scholarly journals Non-convolutional second-order complex-frequency-shifted perfectly matched layers for transient elastic wave propagation

2021 ◽  
Vol 377 ◽  
pp. 113704
Author(s):  
Stijn François ◽  
Heedong Goh ◽  
Loukas F. Kallivokas
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Second Order ◽  
Elastic Wave Propagation ◽  
Complex Frequency ◽  
Order Complex ◽  
Perfectly Matched Layers ◽  
Matched Layers

Modelling Seismic Oceanography Experiments by Using First- and Second-Order Complex Frequency Shifted Perfectly Matched Layers

2009 ◽  
Vol 95 (6) ◽  
pp. 1104-1111 ◽  
Author(s):  
Jean Kormann ◽  
Pedro Cobo ◽  
Manuel Recuero ◽  
Berta Biescas ◽  
Valentí Sallarés
Keyword(s):  
Second Order ◽  
Complex Frequency ◽  
Order Complex ◽  
Perfectly Matched Layers ◽  
Seismic Oceanography ◽  
Matched Layers

Compact second-order time-domain perfectly matched layer formulation for elastic wave propagation in two dimensions

2016 ◽  
Vol 22 (1) ◽  
pp. 20-37 ◽  
Author(s):  
Hisham Assi ◽  
Richard S. Cobbold
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Computational Cost ◽  
Perfectly Matched Layer ◽  
Two Dimensions ◽  
Second Order ◽  
Elastic Wave Propagation ◽  
Discrete Models ◽  
Computational Stability ◽  
Spatial Frequencies

A new second-order formulation is obtained for elastic wave propagation in 2D media bounded by a perfectly matched layer (PML). The formulation uses a complex coordinate stretching approach with a two-parameter stretch function. The final system, consisting of just two second-order displacement equations along with four auxiliary equations, is smaller than existing formulations, thereby simplifying the problem and reducing the computational cost. With the help of a plane-wave analysis, the stability of the continuous formulation is examined. It is shown that by increasing the scaling parameter in the stretch function, any existing instability is moved to higher spatial frequencies. Since discrete models cannot resolve frequencies beyond a certain limit, this can lead to significant computational stability improvements. Numerical results are shown to validate our formulation and to illustrate the improved stability that can be achieved with certain anisotropic media that have known issues.

scholarly journals FICTITIOUS DOMAINS, MIXED FINITE ELEMENTS AND PERFECTLY MATCHED LAYERS FOR 2-D ELASTIC WAVE PROPAGATION

2001 ◽  
Vol 09 (03) ◽  
pp. 1175-1201 ◽  
Author(s):  
E. BÉCACHE ◽  
P. JOLY ◽  
C. TSOGKA
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Finite Elements ◽  
Elastic Wave ◽  
Heterogeneous Media ◽  
Mixed Finite Elements ◽  
Time Discretization ◽  
Elastic Wave Propagation ◽  
Perfectly Matched Layers ◽  
Simple Geometry

We design a new and efficient numerical method for the modelization of elastic wave propagation in domains with complex topographies. The main characteristic is the use of the fictitious domain method for taking into account the boundary condition on the topography: the elastodynamic problem is extended in a domain with simple geometry, which permits us to use a regular mesh. The free boundary condition is enforced introducing a Lagrange multiplier, defined on the boundary and discretized with a nonuniform boundary mesh. This leads us to consider the first-order velocity-stress formulation of the equations and particular mixed finite elements. These elements have three main nonstandard properties: they take into account the symmetry of the stress tensor, they are compatible with mass lumping techniques and lead to explicit time discretization schemes, and they can be coupled with the Perfectly Matched Layer technique for the modeling of unbounded domains. Our method permits us to model wave propagation in complex media such as anisotropic, heterogeneous media with complex topographies, as it will be illustrated by several numerical experiments.

Elastic wave‐propagation simulation in heterogeneous media by the spectral moments method

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1269-1281 ◽  
Author(s):  
Valérie Rousseau ◽  
Claude Benoit ◽  
Roger Bayer ◽  
Michel Cuer ◽  
Gérard Poussigue
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Continued Fraction ◽  
Heterogeneous Media ◽  
Finite Difference Methods ◽  
Second Order ◽  
Elastic Wave Propagation ◽  
Spectral Moments ◽  
Dynamic Matrix ◽  
Moments Method

The second‐order elastic wave propagation equations are solved using the spectral moments method. This numerical method, previously developed in condensed matter physics, allows the computation of Green’s functions for very large systems. The elastic wave equations are transformed in the Fourier domain for time derivatives, and the partial derivatives in space are computed by second‐order finite differencing. The dynamic matrix of the discretized system is built from the medium parameters and the boundary conditions. The Green’s function, calculated for a given source‐receiver couple, is developed as a continued fraction whose coefficients are related to the moments and calculated from the dynamic matrix. The continued fraction coefficients and the moments are computed using a very simple algorithm. We show that the precise estimation of the waveform for the successive waves arriving at the receiver depends on the number of moments used. For long recording times, more moments are needed for an accurate solution. Efficiency and accuracy of the method is illustrated by modeling wave propagation in 1-D acoustic and 2-D elastic media and by comparing the results obtained by the spectral moments method to analytical solutions and classical finite‐difference methods.

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