scholarly journals Perfectly matched absorbing layer for modelling transient wave propagation in heterogeneous poroelastic media

2019 ◽  
Author(s):  
Yanbin He ◽  
Tianning Chen ◽  
Jinghuai Gao
Keyword(s):  
Wave Equations ◽  
Heterogeneous Media ◽  
Near Field ◽  
Weak Form ◽  
Transient Wave ◽  
Absorbing Boundary ◽  
Poroelastic Media ◽  
Elastic Wave Equations ◽  
Absorbing Layer ◽  
Biot’S Equations

Abstract The perfectly matched layer (PML) has been demonstrated to be an efficient absorbing boundary for near-field wave simulation. For heterogeneous media, the property of the PML needs to be carefully specified to avoid numerical instability and artificial reflection because part of it lies at the discontinuous interface. Coupled acoustic-poroelastic (A-P) media or coupled elastic-poroelastic (E-P) media often arise in the field of geophysics. However, PMLs that appropriately terminate these heterogeneous poroelastic media are still lacking. The main purpose of this paper is to explore the application of unsplit PMLs for transient wave modeling in infinite, heterogeneous, coupled A-P media or coupled E-P media. To this end, a consistent derivation of memory-efficient PML formulations for the second-order Biot's equations, elastic wave equations and acoustic wave equations is performed based on complex coordinate transformation using auxiliary differential equations. Furthermore, the interface boundary conditions inside the absorbing layer are rigorously derived for the considered A-P and E-P cases. Finally, the weak form of PML formulations for coupled poroelastic problems is presented. The finite element method is used to validate the proposed PML based on several two-dimensional benchmarks. The accuracy and stability of weak PML formulations are investigated. In particular, for coupled acoustic-poroelastic PML, two extreme (open-pore and sealed-pore) interface conditions are considered and PML results are compared with known analytical solutions. This study demonstrates the ability of the PML to effectively eliminate outgoing bulk waves and surface waves in coupled poroelastic media.

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.

A transparent boundary technique for numerical modeling of elastic waves

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 963-966 ◽  
Author(s):  
Jianlin Zhu
Keyword(s):  
Numerical Modeling ◽  
Boundary Conditions ◽  
Elastic Waves ◽  
Wave Equations ◽  
Normal Incidence ◽  
Absorbing Boundary Conditions ◽  
S Wave ◽  
Absorbing Boundary ◽  
S Waves ◽  
Elastic Wave Equations

In numerical modeling of wave motions, strong reflections from artificial model boundaries may contaminate or mask true reflections from the interior model interfaces. Hence, developing a kind of exterior model boundary transparent to the outgoing waves is of critical importance. Among proposed solutions, e.g., Smith (1974), Kausel and Tassoulas (1981), and Higdon (1991), the most widely used may be the Clayton and Engquist (1977) method of absorbing boundary conditions, based on paraxial approximations for acoustic and elastic‐wave equations. However, absorbing boundary conditions make the reflection coefficients zero only for normal incidence, and suppression of reflected S-waves (Clayton and Engquist, 1977) becomes poorer as the ratio of P- to S-wave velocity ([Formula: see text]) becomes larger.

Spectral‐domain decomposition methods for the solution of acoustic and elastic wave equations

Geophysics ◽  
1996 ◽  
Vol 61 (4) ◽  
pp. 1160-1174 ◽  
Author(s):  
Ezio Faccioli ◽  
Fabio Maggio ◽  
Alfio Quarteroni ◽  
Aldo Taghan
Keyword(s):  
Domain Decomposition ◽  
Wave Equations ◽  
Heterogeneous Media ◽  
Domain Decomposition Method ◽  
Decomposition Methods ◽  
Spectral Domain ◽  
Test Cases ◽  
Domain Decomposition Methods ◽  
Elastic Wave Equations ◽  
The Stability

A new spectral‐domain decomposition method is presented for acoustic and elastodynamic wave propagation in 2-D heterogeneous media. Starting from a variational formulation of the problem, two different approaches are proposed for the spatial discretization: a mixed Fourier‐Legendre and a full Legendre collocation. The matching conditions at subdomain interfaces are carefully analyzed, and the stability and efficiency of time‐advancing schemes are investigated. The numerical validation with some significant test cases illustrates the accuracy, flexibility, and robustness of our methods. These allow the treatment of complex geometries and heterogeneous media while retaining spectral accuracy.

TRIANGLE-QUADRANGLE GRID METHOD FOR POROELASTIC, ELASTIC, AND ACOUSTIC WAVE EQUATIONS

2001 ◽  
Vol 09 (02) ◽  
pp. 681-702 ◽  
Author(s):  
JIANFENG ZHANG
Keyword(s):  
Wave Propagation ◽  
Wave Equations ◽  
Complex Geometry ◽  
Numerical Technique ◽  
Grid Method ◽  
Equilibrium Equations ◽  
Lamb’S Problem ◽  
Poroelastic Media ◽  
Acoustic Media ◽  
Biot’S Equations

A new numerical technique is developed for wave propagation in heterogeneous poroelastic media and mixed poroelastic, elastic and acoustic media. The scheme, based on a first-order hyperbolic Biot's system and a discretization mesh of triangles and quadrangles, solves the problem using integral equilibrium equations around each node, instead of satisfying Biot's differential equations at each node as in the finite-difference method. The surface topography and complex geometrical interfaces can be accurately modeled with the proposed algorithm by making the nodes of triangles and quadrangles follow the curved interfaces. The elastic (acoustic)/poroelastic interface conditions of complex geometry are introduced using the integral equilibrium equations around nodes at the interface based on the continuities of total stresses and velocities between the interface. The free-surface conditions of complex geometrical boundaries are satisfied naturally for the scheme. This work is an extension of the grid method for the heterogeneous elastic media to the heterogeneous poroelastic one. The proposed algorithm is successfully tested against an analytical solution for Lamb's problem when the algorithm is reduced to handle the elastic limit of the Biot's equations. Examples of wave propagation in a poroelastic half-space with a semi-cylindrical pit on the surface and mixed acoustic-poroelastic and elastic-poroelastic models with inclined interfaces are presented.

The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1258-1266 ◽  
Author(s):  
Y. Q. Zeng ◽  
J. Q. He ◽  
Q. H. Liu
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Waves ◽  
Additional Term ◽  
Seismic Wave Propagation ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary ◽  
Poroelastic Media ◽  
Unbounded Media ◽  
Biot’S Equations

The perfectly matched layer (PML) was first introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, a method is developed to extend the perfectly matched layer to simulating seismic wave propagation in poroelastic media. This nonphysical material is used at the computational edge of a finite‐difference algorithm as an ABC to truncate unbounded media. The incorporation of PML in Biot’s equations is different from other PML applications in that an additional term involving convolution between displacement and a loss coefficient in the PML region is required. Numerical results show that the PML ABC attenuates the outgoing waves effectively.

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