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

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.

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Transmission of Dirac Electrons Through Graphene Multilayers with Gaussian Profile

MRS Proceedings ◽

10.1557/opl.2012.175 ◽

2012 ◽

Vol 1371 ◽

Author(s):

J. A. Aguilar-Hernández ◽

J. Madrigal-Melchor ◽

J. C. Martínez-Orozco ◽

I. Rodríguez-Vargas

Keyword(s):

Graphene Sheet ◽

Gaussian Distribution ◽

Matrix Method ◽

Stop Band ◽

Angle Of Incidence ◽

Gaussian Profile ◽

Number Of Layers ◽

T Matrix ◽

The Difference ◽

Maximum Minimum

ABSTRACTIn this work, we use the T-matrix method to study the tunneling of Dirac electrons through graphene multilayers. A graphene sheet is deposited on top of slabs of SiO2-SiC substrates, of which we applied a Gaussian distribution in the size width of the SiC substrate. We calculate the transmittance as a function of energy for different incident angles and different number of layers of the Gaussian distribution. We obtain different stop-band regions. These regions are wider when the width of the barrier is increased. Furthermore, it is possible to tune the width and the position of stop-band with the angle of incidence, the σ value of the Gaussian distribution, and the difference between the maximum-minimum sizes of the barrier.

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A far-field based T-matrix method for two dimensional obstacle scattering

ANZIAM Journal ◽

10.21914/anziamj.v51i0.2581 ◽

2010 ◽

Vol 51 ◽

pp. 215 ◽

Cited By ~ 4

Author(s):

Mahadevan Ganesh ◽

Stuart Collin Hawkins

Keyword(s):

Matrix Method ◽

Far Field ◽

Two Dimensional ◽

T Matrix ◽

Obstacle Scattering

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

Bulletin of the Seismological Society of America ◽

10.1785/bssa0770062192 ◽

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.

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