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- Volume 24, Issue 3, 1976
Geophysical Prospecting - Volume 24, Issue 3, 1976
Volume 24, Issue 3, 1976
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INSTABILITY OF FINITE DIFFERENCE SCHEMES DUE TO BOUNDARY CONDITIONS IN ELASTIC MEDIA*
Authors A. ILAN and D. LOEWENTHALAbstractThe manner in which boundary conditions are approximated and introduced into finite difference schemes may have an important influence on the stability and accuracy of the results. The standard von Neumann condition for stability applies only for points which are not in the vicinity of the boundaries. This stability condition does not take into consideration the effects caused by introducing the boundary conditions to the scheme.
Working on elastic media with free stress boundary conditions we found that the boundary approximation gives rise to serious stability problems especially for regions with high Poisson's ratio. In order to detect these effects apriori and to analyse them, we have used a more elaborate procedure for checking the stability of the scheme which takes into consideration the boundary conditions. It is based on studying a locally spaced time propagating matrix which governs the time‐space behavior of a small region of the grid which includes free surface points.
By using this procedure a better insight into the nature of instability caused by the approximations to the boundary conditions was gained which led us to a new stable approximation for the free surface boundary conditions.
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A STUDY OF THE SEISMIC SIGNATURES OF SEDIMENTATION MODELS USING SYNTHETIC SEISMOGRAMS*
Authors K. KHATTRI and R. GIRAbstractIn modern exploration for hydrocarbons there is a great emphasis on the location of stratigraphic traps and estimation of lithologic information like sand‐shale ratios from seismic data. In order to investigate the possibilities of success in this endeavour we have studied the synthetic seismograms for wave form and spectral characteristic for four basic sedimentation models: (I) interbedded sand‐shale model representing the sediments of generally fluviatile origin, (2) interbedded coal‐shale model representing deltaic deposits, (3) sedimentary models representing transgression and regression of shore lines, and (4) a basal sand model. The results have shown that for the first two models a change in the sand‐shale or coal‐shale ratio results in a characteristically different seismogram. The nature of the seismogram, however, is also strongly dependent on how the sand‐shale or coal shale layers are arranged to ultimately give the same number of total layers, thus implying the same coal‐shale or sand‐shale ratios. The transgression, regression, and basal sand models also produce characteristically different seismic signatures. The spectra of these seismograms show attendant characteristic changes. However, it seems that in the case of real data which are disturbed by noise and the effects of overlying layers these characteristic features may not always be distinguishable.
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CDP RAY MODELING IN THE PRESENCE OF 3‐D PLANE ISOVELOCITY LAYERS OF VARYING DIP AND STRIKE*
By P. HUBRALAbstractVarious Dix‐type formulae are derived, which are useful to approximate travel time functions that can be observed while modeling the common depth point (CDP) technique for 3‐D isovelocity layers of varying dip and strike. All formulae can be used to compute interval velocities and recover the depth model from surface measurements. They are established by making use of the concept of wavefront curvature. Many similarities with known formulae valid for the 2‐D plane isovelocity layer case exist.
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AN ATTEMPT AT THE INVERSION OF REFLECTION DATA*
More LessAbstractThe main problem in seismic prospecting is to infer from the observed reflection response the distribution of density and seismic velocity with depth. This process is generally called the inversion of the reflection data.
For plane waves propagating through plane parallel stratification, it can be shown that at any depth the ratio between the amplitude of the transmitted and reflected wave satisfies the Riccati equation. Based on this equation we have formulated an iterative inversion method, which is found to be suitable for numerical computations. We have applied this method on synthetic reflection data, and found that it provides a very fast and accurate inversion.
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WHERE IS ZERO TIME?*
By J. FARRELLAbstractMis‐ties are all‐too‐common results of seismic surveys made at the same place but at different times with different equipment or by different organizations. Even after removal of positioning or polarity errors, reflection times often appear to differ by several tens of milliseconds. Zero time appears to fluctuate.
How can zero time differ on surveys with only minor differences in acquisition or processing? What can be done to identify the true zero time for each survey?
The first step toward establishing zero time is to record the source pulse. It is well‐known that the different sources currently used in reflection seismic prospecting (propane‐oxygen explosions, compressed‐air discharges, explosives, steam bubbles, mechanical implosions, vibrations, etc.) yield different pressure wavefronts as the input to the seismic reflection system. By recording this wavefront we capture the basic pulse shape and we establish the initial time delay.
The second step is to process the recorded source pulse as if it were reflection data to establish the additional time and shape changes introduced by data processing. Then, display the recorded and processed source pulse as an auxiliary variable at the ends of the seismic section. From this display the interpreter can systematically establish the time shifts appropriate to each picked event. He can determine also whether the pick should be a peak or a trough. He can see why surveys which appear to tie for shallow reflections appear to mis‐tie for deep reflections.
The display of the processed source pulse constitutes a major interpretation aid which, in a readily useable form, increases the information content of the basic seismic section.
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MINI‐SOSIE FOR LAND SEISMOLOGY*
Authors M. G. BARBIER, P. BONDON, R. MELLINGER and J. R. VIALLIXAbstractMini‐sosie consists in using a vibration‐rammer as seismic source and changing the striking rate by varying the engine speed, resulting in a random impulse transmission. The recording instruments are made up of two seismic traces, two constant gain amplifiers and a two‐channel sosie processor which performs the decoding in real time by using the actual transmission times supplied by a captor located on top of the vibration‐rammer's plate. An idea of the possible penetration is given by the recording of a velocity survey. Other results obtained in seismic reflection and refraction are given.
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FUNDAMENTAL FUNCTIONS FOR HORIZONTALLY STRATIFIED EARTH*
By E. SZARANIECAbstractThe potential distribution and the wave propagation in a horizontally stratified earth is considered and the analogy of the mathematical expression for seismic transfer function, electromagnetic and electric kernel functions, and magnetotelluric input impedance is discussed. Although these specific functions are conveniently treated by a separate expression in each method, it is indicated that the function for seismic and electromagnetic methods is mathematically the same with a change in the physical meaning of the variables from one method to the other. Similarly, the identity of the mathematical expressions of the resistivity kernel function and magnetotelluric input impedance is noticed.
In each method a specific geophysical function depends on the thickness and the physical properties of the various layers. Every specific function involves two interdependent fundamental functions, that is Pn and Qn, or Pn and P*n, having different physical meaning for different methods. Specific functions are expressible as a ratio Pn/Qn or P*n/Pn. Fundamental functions may be reduced to polynomials.
The fundamental polynomials Q*n and P*n describing the horizontally stratified media are a system of polynomials orthogonal on the unit circle, of first and second order, respectively. The interpretation of geophysical problems corresponds to the identification of the parameters of a system of fundamental orthogonal polynomials. The theorems of orthogonal polynomials are applied to the solution of identification problems. A formula for calculating theoretical curves and direct resistivity interpretation is proposed for the case of arbitrary resistivity of the substratum.
The basic equation for synthetic seismograms is reformulated in appendix A. In appendix B a method is indicated for the conversion of the seismic transfer function from arbitrary to perfectly reflective substratum.
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SOME EXPERIMENTS ON TRANSVERSE WAVES*
Authors S. SCARASCIA, B. COLOMBI and R. CASSINISAbstractIn‐situ seismic measurements on shear waves propagation both in soft formations (clays) and in hard formations (calcareous rocks), using several field techniques did not result in clear S arrivals.
Particular digital approaches were then used, based on spectral analysis of records, for the selection of the seismic events and the calculation of their propagation velocity.
The actual application of these numerical procedures are described and to some records obtained using the “crosshole” field technique show that the suggested procedures are a substantial contribution to the identification of transverse waves.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 38 (1990)
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Volume 37 (1989)
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Volume 36 (1988)
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Volume 35 (1987)
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Volume 34 (1986)
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Volume 33 (1985)
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Volume 32 (1984)
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Volume 31 (1983)
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Volume 30 (1982)
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Volume 29 (1981)
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Volume 28 (1980)
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Volume 27 (1979)
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Volume 26 (1978)
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Volume 25 (1977)
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Volume 24 (1976)
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Volume 23 (1975)
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Volume 22 (1974)
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Volume 21 (1973)
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Volume 20 (1972)
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Volume 19 (1971)
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Volume 18 (1970)
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Volume 17 (1969)
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Volume 16 (1968)
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Volume 15 (1967)
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Volume 14 (1966)
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Volume 13 (1965)
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Volume 12 (1964)
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Volume 11 (1963)
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Volume 10 (1962)
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Volume 9 (1961)
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Volume 8 (1960)
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Volume 7 (1959)
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Volume 6 (1958)
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Volume 5 (1957)
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Volume 4 (1956)
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Volume 3 (1955)
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Volume 2 (1954)
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Volume 1 (1953)