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- Volume 35, Issue 5, 1987
Geophysical Prospecting - Volume 35, Issue 5, 1987
Volume 35, Issue 5, 1987
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AN ACCURATE SCHEME FOR SEISMIC FORWARD MODELLING*
Authors H. TAL‐EZER, D. KOSLOFF and Z. KORENABSTRACTA new time integration technique for use in forward modelling programmes is introduced. The technique presents an alternative to second‐order temporal differencing. It is based on a Chebyshev expansion of the formal evolution operator to the spatially discretized wave equation. The computational effort in forward modelling based on the new technique is about the same as in methods based on temporal differencing. However, machine accuracy can be obtained. The implementation of the technique to solve the acoustic wave equation in two spatial dimensions is described. Finally, an example of using the technique to solve a problem of wave propagation in a single layer is presented.
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WAVE SCATTERING DECONVOLUTION BY SEISMIC INVERSION*
Authors A.K.M. SARWAR and D.L. SMITHABSTRACTWe propose a wave scattering approach to the problem of deconvolution by the inversion of the reflection seismogram. Rather than using the least‐squares approach, we study the full wave solution of the one‐dimensional wave equation for deconvolution. Randomness of the reflectivity is not a necessary assumption in this method. Both the reflectivity and the section multiple train can be predicted from the boundary data (the reflection seismogram). This is in contrast to the usual statistical approach in which reflectivity is unpredictable and random, and the section multiple train is the only predictable component of the seismogram. The proposed scattering approach also differs from Claerbout's method based on the Kunetz equation.
The coupled first‐order hyperbolic wave equations have been obtained from the equation of motion and the law of elasticity. These equations have been transformed in terms of characteristics. A finite‐difference numerical scheme for the downward continuation of the free‐surface reflection seismogram has been developed. The discrete causal solutions for forward and inverse problems have been obtained. The computer algorithm recursively solves for the pressure and particle velocity response and the impedance log. The method accomplishes deconvolution and impedance log reconstruction. We have tested the method by computer model experiments and obtained satisfactory results using noise‐free synthetic data. Further study is recommended for the method's application to real data.
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LOVE SEAM‐WAVES IN A HORIZONTALLY INHOMOGENEOUS THREE‐LAYERED MEDIUM*
By M. DOBRÓKAABSTRACTUsing the WKBJ‐method the absorption‐dispersion relation and the amplitude functions are derived for Love seam‐waves that propagate in a horizontally inhomogeneous three‐layered medium. To describe the anelastic friction the constant Q‐model is applied. The inhomogeneity that appears in either the elastic moduli or quality factors is assumed to remain weak in the coal as well as in the adjacent layers, which are assumed to have different material properties (asymmetric channel). Using numerical solutions of the dispersion relation, it is shown that the weak horizontal inhomogeneities can be optimally detected using channel‐wave constituents of a frequency near to the Airy frequency while inhomogeneities of the adjacent rock can only be detected at frequencies close to, but higher than, the cut‐off frequency.
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FREQUENCY WAVENUMBER APPROACH OF THE τ‐p TRANSFORM: SOME APPLICATIONS IN SEISMIC DATA PROCESSING*
Authors S.D. BENOLIEL, W.A. SCHNEIDER and R.N. SHURTLEFFAbstractThe τ‐p transform is an invertible transformation of seismic shot records expressed as a function of time and offset into the τ (intercept time) and p (ray parameter) domain. The τ‐p transform is derived from the solution of the wave equation for a point source in a three‐dimensional, vertically non‐homogeneous medium and therefore is a true amplitude process for the assumed model. The main advantage of this transformation is to present a point source shot record as a series of plane wave experiments.
The asymptotic expansion of this transformation is found to be useful in reflection seismic data processing. The τ‐p and frequency‐wavenumber (or f‐k) processes are closely related. Indeed, the τ‐p process embodies the frequency‐wavenumber transformation, so the use of this technique suffers the same limitations as the f‐k technique. In particular, the wavefield must be sampled with sufficient spatial density to avoid wavenumber aliasing.
The computation of this transform and its inverse transform consists of a two‐dimensional Fast Fourier Transform followed by an interpolation, then by an inverse‐time Fast Fourier Transform. This technique is extended from a vertically inhomogeneous three‐dimensional medium to a vertically and laterally inhomogeneous three‐dimensional medium.
The τ‐p transform may create artifacts (truncation and aliasing effects) which can be reduced by a finer spatial density of geophone groups by a balancing of the seismic data and by a tapering of the extremities of the seismic data.
The τ‐p domain is used as a temporary domain where the attack of coherent noise is well addressed; this technique can be viewed as ‘time‐variant f‐k filtering’. In addition, the process of deconvolution and multiple suppression in the τ‐p domain is at least as well addressed as in the time‐offset domain.
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IDEAL PERFORMANCE CRITERIA FOR DECONVOLUTION OPERATORS*
Authors VIJAY P. DIMRI and KIRTI SRIVASTAVAABSTRACTA technique to evaluate an ideal performance of a deconvolution operator has been obtained by dividing the input trace into a number of sections. The error energy is seen to decrease with an increase in the number of sections. Numerical examples show that the error energy becomes zero following a relation between the number of sections, the length of input and the length of the filter.
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A SIMPLE METHOD OF INTERPRETATION OF RESISTIVITY SOUNDING DATA USING EXPONENTIAL APPROXIMATION OF THE KERNEL FUNCTION*
More LessABSTRACTA simple unified equation of apparent resistivity for a general four‐electrode array is developed. The main idea is the analytical integration of the Stefanescu expression for potential over a layered earth by writing an exponential approximation for the kernel function. Finally a matrix equation is developed to estimate the kernel function from observed apparent resistivity values. The general equation automatically reduces to the particular configuration once the electrode separations are modified suitably. Examples for Schlumberger and Wenner configurations are numerically calculated to estimate the precision of the method. Good results in a short execution time are obtained, irrespective of the shape of the apparent resistivity curve. Finally, the full interpretation of one theoretical resistivity curve and two field resistivity curves is demonstrated. The more stable ridge‐regression estimation method is used in the identification of layer parameters from the kernel function.
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GEOPHYSICAL DETECTION OF MINERAL CONDUCTORS IN TROPICAL TERRAINS WITH TARGET CONDUCTORS PARTLY EMBEDDED IN THE CONDUCTIVE OVERBURDEN*
By J.O. BARONGOABSTRACTGround geophysical methods were used in the greenstone belt of Western Kenya as follow‐up of an Input airborne electromagnetic survey. Observation and drilling results showed that the graphite and pyrite bodies, which constitute the main target conductors in the area, either outcrop or reach near to the ground surface. The drilling results further showed that the weathered layer is between 20 m and 60 m thick. Therefore the target conductors are partly embedded in this fairly conductive weathered layer and may be in galvanic contact with it. The geophysical methods were able to delineate the conductors. However, by virtue of the galvanic contact between the conductors and the conductive overburden, the profiles from the horizontal loop EM measurements are highly enhanced. This effect makes interpretation of the profiles possible at low frequencies but difficult at high frequencies. The interpreted EM results show that the target conductors appear shallow and less conductive at higher frequencies. Thus one must choose geophysical instruments and operating frequencies carefully to ensure good results in tropical terrains.
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RESISTIVITY INVERSION WITH A PRIORI INFORMATION*
Authors J. POUS, A. MARCUELLO and P. QUERALTABSTRACTAn inversion algorithm for interpreting electrical soundings based on a probabilistic treatment of the a priori information not only includes all the previous ones, but allows consideration of the constraints between the parameters. By introducing the a priori information, a unique solution among all the equivalent ones is obtained which is coherent with the geological background. Several examples dealing with the usual problems in the automatic interpretation of the electrical soundings illustrate the advantages of this algorithm. Good results are obtained with this method.
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EXAMPLES OF ELECTROMAGNETIC PROSPECTING FOR KARST AND FAULT SYSTEMS*
By D. VOGELSANGABSTRACTElectromagnetic (EM) surveys using the horizontal coplanar loop (‘Slingram’) geometry have been successful in the location of karst aquifer systems in limestone areas of Germany and the Mediterranean. In spite of the rapid changes in shape and resistivity of karst pipes, correlations of significant EM minima can be made by reference to the main structural directions. The EM results have often been verified by drilling. EM prospecting need not be confined to limestone areas. It can be used on all hard rocks where faulting has created vertical zones with a resistivity contrast to the undisturbed rock.
EM siting of wells has proved successful in water‐supply schemes for several places. This method is now being applied as a routine, fast and low‐cost procedure to tap ground‐water resources in hard‐rock areas.
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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)