Photoelastic analysis of Rayleigh wave propagation in wedges

Lewis, David N.; Dally, J. W.

doi:10.1029/jb075i017p03387

Cited by 22 publications

(7 citation statements)

References 8 publications

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“…(See Pilant et al (1964) and Lewis & Dally (1970) for the experimental results). Among these features we point out the occurrence of a peak value in the magnitude of A , around 60" and the uniformly positive phase of A R in the range 50" to 140" approximately.…”

Section: Fro 2 Cycles Of Reflected Transmitted and Additionally Exmentioning

confidence: 94%

“…On the basis of the recomputation of the M-K approximation we conclude that the theory cannot account for various important features of the experimental data, especially for wedge angles less than 90". (See Pilant et al (1964) and Lewis & Dally (1970) for the experimental results). Among these features we point out the occurrence of a peak value in the magnitude of A , around 60" and the uniformly positive phase of A R in the range 50" to 140" approximately.…”

Section: Present Higher Approximationsmentioning

confidence: 98%

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Reflection and Transmission of Rayleigh Waves in a Wedge--I

Viswanathan¹,

Kuo²,

Lapwood³

1971

Geophysical Journal International

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On the basis of the work of Hudson & Knopoff and of Ma1 & Knopoff on the reflection and transmission coefficients for Rayleigh waves in a wedge, higher order approximate solutions are obtained by considering the possible mechanism of generation of the Rayleigh waves in the classic Lamb's problem. The critical ranges of existence of Rayleigh waves in the medium appear to be one of the controlling factors of these coefficients. Whereas the approximate solutions of Hudson & Knopoff and Ma1 & Knopoff are sufficiently good for wedge angles greater than 90°, the present higher approximations yield results which show considerably closer agreement with experimental data not only in the above range but also very particularly for wedge angles less than 90" both in magnitude and phase.

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Section: Fro 2 Cycles Of Reflected Transmitted and Additionally Exmentioning

confidence: 94%

Section: Present Higher Approximationsmentioning

confidence: 98%

Reflection and Transmission of Rayleigh Waves in a Wedge--I

Viswanathan¹,

Kuo²,

Lapwood³

1971

Geophysical Journal International

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“…The coefficients depend on wedge angle and Poisson ratio. The dependence on wedge angle was experimentally investigated by GANGI (1960) andPILANT et al (1964), using the techniques of model experiment, and by LEWIS and DALLY (1970) by means of the photoelastic effect. These results clearly show that the coefficients are subject to very complicated variations, especially where the wedge angle is smaller than 90 ~ .…”

Section: Introductionmentioning

confidence: 99%

Rayleigh wave scattering at wedge corners with major wedge angles

Nakano

Fujii

Takeuchi

1988

PAGEOPH

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Abstract--Theoretical calculations were performed on reflected and transmitted Rayleigh waves and scattered body waves, in the case where a two-dimensional Rayleigh wave is incident to a wedge-shaped medium having a wedge angle between 250 ~ and 290 ~ and arbitrary value of Poisson ratio. The reflection and transmission coefficients of Rayleigh waves were also experimentally measured in cases of wedges with 190 ~ to 330 ~ wedge angles. The method of theoretical analysis and the techniques of experiment are based on those developed in our preceding research (W-1. W-2 and W-3). Compared with the results where the wedge angle is smaller than 180 ~ (W-1 and W-2), all features show consistent variation with wedge angle.

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“…Fujii et al (1984) and expanded the range of Momoi's solution to wedge angles between 72" and 105" and showed solutions corresponded with experimental results. Many other experimental studies of Rayleigh waves in wedges were also completed (de Bremaecker 1958;Knopoff & Gangi 1960;Pilant, Knopoff & Schwab 1964;Lewis & Dally 1970; Gangi are based on assumptions such as the validity of using a 'reference' layered structure with superimposed lateral variations for models in which the heterogeneities are small, and in addition using 'local' modes calculated for the vertical model at each radial point for cases where the large-scale structure of the model vanes. Synthetics generated without these types of assumptions, using the hybrid method and the extensions to it proposed in this document, should be invaluable in helping to understand propagation of regional waves through certain classes of models.…”

Section: Introductionmentioning

confidence: 99%

Seismic representation theorem coupling: synthetic P-SV mode sum seismograms for non-homogeneous paths

Regan

1991

Geophysical Journal International

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S U M M A R YThe hybrid technique developed and demonstrated in this paper will be useful in studies of the propagation of any phase that can be represented in terms of a P-SV mode sum seismogram, across regional transition zones or other heterogeneities. These heterogeneities may exist in regions which form subsegments of a longer, mostly plane-layered, path. Examples of structures of interest through which such waves can be propagated using these techniques include regions of crustal thickening or thinning such as continent ocean transitions or basins, anomalous bodies of any shape located in the path, and sudden transitions from one layered structure to another. Examples of the types of phases than may be propagated through these structures include Rayleigh waves, L,, P,,, R,, S, , and Pg.The hybrid method integrates three different types of numerical methods. The combination of these methods into a single hybrid technique allows consideration of problems which, due to computational and theoretical constraints, cannot be solved by any one of the individual component methods. The first two methods which are part of the hybrid technique are the finite element (FE) or finite difference (FD) method, and the modal propagator matrix (PM) method. Existing implementations of these methods have been modified to be compatible parts of the hybrid method. The third method which forms an integral part of the hybrid technique is the representation theorem (RT) integration method. It is developed, explained and illustrated in this paper. The hybrid method is a generalization of the hybrid method of Regan & Harkrider (1989a, b) for generation of hybrid SH mode-sum seismograms. It is used to produce synthetics for propagation along a long plane-layered path which contains a short segment or segments of heterogeneous structures. For simplicity consider one such short heterogeneous path segment between the source and the receiver. The hybrid method consists of a series of three procedures which propagate the wavefield across the heterogeneous segment of the path. This series of operations may be repeated if other heterogeneous segment occur between the source and the receiver. The first operation of the series uses the PM method to propagate the wavefield from the point or line source, located in a layered half-space, to the beginning of the heterogeneous segment of the path. The second procedure in the series couples the wavefield into the FE or FD grid and propagates it through the heterogeneous segment of the path using the FE or FD method. The third and final procedure in the series couples the wavefield back into and through another layered medium using the RT integration coupling method.The uncertainties inherent in the hybrid method are well understood. A discussion based on the orthogonality relations for Rayleigh waves is used as a basis for two methods, a method for the determination of the accuracy of the hybrid results, and a method which allows the decomposition of the wavefield into seismograms composed of single o...

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Photoelastic analysis of Rayleigh wave propagation in wedges

Cited by 22 publications

References 8 publications

Reflection and Transmission of Rayleigh Waves in a Wedge--I

Reflection and Transmission of Rayleigh Waves in a Wedge--I

Rayleigh wave scattering at wedge corners with major wedge angles

Seismic representation theorem coupling: synthetic P-SV mode sum seismograms for non-homogeneous paths

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