zhu ◽  
Meigen Zhang ◽  
Guihua Long
Keyword(s):  
Wave Equation ◽  
Variable Coefficients ◽  
Scalar Wave ◽  
Scalar Wave Equation
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