Propagation of a compressional pulse in a layered solid

Pekeris, C. L.; Alterman, Z.; Abramovici, F.; Jarosch, H.

doi:10.1029/rg003i001p00025

Cited by 45 publications

(23 citation statements)

References 19 publications

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“…For these distances and time-intervals the whole method is inadequate and the disturbance is much more accurately described by the ray picture. There can be some particular values of the arguments that can determine a very high peak in the excitation function (Pekeris, Alterman & Abramovici 1963) but in general the energy spectrum of the source does not modify essentially the behaviour of the energy spectrum of the disturbance as determined by the transfer function only, except that it makes it highly oscillatory.…”

Section: Transfer Functionsmentioning

confidence: 95%

Mode Theory versus Theoretical Seismograms for a Layered Solid

Abramovici¹

1968

Geophysical Journal International

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Spectral transfer functions are computed for a model consisting of one elastic layer over a homogeneous elastic half-space. Represented in the time domain, the transfer functions are compared with theoretical seismograms for various horizontal distances. The diagnostic diagrams show that the P+--mode, the contribution of which is important in the generation of the PL-waves, is not the continuation of the first locked shear mode below the cut-of€ frequency.

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Section: Transfer Functionsmentioning

confidence: 95%

Mode Theory versus Theoretical Seismograms for a Layered Solid

Abramovici¹

1968

Geophysical Journal International

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“…The method of generalized rays is an outgrowth of research in geophysics from 1950 to 1970. It began with the expansion of the denominator function, Z?~'(co,p) in equation (16), into a series of exponential functions of the type exp( + iwqjHj) where Hj is the thickness of they'th layer [58,65,66]. Each term of the series is identified as a wave traveling along a specific ray path in the medium, and is called a generalized ray integral, the first being the wave from the source directly to the receiver, the second being reflected once, etc.…”

Section: Transient Waves In Layered Mediamentioning

confidence: 99%

Elastic Waves in Solids

Pao

1983

Journal of Applied Mechanics

102

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Research contributions over the past 50 years on the theory and analysis of elastodynamics are reviewed in this paper. Major topics reviewed are: general theories, steady-state waves in waveguides, transient waves in layered media, diffraction and scattering, and one and two-dimensional theories of elastic bodies. A brief discussion on the direct and inverse problems of elastic waves completes this review.As a branch of the theory of elasticity, elastodynamics appears to be a rather new and recent topic in the literature of applied mechanics. Early issues of the JOURNAL OF APPLIED

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“…Second, we assume that f (t) in (2.2) is a Heaviside unit function with rounded shoulders (Refs. [49,65] f (t) = 2 for t > 2 , where the rise time 2 is a measure of the sharpness of f (t). The pressure pulse emitted by the source has thus a triangular shape (a triangular source-pulse), that is, Fig.…”

Section: Numerical Examplesmentioning

confidence: 99%

Generalized ray method for three-dimensional propagation in a penetrable wedge

2018

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A generalized ray solution is presented for the three-dimensional (3-D) acoustic field produced by a transient point source in a rigid-bottom, fast-speed fluid-bottom, and fast-speed elastic-bottom wedge modeling a continental shelf environment. The effect of diffraction (scattering) at the wedge apex is ignored in the solution, but nevertheless the solution is exact and complete for the image component of the field, expressed by a sum of partial waves including a pulse emitted from the source plus a finite number of pulses reflected off the wedge boundaries. Time records of the acoustic pressure illustrating 3-D acoustical propagation effects are evaluated at five receivers located at equal radial range in the horizontal from the source, but different orientation to the source, measured by the azimuthal angle assuming values: 0 • (down-slope), 45 • (obliquely down-slope), 90 • (cross-slope), 135 • (obliquely up-slope), and 180 • (up-slope). The arrival times of the spherical and head waves propagating along various paths are evaluated at each receiver for each bottom. It was found that the time interval between the first arrival and the ultimate arrival diminished, and the pulses became more peaked, as the azimuthal angle of the receiver increased. For the rigid-bottom wedge, we have found that all backscattered pulses are significant at the up-slope receiver. For the fluid-bottom wedge, we have found that: at each receiver, the source-pulse is preceded by the ground wave which is much weaker than the water wave; and, at the up-slope receiver, the backscattered pulses are insignificant. For the elastic-bottom wedge, we have found that: at each receiver, the ground-wave-response begins earlier than that in the fluid-bottom wedge, and thus the record separates out into distinct ground-wave and water-wave phases; and, at the up-slope receiver, the backscattered pulses are significant.

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Propagation of a compressional pulse in a layered solid

Cited by 45 publications

References 19 publications

Mode Theory versus Theoretical Seismograms for a Layered Solid

Mode Theory versus Theoretical Seismograms for a Layered Solid

Elastic Waves in Solids

Generalized ray method for three-dimensional propagation in a penetrable wedge

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