A Perfectly Matched Layer Technique Applied to Lattice Spring Model in Seismic Wavefield Forward Modeling for Poisson’s Solids

Author(s):  
Jinxuan Tang ◽  
Hui Zhou ◽  
Chuntao Jiang ◽  
Muming Xia ◽  
Hanming Chen ◽  
...  

ABSTRACT As a complementary way to traditional wave-equation-based forward modeling methods, lattice spring model (LSM) is introduced into seismology for wavefield modeling owing to its remarkable stability, high-calculation accuracy, and flexibility in choosing simulation meshes, and so forth. The LSM simulates seismic-wave propagation from a micromechanics perspective, thus enjoying comprehensive characterization of elastic dynamics in complex media. Incorporating an absorbing boundary condition (ABC) is necessary for wavefield modeling to avoid the artificial reflections caused by truncated boundaries. To the best of our knowledge, the perfectly matched layer (PML) method has been a routine ABC in the wave-equation-based numerical modeling of wave physics. However, it has not been used in the nonwave-equation-based LSM simulations. In this work, we want to apply PML to LSM to attenuate the boundary reflections. We divide the whole simulation region into PML region and inner region, PML region surrounds the inner region. To incorporate PML to LSM, we establish elastic-wave equations corresponding to LSM. The simulation in the PML region is conducted using the established wave equations and the simulation in the inner region is conducted using LSM. Three simulation examples show that the PML scheme is effective and outperforms Gaussian ABC.

Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. T29-T39 ◽  
Author(s):  
Hanming Chen ◽  
Hui Zhou ◽  
He Lin ◽  
Shangxu Wang

Arbitrarily wide-angle wave equation (AWWE) is a space domain, high-order one-way wave equation (OWWE). Its accuracy can be arbitrarily increased, and it is amenable to easy numerical implementation. Those properties make it outstanding among the existing OWWEs and further enable it to be a desirable tool for migration. We extend the perfectly matched layer (PML) to 3D scalar AWWE to provide a good approach to suppress artifacts arising at truncation boundaries. We follow the concept of complex coordinate stretching, and the derivation procedure of PML for AWWE is straightforward. An existing finite-difference scheme is adopted to fit the split PML formulation and its stability is observed through numerical examples. The performance of the developed PML condition is compared with two different wave-equation based absorbing boundary conditions. Numerical results illustrate that the PML condition used in AWWE propagator can effectively absorb the propagating waves and evanescent waves at a price of limited additional computation cost.


Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. T301-T311 ◽  
Author(s):  
Xiao Ma ◽  
Dinghui Yang ◽  
Xueyuan Huang ◽  
Yanjie Zhou

The absorbing boundary condition plays an important role in seismic wave modeling. The perfectly matched layer (PML) boundary condition has been established as one of the most effective and prevalent absorbing boundary conditions. Among the existing PML-type conditions, the complex frequency shift (CFS) PML attracts considerable attention because it can handle the evanescent and grazing waves better. For solving the resultant CFS-PML equation in the time domain, one effective technique is to apply convolution operations, which forms the so-called convolutional PML (CPML). We have developed the corresponding CPML conditions with nonconstant grid compression parameter, and used its combination algorithms specifically with the symplectic partitioned Runge-Kutta and the nearly analytic SPRK methods for solving second-order seismic wave equations. This involves evaluating second-order spatial derivatives with respect to the complex stretching coordinates at the noninteger time layer. Meanwhile, two kinds of simplification algorithms are proposed to compute the composite convolutions terms contained therein.


2020 ◽  
Author(s):  
J. Tang ◽  
H. Zhou ◽  
M. Xia ◽  
C. Jiang ◽  
H. Chen ◽  
...  

Author(s):  
Yanbin He ◽  
Tianning Chen ◽  
Jinghuai Gao

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.


1977 ◽  
Vol 67 (6) ◽  
pp. 1529-1540 ◽  
Author(s):  
Robert Clayton ◽  
Björn Engquist

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.


Solid Earth ◽  
2018 ◽  
Vol 9 (6) ◽  
pp. 1277-1298
Author(s):  
Xiaoyu Zhang ◽  
Dong Zhang ◽  
Qiong Chen ◽  
Yan Yang

Abstract. The forward modeling of a scalar wave equation plays an important role in the numerical geophysical computations. The finite-difference algorithm in the form of a second-order wave equation is one of the commonly used forward numerical algorithms. This algorithm is simple and is easy to implement based on the conventional grid. In order to ensure the accuracy of the calculation, absorption layers should be introduced around the computational area to suppress the wave reflection caused by the artificial boundary. For boundary absorption conditions, a perfectly matched layer is one of the most effective algorithms. However, the traditional perfectly matched layer algorithm is calculated using a staggered grid based on the first-order wave equation, which is difficult to directly integrate into a conventional-grid finite-difference algorithm based on the second-order wave equation. Although a perfectly matched layer algorithm based on the second-order equation can be derived, the formula is rather complex and intermediate variables need to be introduced, which makes it hard to implement. In this paper, we present a simple and efficient algorithm to match the variables at the boundaries between the computational area and the absorbing boundary area. This new boundary-matched method can integrate the traditional staggered-grid perfectly matched layer algorithm and the conventional-grid finite-difference algorithm without formula transformations, and it can ensure the accuracy of finite-difference forward modeling in the computational area. In order to verify the validity of our method, we used several models to carry out numerical simulation experiments. The comparison between the simulation results of our new boundary-matched algorithm and other boundary absorption algorithms shows that our proposed method suppresses the reflection of the artificial boundaries better and has a higher computational efficiency.


Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 963-966 ◽  
Author(s):  
Jianlin Zhu

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.


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