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- Volume 28, Issue 6, 1980
Geophysical Prospecting - Volume 28, Issue 6, 1980
Volume 28, Issue 6, 1980
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AN OPTIMIZED TECHNIQUE FOR DETERMINING STACKING VELOCITY FROM SEISMIC REFLECTION DATA*
Authors K. KHATTRI, P.K. VIG and N.D.J. RAOAbstractA new method of estimating seismic stacking velocity from reflection seismograms is based on Fibonacci search technique and provides the highest rate of reduction of the interval of uncertainty of the stacking velocity. A review of the Fibonacci search strategy is presented, the application of the method is illustrated with synthetic and field examples.
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DEBUBBLING: A GENERALIZED LINEAR INVERSE APPROACH*
Authors S. LEVY and R.M. CLOWESAbstractOn seismograms recorded at sea bubble pulse oscillations can present a serious problem to an interpreter. We propose a new approach, based on generalized linear inverse theory, to the solution of the debubbling problem. Under the usual assumption that a seismogram can be modelled as the convolution of the earth's impulse response and a source wavelet we show that estimation of either the wavelet or the impulse response can be formulated as a generalized linear inverse problem. This parametric approach involves solution of a system of equations by minimizing the error vector (ΔX = Xobs– Xcal) in a least squares sense. One of the most significant results is that the method enables us to control the accuracy of the solution so that it is consistent with the observational errors and/or known noise levels.
The complete debubbling procedure can be described in four steps: (1) apply minimum entropy deconvolution to the observed data to obtain a deconvolved spike trace, a first approximation to the earth's response function; (2) use this trace and the observed data as input for the generalized linear inverse procedure to compute an estimated basic bubble pulse wavelet; (3) use the results of steps 1 and 2 to construct the compound source signature consisting of the primary pulse plus appropriate bubble oscillations; and (4) use the compound source signature and the observed data as input for the generalized linear inverse method to determine the estimated earth impulse response—a debubbled, deconvolved seismogram. We illustrate the applicability of the new approach with a set of synthetic seismic traces and with a set of field seismograms.
A disadvantage of the procedure is that it is computationally expensive. Thus it may be more appropriate to apply the technique in cases where standard analysis techniques do not give acceptable results. In such cases the inherent advantages of the method may be exploited to provide better quality seismograms.
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COMMON OFFSET PLANE MIGRATION (COPMIG)*
Authors J.W. SATTLEGGER, P.K. STILLER, J.A. ECHTERHOFF and M.K. HENTSCHKEAbstractThe quality of results of migration before stack is sensitive to inaccuracies in the velocity field applied. This does not hold if only traces of similar sources‐receiver distances (common offset traces) enter the migration process. In this case, velocity deviations generate minor shifts in travel times of migrated interfaces but no deterioration in quality. These time shifts are proportional to both the velocity error and the square of the source‐receiver distance.
The above observations suggest the following migration scheme: migrate separately the traces of the various common offset planes or groups of neighbouring common offset planes; for every common midpoint plane and as a function of travel‐time perform a residual NMO search to find trajectories t) =t)o+px)2 of maximum coherency along which migrated events are aligned; correct for residual NMO and stack the migration results obtained in the various common offset planes to obtain the final migration result.
This process not only takes care of inaccurate migration velocities but also corrects partly for effects of refraction.
It is shown by means of an example that good migration results are generated even with a considerably deviating velocity field.
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WAVELET DECONVOLUTION USING A SOURCE SCALING LAW*
Authors A.M. ZIOLKOWSKI, W.E. LERWILL, D.W. MARCH and L.G. PEARDONAbstractWe present a new method for the extraction and removal of the source wavelet from the reflection seismogram. In contrast to all other methods currently in use, this one does not demand that there be any mathematically convenient relationship between the phase spectrum of the source wavelet and the phase spectrum of the earth impulse response. Instead, it requires a fundamental change in the field technique such that two different seismograms are now generated from each source‐receiver pair: the source and receiver locations stay the same, but the source used to generate one seismogram is a scaled version of the source used to generate the other. A scaling law provides the relationship between the two source signatures and permits the earth impulse response to be extracted from the seismograms without any of the usual assumptions about phase.
We derive the scaling law for point sources in an homogeneous isotropic medium. Next, we describe a method for the solution of the set of three simultaneous equations and test it rigorously using a variety of synthetic data and two types of synthetic source waveform: damped sine waves and non‐minimum‐phase air gun waveforms. Finally we demonstrate that this method is stable in the presence of noise.
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SOURCE ARRAY SCALING FOR WAVELET DECONVOLUTION*
More LessAbstractA seismic source array is normally composed of elements spaced at distances less than a wavelength while the overall dimensions of the array are normally of the order of a wavelength. Consequently, unpredictable interaction effects occur between element and the shape of the far field wavelet, which is azimuth‐dependent, can only be determined by measurements in the far field. Since such measurements are very often impossible to make, the shape of the wavelet—particularly its phase spectrum—is unknown.
A theoretical design method for overcoming this problem is presented using two scaled arrays. The far field source wavelets from the source arrays have the same azimuth dependence at scaled frequencies, and the far field wavelets along any azimuth are related by a simple scaling law. Two independent seismograms are generated by the two scaled arrays for each pair of source‐receiver locations, the source wavelets being related by the scaling law.
The technique thus permits the far field waveform of an array to be determined in situations where it is impossible to measure it. Furthermore it permits the array design criteria to be changed: instead of sacrificing useful signal energy for the sake of the phase spectrum, the array may be designed to produce a wavelet with desired amplitude characteristics, without much regard for phase.
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CORRELATION METHODS OF TRANSFORMATION AND INTERPRETATION OF GEOPHYSICAL ANOMALIES*
Authors V.I. SHRAIBMAN, M.S. ZHDANOV and O.V. VITVITSKYAbstractThe methods of anomaly transformations considered are based on a system of combined analysis of the geophysical field and a priori) information on the structure of a geological object. The methods involve calculation of a transformative polynomial (describing geophysical noise) which makes it possible to separate the residual field component related to the geological characteristic under study in a correlatively optimal way.
The structure of the transformative polynomial is determined by the nature of the geophysical noise that is eliminated by the field transformation. Various correlation methods of anomaly transformations arise, depending on the structure of the transformative polynomial chosen.
By way of example, the correlation method employed for separating the geophysical anomalies is shown to be highly effective in investigating the local geological structure.
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A STUDY OF ABYSSAL FRACTURES IN THE UKRAINIAN SHIELD BY GEOPHYSICAL METHODS*
By K.F. TYAPKINAbstractAccording to data presented by YU.A. Kosigin, 84% of all endogenous mineral deposits are in some direct or indirect relation with the fractures of the earth's crust. Therefore the discovery and the study of the spatial disposition of the fractures is the most important object for geophysicists. Abyssal fractures are of particular interest.
By geophysical methods one can find the geometrical parameters of abyssal fractures such as their extent, the depth of formation, the breadth of the zones, and the amplitude of the relative displacement of separated blocks.
The methods determining these parameters are widely known. A calculation of the difference in the levels of the erosion cuts of the blocks are of particular interest under shield conditions. A method to calculate this difference by gravity interpretation of “step” anomalies and by using the gradient model of the earth's crust is proposed.
A comparision of the results of gravimetry and magnetometry with those of deep seismic soundings shows that the fractures of the first and the second order in the Ukrainian shield cut the earth's crust and part of the upper mantle so they can be qualified as abyssal fractures.
In the Ukrainian shield the spatial regularities of the fractures determined by geophysical methods can be used for the prognosis of the ore deposits.
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GEOELECTRIC MODELS IN ENGINEERING GEOPHYSICS*
Authors A.A. OGILVY, V.A. BOGOSLOVSKY and E.N. KUZMINAAbstractMan's engineering activities are concentrated on the uppermost part of the earth's crust which is called engineering‐geologic zone. This zone is characterized by a significant spatialtemporal variation of the physical properties status of rocks, and saturating waters. This variation determines the specificity of geophysical and, particularly, geoelectrical investigations.
Planning of geoelectric investigations in the engineering‐geologic zone and their subsequent interpretation requires a priori) geologic‐geophysical information on the main peculiarities of the engineering‐geologic and hydrogeologic conditions in the region under investigation. This information serves as a basis for the creation of an initial geoelectric model of the section. Following field investigations the model is used in interpretation. Formalization of this a priori) model can be achieved by the solution of direct geoelectric problems. An additional geologic‐geophysical information realized in the model of the medium allows to diminish the effect of the “principle of equivalence” by introducing flexible limitations in the section's parameters. Further geophysical observations as well as the correlations between geophysical and engineering‐geologic parameters of the section permit the following step in the specification of the geolectric model and its approximation to the real medium. Next correction of this model is made upon accumulation of additional information. The solution of inverse problems with the utilization of computer programs permits specification of the model in the general iterational cycle of interpretation.
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THE QUANTITATIVE INTERPRETATION OF DIPOLE SOUNDINGS BY MEANS OF THE RESISTIVITY TRANSFORM FUNCTION*
By D. PATELLAAbstractIn this paper a theorem is demonstrated which allows—after the introduction of a suitable dipole kernel function or dipole resistivity transform function—to write the apparent resistivity function as an Hankel transformable integral expression.
As a practical application of the theorem a procedure of quantitative interpretation of dipole soundings is suggested in which the dipole resistivity transform function obtained after inversion of the original dipole apparent resistivity data is used to control the goodness of the set of layering parameters which have been derived with our previous method of transformation of dipole sounding curves into equivalent Schlumberger diagrams.
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THE INTERPRETATION OF THE VERTICAL FAULT PROBLEM IN GEOELECTRICS USING HANKEL INTEGRAL*
By D. PATELLAAbstractIt is shown how to interpret, without curve‐matching, Schlumberger resistivity soundings carried out with the array parallel to the surface trace of a vertical boundary plane separating two media with different resistivities (the vertical fault problem). To this end, it is demonstrated that the apparent resistivity function can be expressed as an Hankel‐transformable integral that allows to invert the apparent resistivity curve into an associated resistivity transform curve. The study of the asymptotical properties of this function and of some mathematical properties of a related reduced transform function allows to realize a simple procedure for deriving the parameters of the model. In practice, this procedure consists in fitting a straight‐line to a semi‐logarithmic plot of the reduced transform function and in evaluating the intercept along the vertical axis and the slope.
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ELECTRICAL SOUNDING OF A HALF‐SPACE WITH A MONOTONIC CONTINUOUS VARIATION OF THE RESISTIVITY WITH DEPTH*
Authors H.K. SATO and E.S. SAMPAIOAbstractThe interpretation of electrical sounding data for a subsurface with monotonic continuous variation of the resistivity with depth is becoming increasingly necessary. The contribution of this article is the derivation of the solution for the Wenner and the Schlumberger apparent resistivity functions for a resistivity varying as a real power of a linear positive function of the depth. The interpretation of sounding data in these cases can be used to estimate the variation of the porosity or the salt content of the pore water with depth.
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EFFET TOPOGRAPHIQUE EN PROSPECTION ELECTRIQUE*
Authors A. CECCHINI and J.P. ROCROIAbstractThe computation of the electrical potential created by a source of direct current in a horizontally stratified earth is easy, and it is now a common practice to interpret, by manual or automatic procedures, the maps of apparent resistivity or of mise‐à‐la‐masse surveys.
The study of 3‐D cases requires a computer cost too high for a general use, and the available techniques usually refer only to an anomalous body embedded in a stratified medium. In fact, it often happens that the surface of the ground cannot be regarded as a plane, an assumption which can cause large discrepancies between the observed and the calculated potentials. A first estimate of these discrepancies can be made by assuming that the earth's surface makes a dihedron and the underground consists either of one homogeneous medium or of several media whose plane interfaces pass through the edge of the ground surface dihedron. Although very schematic, this approximate model can provide a useful information on the effect of the relief.
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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)