Absorbing boundary conditions for acoustic media

Geophysics ◽  
1985 ◽  
Vol 50 (6) ◽  
pp. 892-902 ◽  
Author(s):  
R. G. Keys
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Plane Waves ◽  
Basic Element ◽  
Absorbing Boundary Conditions ◽  
Boundary Operator ◽  
Order Differential Operator ◽  
Absorbing Boundary ◽  
Boundary Operators

By decomposing the acoustic wave equation into incoming and outgoing components, an absorbing boundary condition can be derived to eliminate reflections from plane waves according to their direction of propagation. This boundary condition is characterized by a first‐order differential operator. The differential operator, or absorbing boundary operator, is the basic element from which more complicated boundary conditions can be constructed. The absorbing boundary operator can be designed to absorb perfectly plane waves traveling in any two directions. By combining two or more absorption operators, boundary conditions can be created which absorb plane waves propagating in any number of directions. Absorbing boundary operators simplify the task of designing boundary conditions to reduce the detrimental effects of outgoing waves in many wave propagation problems.

An optimal absorbing boundary condition for elastic wave modeling

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 296-301 ◽  
Author(s):  
Chengbin Peng ◽  
M. Nafi Toksöz
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Short Note ◽  
Absorbing Boundary Conditions ◽  
Parallel Computer ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary

Absorbing boundary conditions are widely used in numerical modeling of wave propagation in unbounded media to reduce reflections from artificial boundaries (Lindman, 1975; Clayton and Engquist, 1977; Reynolds, 1978; Liao et al., 1984; Cerjan et al., 1985; Randall, 1988; Higdon, 1991). We are interested in a particular absorbing boundary condition that has maximum absorbing ability with a minimum amount of computation and storage. This is practical for 3-D simulation of elastic wave propagation by a finite‐difference method. Peng and Toksöz (1994) developed a method to design a class of optimal absorbing boundary conditions for a given operator length. In this short note, we give a brief introduction to this technique, and we compare the optimal absorbing boundary conditions against those by Reynolds (1978) and Higdon (1991) using examples of 3-D elastic finite‐difference modeling on an nCUBE-2 parallel computer. In the Appendix, we also give explicit formulas for computing coefficients of the optimal absorbing boundary conditions.

scholarly journals Boundary RG flows for fermions and the mod 2 anomaly

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Philip Boyle Smith ◽  
David Tong
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Central Charge ◽  
Boundary Operator ◽  
Majorana Fermions ◽  
Boundary State ◽  
Infra Red ◽  
Boundary Operators ◽  
Relevant Operator

Boundary conditions for Majorana fermions in d=1+1d=1+1 dimensions fall into one of two SPT phases, associated to a mod 2 anomaly. Here we consider boundary conditions for 2N2N Majorana fermions that preserve a U(1)^NU(1)N symmetry. In general, the left-moving and right-moving fermions carry different charges under this symmetry, and implementation of the boundary condition requires new degrees of freedom, which manifest themselves in a boundary central charge gg. We follow the boundary RG flow induced by turning on relevant boundary operators. We identify the infra-red boundary state. In many cases, the boundary state flips SPT class, resulting in an emergent Majorana mode needed to cancel the anomaly. We show that the ratio of UV and IR boundary central charges is given by g^2_{IR} / g^2_{UV} = \mathrm{dim} \, \mathcal{O}gIR2/gUV2=dim𝒪, the dimension of the perturbing boundary operator. Any relevant operator necessarily has \mathrm{dim} \, \mathcal{O} < 1dim𝒪<1, ensuring that the central charge decreases in accord with the gg-theorem.

scholarly journals Frequency-domain elastic wavefield simulation with hybrid absorbing boundary conditions

2019 ◽  
Vol 16 (4) ◽  
pp. 690-706
Author(s):  
Zhencong Zhao ◽  
Jingyi Chen ◽  
Xiaobo Liu ◽  
Baorui Chen
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Boundary Conditions ◽  
Frequency Domain ◽  
Time Domain ◽  
Absorbing Boundary Conditions ◽  
Elastic Media ◽  
Absorbing Boundary ◽  
Wavefield Simulation ◽  
The Time Domain

Abstract The frequency-domain seismic modeling has advantages over the time-domain modeling, including the efficient implementation of multiple sources and straightforward extension for adding attenuation factors. One of the most persistent challenges in the frequency domain as well as in the time domain is how to effectively suppress the unwanted seismic reflections from the truncated boundaries of the model. Here, we propose a 2D frequency-domain finite-difference wavefield simulation in elastic media with hybrid absorbing boundary conditions, which combine the perfectly matched layer (PML) boundary condition with the Clayton absorbing boundary conditions (first and second orders). The PML boundary condition is implemented in the damping zones of the model, while the Clayton absorbing boundary conditions are applied to the outer boundaries of the damping zones. To improve the absorbing performance of the hybrid absorbing boundary conditions in the frequency domain, we apply the complex coordinate stretching method to the spatial partial derivatives in the Clayton absorbing boundary conditions. To testify the validity of our proposed algorithm, we compare the calculated seismograms with an analytical solution. Numerical tests show the hybrid absorbing boundary condition (PML plus the stretched second-order Clayton absorbing condition) has the best absorbing performance over the other absorbing boundary conditions. In the model tests, we also successfully apply the complex coordinate stretching method to the free surface boundary condition when simulating seismic wave propagation in elastic media with a free surface.

III‐posedness of absorbing boundary conditions for migration

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 593-603 ◽  
Author(s):  
Louis H. Howell ◽  
Lloyd N. Trefethen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Order Condition ◽  
Third Order ◽  
Absorbing Boundary ◽  
Finite Speed ◽  
Ill Posed ◽  
Migration Equation ◽  
Well Posed

Absorbing boundary conditions for wave‐equation migration were introduced by Clayton and Engquist. We show that one of these boundary conditions, the B2 (second‐order) condition applied with the 45° (third‐order) migration equation, is ill‐posed. In fact, this boundary condition is subject to two distinct mechanisms of ill‐posedness: a Kreiss mode with finite speed at one boundary and another mode of a new kind involving wave propagation at unbounded speed back and forth between two boundaries. Unlike B2, the third‐order Clayton‐Engquist boundary condition B3 is well‐posed. However, we show that it is impossible for any boundary condition of Clayton‐Engquist type of order higher than one to be well‐posed with a migration equation whose order is higher than three.

scholarly journals A Generating - Absorbing Boundary Condition Applied to Wave - Current Interactions Using the Method of Fundamental Solutions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammed Loukili ◽  
Kamila Kotrasova ◽  
Amine Bouaine
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Fundamental Solutions ◽  
Absorbing Boundary Conditions ◽  
Method Of Fundamental Solutions ◽  
Computational Domain ◽  
Numerical Wave Tank ◽  
Absorbing Boundary ◽  
Wave Properties

Abstract The purpose of this work is to study the feasibility and efficiency of Generating Absorbing Boundary Conditions (GABCs), applied to wave-current interactions using the Method of Fundamental Solutions (MFS) as radial basis function, the problem is solved by collocation method. The objective is modeling wave-current interactions phenomena applied in a Numerical Wave Tank (NWT) where the flow is described within the potential theory, using a condition without resorting to the sponge layers on the boundaries. To check the feasibility and efficiency of GABCs presented in this paper, we verify accurately the numerical solutions by comparing the numerical solutions with the analytical ones. Further, we check the accuracy of numerical solutions by trying a different number of nodes. Thereafter, we evaluate the influence of different aspects of current (coplanar current, without current, and opposing current) on the wave properties. As an application, we take into account the generating-absorbing boundary conditions GABCs in a computational domain with a wavy downstream wall to confirm the efficiency of the adopted numerical boundary condition.

An absorbing boundary condition for acoustic-wave propagation using a mesh-free method

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. T145-T154 ◽  
Author(s):  
Junichi Takekawa ◽  
Hitoshi Mikada
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Acoustic Wave ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary Condition ◽  
Acoustic Wave Propagation ◽  
Absorbing Boundary ◽  
Mesh Free ◽  
Mesh Free Method

We have developed an absorbing boundary condition for acoustic-wave propagation using a mesh-free method without sacrificing the flexibility of the mesh-free framework. When we simulate acoustic-wave propagation using a numerical method, artificial reflections from model edges induced by a truncated computational domain should be avoided. Although many absorbing boundary conditions have been developed, most of them have been based on a regular latticed alignment of grids or nodes, and the efficiency of such absorbing boundary conditions for irregular arrangement of grids or nodes has not been examined yet. We have studied the artificial reflections generated at the boundaries of a model for a mesh-free method, and we have proposed a novel approach for suppressing the artifacts. The method uses a hybrid approach with a transition zone, in which the wavefield is estimated by a weighted average of solutions from the one- and two-way wave equations. Numerical experiments indicate that the proposed method can provide good performance in suppression of the artificial edge reflections even for irregular distributions of calculation points in the vicinity of model edges.

CONTINUED-FRACTION ABSORBING BOUNDARY CONDITIONS FOR THE WAVE EQUATION

2000 ◽  
Vol 08 (01) ◽  
pp. 139-156 ◽  
Author(s):  
MURTHY N. GUDDATI ◽  
JOHN L. TASSOULAS
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Transient Analysis ◽  
Continued Fraction ◽  
Finite Difference Methods ◽  
Unbounded Domains ◽  
Absorbing Boundary Conditions ◽  
High Order ◽  
Absorbing Boundary ◽  
Wave Phenomena

Absorbing boundary conditions are generally required for numerical modeling of wave phenomena in unbounded domains. Local absorbing boundary conditions are generally preferred for transient analysis because of their computational efficiency. However, their accuracy is severely limited because the more accurate high-order boundary conditions cannot be implemented easily. In this paper, a new arbitrarily high-order absorbing boundary condition based on continued fraction approximation is presented. Unlike the existing boundary conditions, this one does not contain high-order derivatives, thus making it amenable to implementation in conventional C0 finite element and finite difference methods. The superior numerical properties and implementation aspects of this boundary condition are discussed. Numerical examples are presented to illustrate the performance of these new high-order boundary condition.

Relationship between Liao and Clayton-Engquist absorbing boundary conditions: Acoustic case

1995 ◽  
Vol 85 (3) ◽  
pp. 954-956
Author(s):  
Ningya Cheng ◽  
Chuen Hon Cheng
Keyword(s):  
Boundary Condition ◽  
Reflection Coefficient ◽  
Boundary Conditions ◽  
Closed Form ◽  
Differential Form ◽  
Short Note ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary ◽  
Close Relationship

Abstract In this short note, we derive the differential form of Liao's multi-transmitting formula. The reflection coefficient of the multi-transmitting formula in the acoustic case is obtained in closed form. These formulas are compared with Clayton-Engquist absorbing boundary condition and are shown to have a very close relationship.

Sign in / Sign up

Export Citation Format

Share Document