Reflections From Multiple Transition Layers Part Ii—experimental Investigation

Berryman, L. H.; Goupillaud, Pierre L.; Waters, K. H.

doi:10.1190/1.1438463

Cited by 7 publications

(2 citation statements)

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“…The mathematical solution for the response of a multi-layer system has been given by Berryman, Goupillaud and Waters (1958) and developed by several others. These solutions are of great mathematical elegance.…”

Section: Multiple Reflectionsmentioning

confidence: 99%

Attacking the Problems of the Synthetic Seismogram

Anstey

1960

Geophysical Prospecting

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The four problems considered are the definition and simulation of the filtering effects which occur in the earth between the explosive and the case of the geophone, the problem of errors in the time scale of the synthetic record, the simulation of multiple reflection effects, and the difficulty of finding a representative comparison trace on the field record. A partial solution to the first of these is offered by SIRAN, examples of whose operation are presented. A method of assessing allowable errors in the time scale is discussed. Multiple reflections may be introduced by the preparation of multiple-corrected reflectioncoefficient logs on a digital computer such as the IBM Tog. The particular problems of multiple reflections from the base of the weathered layer (including "ghost" reflections) are discussed. The preparation of a "composite" trace is shown to be a partial solution to the problem of the comparison with the field record.Undoubtedly the greatest problem confronting us in the field of synthetic seismograms concerns the manner in which they can be used. However, the present paper is concerned mainly with problems arising when they are made; the four problems of primary concern are: (i) the problem of simulating the filtering which occurs in the earth, (ii) the problem of errors in the time scale of the synthetic record, (iii) the problem of selecting a comparison trace from the field record, and (iv) the problem of multiple reflections, transmission losses, and ghosts.These are discussed in turn. THE EARTH FILTERINGThere are at least five filtering or pulse shaping actions between the explosion and the case .of the geophone.These are associated with: (i) The length and manner of detonation of the column of explosive.(ii) The region of non-linear propagation near the shot. (iii) The normal low-pass and high-pass filtering effects associated with spherically spreading waves in earth materials.

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Section: Multiple Reflectionsmentioning

confidence: 99%

Attacking the Problems of the Synthetic Seismogram

Anstey

1960

Geophysical Prospecting

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“…The limitation in all of these cases is that the solution is given in terms of special functions. In addition I-D synthetic seismograms in a vertically inhomogeneous medium have been calculated using either combinations of transition layers (Berryman, Goupillaud & Waters 1958;Bortfeld 1960;Scholte 1961;Gupta 1965) or layer-matrix formulations (Thomson 1950;Haskell 1953;Wuenschel 1960;Pai 1985;Dietrich & Bouchon 1985).…”

Section: Introductionmentioning

confidence: 99%

Comparison of the WKBJ and truncated asymptotic methods for an acoustic medium

Yedlin

Seymour

Zelt

1990

Geophysical Journal International

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A new time-domain method for solving the 1-D acoustic wave equation with smoothly varying density and bulk modulus is used to analyse the propagation of waves in a smoothly varying medium. The new 'truncated asymptotic' method is exact for a large class of inhomogeneities and hence does not require the usual restriction of geometrical optics, that the wavelength be much less than the material stratification length.The truncated asymptotic solution is used as a benchmark to analyse a two-term WKBJ approximation for one of four classes of velocity functions. The velocity functions are such that the truncated asymptotic solutions are exact. For the case of small and intermediate velocity gradients, the WKBJ solution performs well when the length scale of the transition zone is of the same order, or larger, than the length of the applied wavelet. For steeper velocity gradients, the WKBJ solutions differs significantly from the exact truncated asymptotic solution.

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