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- Volume 35, Issue 3, 1987
Geophysical Prospecting - Volume 35, Issue 3, 1987
Volume 35, Issue 3, 1987
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DETECTION OF THIN BEDS WITH THE PSEUDO‐ACOUSTIC IMPEDANCE SECTION*
More LessAbstractThe conventional seismic response of a thin bed approximates the time derivative of the incident wavelet, whereas the pseudo‐impedance response approximates the incident wavelet. Consequently the pseudo‐impedance response of a geological sequence composed of thin beds is simpler and easier to interpret than the conventional response.
By calibrating the sonic log data with check‐shot data and performing zero‐phase seismic processing, the fit of the sonic log and pseudo‐velocity section is improved. Discrepancies in amplitude and phase, however, generally remain.
A five‐step processing and interpretation procedure, which benefits from multichannel interpretation along the model seismic section generated from the sonic logs, is described.
The method has been tested with field data. In the test the detection of thin beds and the estimation of the natural gas content was more reliable with the proposed procedure than with the conventional method.
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MODELING OF SH‐WAVE PROPAGATION IN AN IRREGULARLY LAYERED MEDIUM‐APPLICATION TO SEISMIC PROFILES NEAR A DOME*
By M. CAMPILLOABSTRACTAn approach that relies on a discrete representation of seismic wavefields allows the computation of synthetic SH‐seismograms in a laterally varying medium with plane and curved interfaces in the two dimensional (2‐D) case. The diffracting interface is represented by an array of body forces located along the interface at equal spacing. The numerical treatment is limited to the irregular boundary while the propagation in flat layered zones is obtained by the reflection‐transmission matrix method. As an example we have studied the case of a dome in a stratified medium. The solutions obtained verify the reciprocity theorem with good accuracy. The computation of vertical profiles and of surface reflection profiles illustrates the effects of diffraction and the importance of lateral propagation in such a structure.
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THREE‐DIMENSIONAL KINEMATIC MIGRATION IN VARIABLE VELOCITY MEDIA*
Authors JING WEN and G.A. McMECHANABSTRACTA three‐dimensional (3‐D) kinematic migration algorithm for media in which migration velocity varies linearly with depth is developed, implemented and tested. The algorithm is based on the concept that a single reflection or diffraction in a (zero‐ or finite‐offset) trace may have originated at any point on a constant traveltime surface within the Earth defined by the observed two‐way traveltime. The envelope of all such constant time surfaces, for all observed reflections and diffractions produced by one reflector, is the desired migrated 3‐D image. The optimal envelope position in depth is determined, beneath each point on a regular grid, by a statistical imaging condition; an incremental function of depth containing the number of constant time surfaces passing through that depth increment is cross‐correlated with a Gaussian function whose width is chosen to correspond to the vertical scale of the features of interest.
The numerical procedures are based on the observation that, in a medium in which velocity varies linearly with depth, ray segments are circular so traveltimes can be computed analytically. Also, traveltimes are independent of azimuth so the 3‐D problem can be collapsed into an equivalent 2‐D problem.
The algorithm is illustrated and tested by application to synthetic data and to scale‐model data from the Seismic Acoustics Laboratory at the University of Houston.
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PHASE ERRORS OF FINITE‐DIFFERENCE MIGRATION*
Authors C. M. BEAUMONT, J. F. BOYCE and R. SILVAAbstractA quantitative analysis of the various approximations to the scalar wave equation used in seismic migration can be obtained by a study of the resulting phase errors. In the space‐time domain the effects of different modes of parameter optimization are displayed. In the space‐frequency domain the spatial derivatives may be expanded as a linear filter operator whose coefficients are determined by requiring that the resulting phase shifts agree with those that arise from planar wave solutions of the exact wave equation over a range of angles and frequencies.
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COMPUTATION OF SIGNATURES OF LINEAR AIRGUN ARRAYS*
More LessAbstractFar‐field signatures from an airgun array are usually obtained by carrying out extensive field measurements. In order to decrease the need for such measurements, we have developed a method for computing signatures from linear airgun arrays where the distances between the airguns are such that the non‐linear interaction among the airguns is negligible.
The signature from a single airgun of a given type is computed from the following airgun parameters: airgun chamber volume, chamber pressure, airgun depth and position of the waveshape plate within the chamber. For calibration purposes, a recorded signature for one set of airgun parameters has to be provided for each type of airgun. The signatures are computed by using empirical relations between signature properties and the airgun parameters, and by treating the primary and bubble pulses separately.
The far‐field signature from a linear airgun array can now be computed by summation of the delayed signatures from the airguns in the array. Practical results are shown for an array with different PAR (Bolt) 1500 C airguns.
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CALCULATION OF POTENTIAL FIELDS FOR STOCHASTIC MODELS OF HETEROGENEOUS GEOLOGICAL OBJECTS*
Authors G.S. VAKHROMEYEV and A.Y. DAVYDENKOABSTRACTThe solution of the direct problem of magnetic and gravity prospecting for heterogeneous objects is discussed from the view‐point of the probability description of object models and the anomalous effects caused by them. Three stochastic models for the determination of the basic characteristics of non‐stationary geophysical fields above the finite objects are suggested: linear, with a random distribution of the physical properties and fixed source geometry; non‐linear, of a single object with random parameters, and an ensemble of random sources. With the methods suggested for the formalized description of the structure of heterogeneous objects for those models, expressions are derived enabling the calculation of mathematical expectations, dispersions and correlation functions of anomalous effects.
Model examples illustrate the application of stochastic modeling for the study of the influence of the character and dimensions of heterogeneities of the internal structure of the disturbing bodies on the probability characteristics of expected anomalous effects. It is shown that the assumption of the random character of the anomalous effect can be used for direct calculation of the optimum Wiener filter enabling the recovery of the shape of anomaly contaminated by random noise, as well as for calculating an observation step that is sufficient for recording the expected anomalous effects with prescribed accuracy.
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AN APPLICATION OF FAST ALGORITHMS TO NUMERICAL ELECTROMAGNETIC MODELING*
Authors V. BEZVODA and K. SEGETHABSTRACTNumerical electromagnetic modeling by the finite‐difference or finite‐element methods leads to a large sparse system of linear algebraic equations. Fast direct methods, requiring an order of at most q log q arithmetic operations to solve a system of q equations, cannot easily be applied to such a system. This paper describes the iterative application of a fast method, namely cyclic reduction, to the numerical solution of the Helmholtz equation with a piecewise constant imaginary coefficient of the absolute term in a plane domain. By means of numerical tests the advantages and limitations of the method compared with classical direct methods are discussed. The iterative application of the cyclic reduction method is very efficient if one can exploit a known solution of a similar (e.g., simpler) problem as the initial approximation. This makes cyclic reduction a powerful tool in solving the inverse problem by trial‐and‐error.
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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)