A Nonconvolutional, Split-Field, Perfectly Matched Layer for Wave Propagation in Isotropic and Anisotropic Elastic Media: Stability Analysis

2008 ◽  
Vol 98 (4) ◽  
pp. 1811-1836 ◽  
Author(s):  
K. C. Meza-Fajardo ◽  
A. S. Papageorgiou
Keyword(s):  
Wave Propagation ◽  
Stability Analysis ◽  
Perfectly Matched Layer ◽  
Elastic Media ◽  
Anisotropic Elastic ◽  
Split Field

On the existence of type-6 transonic states in linear elastic media of cubic symmetry

1987 ◽  
Vol 411 (1840) ◽  
pp. 251-263 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Elastic Solid ◽  
Mechanics Of Solids ◽  
Elastic Media ◽  
Slowness Surface ◽  
Cubic Symmetry ◽  
Linear Elastic ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

Crucial to the understanding of surface-wave propagation in an anisotropic elastic solid is the notion of transonic states, which are defined by sets of parallel tangents to a centred section of the slowness surface. This study points out the previously unrecognized fact that first transonic states of type 6 (tangency at three distinct points on the outer slowness branch S 1 ) indeed exist and are the rule, rather than the exception, in so-called C 3 cubic media (satisfying the inequalities c 12 + c 44 > c 11 - c 44 > 0); simple numerical analysis is used to predict orientations of slowness sections in which type-6 states occur for 21 of the 25 C 3 cubic media studied previously by Chadwick & Smith (In Mechanics of solids , pp. 47-100 (1982)). Limiting waves and the composite exceptional limiting wave associated with such type-6 states are discussed.

scholarly journals Modeling of random anisotropic elastic media and impact on wave propagation

2010 ◽  
pp. 241-253
Author(s):  
Quang-Anh Ta ◽  
Didier Clouteau ◽  
Régis Cottereau Cottereau
Keyword(s):  
Wave Propagation ◽  
Anisotropic Material ◽  
Tensor Field ◽  
Elasticity Tensor ◽  
Positive Definite ◽  
Elastic Media ◽  
New Model ◽  
Anisotropy Index ◽  
Anisotropic Elastic ◽  
Non Gaussian

The class of stochastic non-gaussian positive-definite fields with minimal parameterization proposed by Soize (Soize, 2006) to model the elasticity tensor field of a random anisotropic material shows an anisotropy index which grows with the fluctuation level. This property is in contradiction with experimental results in geophysics where the anisotropy index remains limited whatever the fluctuation level. Hence, the main purpose of this paper is to generalize the Soize’s model in order to account independently for the anisotropy index and the fluctuation level. It is then shown that this new model leads to major differences in the wave propagation regimes.

scholarly journals Modeling of random anisotropic elastic media and impact on wave propagation

2010 ◽  
Vol 19 (1-3) ◽  
pp. 241-253 ◽  
Author(s):  
Quang-Anh Ta ◽  
Didier Clouteau ◽  
Régis Cottereau
Keyword(s):  
Wave Propagation ◽  
Elastic Media ◽  
Anisotropic Elastic

Wave propagation in transversely isotropic elastic media - II. Surface waves

1989 ◽  
Vol 422 (1862) ◽  
pp. 67-101 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Theoretical Background ◽  
Clear Understanding ◽  
Elastic Media ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

The treatment of homogeneous plane waves given in part I provides the basis for the detailed study of the nature of surface-wave propagation in transversely isotropic elastic media presented in this paper. The investigation is made within the framework of the existence theorem of Barnett and Lothe and the developments underlying its proof. The paper begins with a survey of this essential theoretical background, outlining in particular the formulation of the secular equation for surface waves in the real form F(v) = 0, F(v) being a nonlinear combination of definite integrals involving the acoustical tensor Q (⋅) and the associated tensor R (⋅,⋅) introduced in part I. The calculation of F(v) for a transversely isotropic elastic material is next undertaken, first, in principle, for an arbitrary orientation of the axis of symmetry, then for the α and β configurations, shown in part I to contain all the exceptional transonic states. In the rest of the paper the determination of F(v) is completed, in closed form, for the α and β configurations and followed in each case by a discussion of the properties of F(v) and illustrative numerical results. This combination of analysis and computation affords a clear understanding of surface-wave behaviour in the exceptional configurations comprising, in the classification of part I, cases 1, 2 and 3. The findings for case 1 exhibit continuous transitions, within the α configurations, between subsonic and supersonic surface-wave propagation. Those for case 3 prove that there are discrete orientations of the axis for which no genuine surface wave can propagate and that this degeneracy typically has a marked influence on surface-wave properties in a sizeable sector of neighbouring β configurations. Neither effect appears in previous accounts of surface-wave propagation in anisotropic elastic media.

Finite‐difference modeling of elastic wave propagation: A nonsplitting perfectly matched layer approach

Geophysics ◽  
2003 ◽  
Vol 68 (5) ◽  
pp. 1749-1755 ◽  
Author(s):  
Tsili Wang ◽  
Xiaoming Tang
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Shear Velocity ◽  
Perfectly Matched Layer ◽  
Elastic Wave Propagation ◽  
Dipole Source ◽  
Flexural Wave ◽  
Field Approach ◽  
Split Field

In this paper, we present a nonsplitting perfectly matched layer (NPML) method for the finite‐difference simulation of elastic wave propagation. Compared to the conventional split‐field approach, the new formulation solves the same set of equations for the boundary and interior regions. The nonsplitting formulation simplifies the perfectly matched layer (PML) algorithm without sacrificing the accuracy of the PML. In addition, the NPML requires nearly the same amount of computer storage as does the split‐field approach. Using the NPML, we calculate dipole and quadrupole waveforms in a logging‐while‐drilling environment. We show that a dipole source produces a strong pipe flexural wave that distorts the formation arrivals of interest. A quadrupole source, however, produces clean formation arrivals. This result indicates that a quadrupole source is more advantageous over a dipole source for shear velocity measurement while drilling.

A Stability Analysis of the Perfectly Matched Layer Method

1999 ◽  
Author(s):  
S. J. Yakura ◽  
David Dietz ◽  
Andy Greenwood ◽  
Ernest Baca
Keyword(s):  
Stability Analysis ◽  
Perfectly Matched Layer ◽  
Layer Method
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