Application of Mixed Boundary Condition to Wave Equation Forward Modeling in 2.5D VTI Medium

2012 ◽  
Vol 588-589 ◽  
pp. 1380-1385
Author(s):  
Gui Hua Li ◽  
Jian Guo Feng ◽  
Nian Tian Lin ◽  
Gui Liang Li ◽  
Min Guo
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Seismic Wave Propagation ◽  
Feature Analysis ◽  
Staggered Grid ◽  
Limited Area ◽  
Absorbing Boundary ◽  
Seismic Records ◽  
Vti Media

A key issue in the wave equation simulation of seismic records is the boundary conditions. Due to computer memory and computation and other restrictions, can only be solved on a limited area, which will cause the introduction of an artificial reflector. So as to simulation of seismic wave propagation in an infinite medium, the boundary conditions must be constructed so that the interface of the reflection as little as possible. In 2.5D VTI media feature analysis absorbing boundary of higher order velocity-stress staggered-grid finite difference method are established. The mixed boundary of the feature analysis absorbing boundary plus damping attenuation condition is used in 2.5 D VTI numerical simulations, simulation results show that this method is an efficient absorption and attenuation boundary conditions.

Stability of wide‐angle absorbing boundary conditions for the wave equation

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1153-1163 ◽  
Author(s):  
R. A. Renaut ◽  
J. Petersen
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Least Squares ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Wide Angle ◽  
Courant Number ◽  
Absorbing Boundary ◽  
Wide Range ◽  
Artificial Boundaries

Numerical solution of the two‐dimensional wave equation requires mapping from a physical domain without boundaries to a computational domain with artificial boundaries. For realistic solutions, the artificial boundaries should cause waves to pass directly through and thus mimic total absorption of energy. An artificial boundary which propagates waves in one direction only is derived from approximations to the one‐way wave equation and is commonly called an absorbing boundary. Here we investigate order 2 absorbing boundary conditions which include the standard paraxial approximation. Absorption properties are compared analytically and numerically. Our numerical results confirm that the [Formula: see text] or Chebychev‐Padé approximations are best for wide‐angle absorption and that the Chebychev or least‐squares approximations are best for uniform absorption over a wide range of incident angles. Our results also demonstrate, however, that the boundary conditions are stable for varying ranges of Courant number (ratio of time step to grid size). We prove that there is a stability barrier on the Courant number specified by the coefficients of the boundary conditions. Thus, proving stability of the interior scheme is not sufficient. Furthermore, waves may radiate spontaneously from the boundary, causing instability, even if the stability bound on the Courant number is satisfied. Consequently, the Chebychev and least‐squares conditions may be preferred for wide‐angle absorption also.

scholarly journals Absorbing boundary conditions for wave‐equation migration

Geophysics ◽  
1980 ◽  
Vol 45 (5) ◽  
pp. 895-904 ◽  
Author(s):  
Robert W. Clayton ◽  
Björn Engquist
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Final Section ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Seismic Section ◽  
Difference Wave ◽  
Different Types ◽  
Almost All ◽  
The Cost

The standard boundary conditions used at the sides of a seismic section in wave‐equation migration generate artificial reflections. These reflections from the edges of the computational grid appear as artifacts in the final section. Padding the section with zero traces on either side adds to the cost of migration and simply delays the inevitable reflections. We develop stable absorbing boundary conditions that annihilate almost all of the artificial reflections. This is demonstrated analytically and with synthetic examples. The absorbing boundary conditions presented can be used with any of the different types of finite‐difference wave‐equation migration, at essentially no extra cost.

scholarly journals Absorbing boundary conditions for acoustic and elastic wave equations

1977 ◽  
Vol 67 (6) ◽  
pp. 1529-1540 ◽  
Author(s):  
Robert Clayton ◽  
Björn Engquist
Keyword(s):  
Boundary Conditions ◽  
Elastic Wave ◽  
Wave Equations ◽  
Absorbing Boundary Conditions ◽  
Limited Area ◽  
Absorbing Boundary ◽  
Physical Behavior ◽  
Wide Range ◽  
Elastic Wave Equations ◽  
Numerical Wave

abstract Boundary conditions are derived for numerical wave simulation that minimize artificial reflections from the edges of the domain of computation. In this way acoustic and elastic wave propagation in a limited area can be efficiently used to describe physical behavior in an unbounded domain. The boundary conditions are based on paraxial approximations of the scalar and elastic wave equations. They are computationally inexpensive and simple to apply, and they reduce reflections over a wide range of incident angles.

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