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- Volume 33, Issue 2, 1985
Geophysical Prospecting - Volume 33, Issue 2, 1985
Volume 33, Issue 2, 1985
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TUTORIAL DISTRIBUTION OF ALTERNATING ELECTRICAL CHARGES IN A CONDUCTING MEDIUM*
More LessABSTRACTThe main features of the distribution of volume and surface charges in a conducting medium can be described separately for direct and alternating electromagnetic fields. The density of charges depends on the conductivity of a medium and on the electrical field. The relation is particularly simple for the quasi‐stationary field, i.e., when the influence of displacement currents is negligible. Conditions are formulated under which electrical charges arise in a conducting medium: electrical charges are shown to exist for direct and quasi‐stationary fields when there is a component of electric field parallel to the gradient of conductivity. The density of these charges is proportional to the applied electric field.
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A NONITERATIVE PROCEDURE FOR INVERTING PLANE‐WAVE REFLECTION DATA AT SEVERAL ANGLES OF INCIDENCE USING THE RICCATI EQUATION*
Authors N. D. BREGMAN, C. H. CHAPMAN and R. C. BAILEYABSTRACTVarious exact methods of inverting the complete waveform of vertical seismic reflection data to produce acoustic impedance profiles have been suggested. These inverse methods generally remain valid for nonvertical, plane‐wave data, provided total reflection does not occur. Thus, in principle, the “seismogram” at each ray parameter in a slant stack can be interpreted separately.
Rather than invert each plane‐wave seismogram separately, they can all be interpreted simultaneously and an “average” model thus obtained. Inversion for both the velocity and the density also becomes possible when two or more plane‐wave seismograms are simultaneously inverted. The theory for a noniterative inversion method, based on the time‐domain Riccati equation, is discussed. Numerical examples of inversions using this technique on synthetic data demonstrate its numerical stability and the advantage of simultaneous inversion of several seismograms to reduce the effect of noise in the data and increase the stability of the inversion process.
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HOW DO SHEAR WAVE EVENTS AFFECT NORMAL P‐WAVE RECORDS?*
Authors L. AMEELY, H. A. K. EDELMANN and J. FERTIGABSTRACTIt has been known since the beginning of reflection seismics that several disturbing events seen in seismic records are caused by waves with S‐wave velocities instead of P‐wave velocity. When using dynamite and recording with vertical geophones these events are primarily caused by converted waves.
On the basis of known P‐ and S‐wave velocities in a certain area a theoretical seismogram is calculated, displaying traveltime as well as energy relation for different wave configurations. By comparison with seismograms recorded in the same area it can be shown that converted wave events can be clearly recognized.
These events can be described theoretically. Thus, either more effective computer programs can be applied to eliminate these disturbing events, or these events can be evaluated to get additional information about specific strata.
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STABILIZATION OF NORMAL‐INCIDENCE SEISMOGRAM INVERSION REMOVING THE NOISE‐INDUCED BIAS*
By R.‐G. FERBERABSTRACTA main problem in computing reflection coefficients from seismograms is the instability of the inversion procedure due to noise. This problem is attacked for two well‐known inversion schemes for normal‐incidence reflection seismograms. The crustal model consists of a stack of elastic, laterally homogeneous layers between two elastic half‐spaces. The first method, which directly computes the reflection coefficients from the seismogram is called “Dynamic Deconvolution”. The second method, here called “Inversion Filtering”, is a two‐stage procedure. The first stage is the construction of a causal filter by factorization of the spectral function via Levinson‐recursion. Filtering the seismogram is the second stage. The filtered seismogram is a good approximation for the reflection coefficients sequence (unless the coefficients are too large).
In the non‐linear terms of dynamic deconvolution and Levinson‐recursion the noise could play havoc with the computation. In order to stabilize the algorithms, the bias of these terms is estimated and removed. Additionally incorporated is a statistical test for the reflection coefficients in dynamic deconvolution and the partial correlation coefficients in Levinson‐recursion, which are set to zero if they are not significantly different from noise.
The result of stabilization is demonstrated on synthetic seismograms. For unit spike source pulse and white noise, dynamic deconvolution outperforms inversion filtering due to its exact nature and lesser computational burden. On the other hand, especially in the more realistic bandlimited case, inversion filtering has the great advantage that the second stage acts linearly on the seismogram, which allows the calculation of the effect of the inversion procedure on the wavelet shape and the noise spectrum.
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CONTINUOUS CALIBRATION OF MARINE SEISMIC SOURCES*
By P. NEWMANABSTRACTThe success of signature deconvolution in optimizing both signal‐to‐noise ratio and time resolution in the seismic section depends critically upon obtaining an accurate estimate of the far‐field source signature. Various deterministic estimation schemes have been proposed in recent years, most of which involve direct monitoring of source output within the water layer.
As an alternative to elaborate and error‐prone source monitoring schemes during data acquisition, a simple modification to any source array permits subsequent estimation of far‐field signatures directly from reflected signal. The new method requires the inclusion within any chosen source array of a simple point source, the “reference” source. Initial experiments employed a water gun as the reference source, characterized by a concise implosive signature with peak‐to‐peak amplitude of approximately 2 bar·m within the seismic sprectrum.
In operation the reference source is fired shortly before the main array (typically 2 s during initial trials) and the usual record length is extended by a similar amount. Each recorded trace then comprises two results: the subsurface response to the reference source signal followed by the response of the same subsurface to the main array. The disparities in source amplitudes and NMO differentials ensure that interference effects are negligible in the main recording.
Time‐ or frequency‐domain methods can be employed to extract the main array signature from the dual dataset or to invert this to some preferred wavelet simultaneously. As an additional benefit the reference source yields excellent high‐resolution profiles of the shallow geology.
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MAXIMUM‐LIKELIHOOD ESTIMATION OF SEISMIC IMPULSE RESPONSES*
Authors B. URSIN and O. HOLBERGABSTRACTA seismic trace is assumed to consist of a known signal pulse convolved with a reflection coefficient series plus a moving average noise process (colored noise). Multiple reflections and reverberations are assumed to be removed from the trace by conventional means. The method of maximum likelihood (ML) is used to estimate the reflection coefficients and the unknown noise parameters. If the reflection coefficients are known from well logs, the seismic pulse and the noise parameters can be estimated.
The maximum likelihood estimation problem is reduced to a nonlinear least‐squares problem. When the further assumption is made that the noise is white, the method of maximum likelihood is equivalent to the method of least squares (LS). In that case the sampling rate should be chosen approximately equal to the Nyquist rate of the trace. Statistical and numerical properties of the ML‐ and the LS‐estimates are discussed briefly. Synthetic data examples demonstrate that the ML‐method gives better resolution and improved numerical stability compared to the LS‐method.
A real data example shows the ML‐ and LS‐method applied to stacked seismic data. The results are compared with reflection coefficients obtained from well log data.
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FORWARD MODELING IN THE FREQUENCY‐SPACE DOMAIN*
Authors P. G. KELAMIS and E. KJARTANSSONABSTRACTForward modeling of zero‐offset data is performed in the frequency‐space domain using a one‐way extrapolation equation. The use of the frequency domain offers several advantages over conventional time domain methods. The greatest advantage of the frequency domain is that all time derivatives are evaluated exactly by a simple multiplication. Synthetic zero‐offset sections are computed with a high degree of accuracy for arbitrary velocity and reflectivity structures. Examples are shown for realistic complicated models and compared with results from physical modeling.
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THE GRAVITY AND MAGNETIC FIELDS FROM ELLIPSOIDAL BODIES IN THE WAVENUMBER DOMAIN*
More LessABSTRACTWavenumber domain expressions for bodies with elliptical cross‐section and of ellipsoidal shape have been developed both for homogeneous bodies and for certain bodies of density/magnetization varying linearly with depth or, more generally, according to a polynomial with depth. The simple expressions thus obtained lend themselves to an easy analysis, especially for long and short wavelengths. At the long‐wavelength end of the spectra their decay is governed by an exponential with a decay “depth” equal to the depth to the center of mass. At the short‐wavelength end this depth is replaced by the depth to the upper focus of the ellipsoid (or the elliptic cross‐section). For vertically inhomogeneous ellipsoids the decay rate is also dependent on the product of the vertical gradient of density/magnetization and their semi‐axes.
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EM COUPLING IN MULTIFREQUENCY IP AND A GENERALIZATION OF THE COLE‐COLE IMPEDANCE MODEL*
By R. J. BROWNABSTRACTThe Cole‐Cole relaxation model has been found to provide good fits to multifrequency IP data and is derivable mathematically from a reasonable, albeit greatly simplified, physical model of conduction in porous rocks. However, the Cole‐Cole model is used to represent the mutual impedance due to inductive or electromagnetic coupling on an empirical basis: this use has not been similarly justified by derivation from any simple physical representation of, say, a half‐space, layered or uniform.
A uniform conductive half‐space can be represented as a simple subsurface loop with particular resistive and inductive properties. Based upon this, a mathematical expression for the mutual impedance between the two pairs of electrodes of a dipole‐dipole array is derived and designated “model I”. It is seen that a degenerate case of model I is the Cole‐Cole model with frequency exponent c= 1. Model I is thus more general than the Cole‐Cole expression and must provide at least as good a fit to a set of field data. Provision for variation of c from unity could be made in model I equally well as for the Cole‐Cole model although, at present, this would be a purely empirical alteration.
Model I contains four parameters, one of which is, in effect, the resistivity of the half‐space. Therefore only three parameters are involved in the model I expressions for normalized amplitude and for phase of the EM‐coupling mutual impedance. Model I is compared with previously published “standard” values for two different dipole separations. Under particular constraints, model I is shown to provide better fits than the Cole‐Cole model (with c= 1) over particular frequency ranges, specifically at very low frequencies and at moderately high frequencies where the model I phase curve follows the standard phase curve across the axis to positive values (negative coupling).
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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)