Matrix methods in synthetic seismograms

Chin, R. C. Y.; Hedstrom, G. W.; Thigpen, L.

doi:10.1111/j.1365-246x.1984.tb01944.x

Cited by 46 publications

(22 citation statements)

References 20 publications

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“…The problem with the exponential dichotomy arises in the high-frequency range, when some of the eigenvalues of A have large real parts with opposite signs, resulting in rapidly decaying as well as growing exponentials (Chin et al, 1984). These are associated with standing waves attenuated in both senses along the axial direction.…”

Section: Solution Of the State Equationmentioning

confidence: 99%

High-frequency response of isotropic-laminated cylindrical shells modeled by a layer-wise theory

Braga

Rivas

2005

International Journal of Solids and Structures

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In this paper, the high-frequency response of isotropic-laminated cylindrical shells is investigated using a layer-wise theory. The cylindrical shell is discretized in an arbitrary number of layers in the radial direction, and a three-dimensional stress state is assumed in each layer. Approximate numerical results obtained by the layer-wise theory are compared with the exact wave-dispersion analytical results. The very good agreement between approximate and exact results indicates that the layer-wise theory can accurately describe of the dynamic response of cylindrical shells in the high-frequency (short-wavelength) range.

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Section: Solution Of the State Equationmentioning

confidence: 99%

High-frequency response of isotropic-laminated cylindrical shells modeled by a layer-wise theory

Braga

Rivas

2005

International Journal of Solids and Structures

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“…(4) for the transfer matrix by using the geometric integrator concept. However, it is well known the transfer matrix method becomes inherently unstable due to the coexistence of exponentially decaying and growing matrix elements associated with nonhomogeneous waves, the problem that has been known as 'exponential dichotomy' in the numerical solution of linear matrix di erential equations (Chin et al, 1984;Wang and Rokhlin, 2004a). The sti ness matrix method is unconditionally stable (Wang and Rokhlin, 2001;Rokhlin and Wang, 2002).…”

Section: Outline Of the Approachmentioning

confidence: 99%

Recursive geometric integrators for wave propagation in a functionally graded multilayered elastic medium

Wang

Rokhlin

2004

Journal of the Mechanics and Physics of Solids

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“…This new method will be called 'invariant embedding' based on the nomenclature in the review paper of Chin, Hedstrom & Thigpen (1984). We demonstrate the superior numerical stability and computational efficiency of the invariant embedding technique compared with the propagator formulation using a variety of numerical examples.…”

Section: Introductionmentioning

confidence: 97%

2-D reflectivity method and synthetic seismograms for irregularly layered structures-II. Invariant embedding approach

Koketsu

Takenaka

1991

Geophysical Journal International

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S U M M A R YLaterally varying interfaces cause coupling between wavenumbers so that seismograms in two-dimensionally layered media can be synthesized by means of 'supermatrices', which include the coupled contributions of all the wavenumbers. We introduce reflection and transmission 'supennatrices' in order to eliminate numerical problems arising from loss of precision for evanescent waves in the seismogram synthesis. An interface is assumed to be such that the reflected and transmitted wavefields on its two sides can be represented as purely upgoing and downgoing waves, i.e. the Rayleigh ansatz is imposed. The computational demands of this method can be kept to a minimum by exploiting propagation invariants in the coupled wavenumber domain.The superior performance of this 'invariant embedding' approach when compared to propagator or finite difference schemes is illustrated by application to the response of sedimentary basins to excitation by an incident plane wave or a line force. The results are in good general agreement with the other methods, but show greater numerical stability and computational efficiency. In the case of a single interface the 'invariant embedding' procedure for P-SV-waves takes 45 per cent less computation time and 29 per cent less memory than the propagator method of Koketsu (1987a,b). The gains are reduced in a multilayer case because of the level of computation required to calculate the addition rules for the large reflection and transmission supermatrices.

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Matrix methods in synthetic seismograms

Cited by 46 publications

References 20 publications

High-frequency response of isotropic-laminated cylindrical shells modeled by a layer-wise theory

High-frequency response of isotropic-laminated cylindrical shells modeled by a layer-wise theory

Recursive geometric integrators for wave propagation in a functionally graded multilayered elastic medium

2-D reflectivity method and synthetic seismograms for irregularly layered structures-II. Invariant embedding approach

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