Radiation characteristics of elastodynamic line sources buried in layered media with periodic interfaces. II. P- and SV-wave analysis

1987 ◽  
Vol 77 (6) ◽  
pp. 2192-2211
Author(s):  
Vijay K. Varadan ◽  
Akhlesh Lakhtakia ◽  
Vasundara V. Varadan ◽  
Charles A. Langston
Keyword(s):  
Half Space ◽  
Elastic Plate ◽  
Matrix Method ◽  
Scattering Problem ◽  
Finite Size ◽  
Layered Media ◽  
Elastic Half Space ◽  
P Wave ◽  
Radiation Characteristics ◽  
T Matrix

Abstract A method for determining for determining the elastodynamic (P and SV waves) radiation characteristics of finite-size sources buried in horizontally layered media, having periodically corrugated interfaces, is described. In particular, the example problem chosen to illustrate the procedure is as follows: a solid plate lies on top of a solid half-space; the solid-solid interface has been taken to be planar, but traction-free conditions prevail on the other boundary of the elastic plate, which surface is also periodically corrugated; and the source has been taken to be an isotropic, P-wave line source located inside the elastic plate. The technique presented utilizes the plane wave spectral decomposition of the relevant fields within the framework of the extended boundary condition method or the T matrix method. Since the T-matrix method is a matrix approach, it is very attractive computationally and is certainly more tractable than a method based on the direct solution of the integral equations involved in the scattering problem. Numerical results are given to delineate the various features of the field diffracted into the elastic half-space, as well as the displacement field induced on the traction-free boundary of the elastic plate. The specific example examined is directly related to regional wave propagation in a continental crustal wave guide.

The Transition Matrix Formalism for the Scattering of an Alluvium on an Elastic Half-Space

2007 ◽  
Author(s):  
Wen-I Liao ◽  
Tsung-Jen Teng ◽  
Shiang-Jung Wang
Keyword(s):  
Half Space ◽  
Transition Matrix ◽  
Plane Waves ◽  
Three Dimensional ◽  
Scattering Matrix ◽  
Elastic Half Space ◽  
Basis Functions ◽  
Matrix Formalism ◽  
T Matrix ◽  
Singular Wave

This paper develops the transition matrix formalism for scattering from an three-dimensional alluvium on an elastic half-space. Betti’s third identity is employed to establish orthogonality conditions among basis functions that are Lamb’s singular wave functions. The total displacements and associated tractions exterior and interior to the surface are expanded in a Rayleigh series. The boundary conditions are applied and the T-matrix is derived. A linear transformation is utilized to construct a set of orthogonal basis functions. The transformed T-matrix is related to the scattering matrix and it is shown that the scattering matrix is symmetric and unitary and that the T-matrix is symmetric. Typical numerical results obtained by incident plane waves for verification are presented.

Seismogram synthesis for multi-layered media with irregular interfaces by global generalized reflection/transmission matrices method. I. Theory of two-dimensional SH case

1990 ◽  
Vol 80 (6A) ◽  
pp. 1696-1724 ◽  
Author(s):  
Xiao-fei Chen
Keyword(s):  
Matrix Method ◽  
Computation Time ◽  
Source Area ◽  
Layered Media ◽  
Two Dimensional ◽  
Finite Frequency ◽  
Number Of Layers ◽  
Efficient Scheme ◽  
T Matrix ◽  
Irregular Topography

Abstract In this paper, we present a new method of seismogram synthesis for multi-layered media with irregular interfaces due to an arbitrary source. This method can be viewed as either an extension of the T matrix method for an inclusion to multi-layered media by introducing the global generalized R/T matrices, or an extension of the generalized R/T coefficients method for horizontally layered media to irregular layered ones by incorporating the T matrix method. The formulation obtained in this paper is expressed in terms of the global generalized R/T matrices. These global generalized R/T matrices can be determined from integrals along each interface and integral over source area via a recursive relation. This formulation provides an efficient scheme of computation, especially when the number of layers increases. Also, this formulation can be applied to any finite frequency, although for higher frequency it needs more computation time than for lower frequency. As examples, we give solutions of three specific problems, namely, horizontally layered media, irregular topography, and an irregular layer over a half-space.

Wave Scattering by Crack Under Shock P-Wave in an Elastic Half-Space

2021 ◽  
Author(s):  
Hai Zhang ◽  
Tianyu Zhao ◽  
Dai Wang ◽  
Qiang Pei ◽  
Ying Xu ◽  
...  
Keyword(s):  
Half Space ◽  
Wave Scattering ◽  
Elastic Half Space ◽  
P Wave

Static deformation of a multilayered magneto-electro-elastic half-space structures due to vertical inner loading

2021 ◽  
pp. 108128652110495
Author(s):  
Peizhuo Wang ◽  
Dongchen Qin ◽  
Peng Shen ◽  
Jiangyi Chen
Keyword(s):  
Half Space ◽  
Vector Function ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Gaussian Quadrature ◽  
Elastic Half Space ◽  
Point Load ◽  
Static Deformation ◽  
Function System ◽  
Adaptive Gaussian Quadrature

The static deformation in a multilayered magneto-electro-elastic half-space under vertical inner loading is calculated using a vector function system approach and a stiffness matrix method. Firstly, the displacement, stress, and inner loading are expanded using the vector function system, and the N-type and L&M-type problems related to the expansion coefficient are constructed. Secondly, the stable stiffness matrix method is used to solve the expansion coefficients of the L&M-type problem. After introducing the boundary condition and the discontinuity of the stress caused by inner loading, the displacement and stress are calculated through adaptive Gaussian quadrature. Finally, the numerical examples considering the circular load and point load are designed and analyzed, respectively.

On the Unbonded Contact Between Plates and an Elastic Half Space

1969 ◽  
Vol 36 (2) ◽  
pp. 198-202 ◽  
Author(s):  
Y. Weitsman
Keyword(s):  
Approximate Solution ◽  
Tensile Stress ◽  
Half Space ◽  
Elastic Plate ◽  
Elastic Half Space ◽  
Elastic Support ◽  
Elastic Region ◽  
Concentrated Load

In this paper an approximate solution is presented for the radius of contact between an elastic plate and a semi-infinite elastic half space. The plate is assumed to rest on the supporting half space without bond, and to be pressed against the elastic region by a concentrated load. In the absence of bonding no tensile stress can be transmitted across the interface between the plate and its elastic support so that contact takes place only within a circle centered about the concentrated load. Outside of this circle the plate lifts up and is no longer in contact with the elastic region.

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