Seismic wave propagation in a borehole using the finite‐difference method

1984 ◽  
Author(s):  
Federico Pardo‐Casas ◽  
Ralph A. Stephen ◽  
C. H. Cheng
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Seismic Wave ◽  
Difference Method ◽  
Seismic Wave Propagation ◽  
The Finite Difference Method

An improved immersed boundary finite-difference method for seismic wave propagation modeling with arbitrary surface topography

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. T311-T322 ◽  
Author(s):  
Wenyi Hu
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Surface Topography ◽  
Seismic Wave ◽  
Difference Method ◽  
Forward Modeling ◽  
Seismic Wave Propagation ◽  
Immersed Boundary

To accurately simulate seismic wave propagation for the purpose of developing modern land data processing tools, especially full-waveform inversion (FWI), we have developed an efficient high-order finite-difference forward-modeling algorithm with the capability of handling arbitrarily shaped free-surface topography. Unlike most existing forward-modeling algorithms using curvilinear grids to fit irregular surface topography, this finite-difference algorithm, based on an improved immersed boundary method, uses a regular Cartesian grid system without suffering from staircasing error, which is inevitable in a conventional finite-difference method. In this improved immersed boundary finite-difference (IBFD) algorithm, arbitrarily curved surface topography is accounted for by imposing the free-surface boundary conditions at exact boundary locations instead of using body-conforming grids or refined grids near the boundaries, thus greatly reducing the complexity of its preprocessing procedures and the computational cost. Furthermore, local continuity, large curvatures, and subgrid curvatures are represented precisely through the employment of the so-called dual-coordinate system — a local cylindrical and a global Cartesian coordinate. To properly describe the wave behaviors near complex free-surface boundaries (e.g., overhanging structures and thin plates, or other fine geometry features), the wavefields in a ghost zone required for the boundary condition enforcement are reconstructed accurately by introducing a special recursive interpolation technique into the algorithm, which substantially simplifies the boundary treatment procedures and further improves the numerical performance of the algorithm, as demonstrated by the numerical experiments. Numerical examples revealed the performance of the IBFD method in comparison with a conventional finite-difference method.

APPLICATION OF A NUMERICAL-ANALYTICAL METHOD FOR SOLVING A ONE-DIMENSIONAL WAVE EQUATION

Akustika ◽  
2021 ◽  
pp. 22
Author(s):  
Vladimir Mondrus ◽  
Dmitrii Sizov
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Analytical Method ◽  
One Dimensional ◽  
Numerical Analytical Method ◽  
The Finite Difference Method ◽  
Dimensional Wave

The article contains a solution to the problem of wave propagation in a one-dimensional rod from the initial impact. A numerical-analytical method is used to solve the problem. The numerical part of the method is based on the application of the idea of the finite difference method. The analytical part uses the concept of Green’s function to solve the problem in terms of the spatial coordinate in the considered area. The results include graphs of the solution obtained at different points in time.

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