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- Volume 22, Issue 4, 1974
Geophysical Prospecting - Volume 22, Issue 4, 1974
Volume 22, Issue 4, 1974
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THE QUALITY OF SOME TWO‐DIMENSIONAL FILTERS IN SEPARATING REGIONAL AND LOCAL GRAVITY ANOMALIES *
More LessAbstractThe separation of regional from local gravity anomalies by means of the application of two‐dimensional linear filters is analyzed. It was found that optimization of the filter in the least squares sense leads to filters that produce strong localized concentrations of the error, which may erroneously be interpreted as anomalies. For this reason the maximum absolute value of the error is a more important criterion for the quality of the filter than the root mean square error. This maximum absolute error is minimized by the minimax filter. Intermediate filters are derived which give a transition zone which comes appreciably closer to that of the optimal filter at only a small price in terms of increase of the maximum absolute error.
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THE INTERPRETATION OF INDUCED‐POLARIZATION SOUNDING CURVES IN THE FREQUENCY DOMAIN *
By R. D. BARKERAbstractTwo‐layer type curves of apparent frequency effect for the Wenner configuration are presented. The formulation is based on the normal definition of frequency effect in terms of resistivities measured at different frequencies plus the definition of apparent resistivity over two horizontal layers as a function of first and second layer resistivities. The use of these type curves in the interpretation of multilayer apparent frequency‐effect curves is described and some field examples are given.
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ESTIMATION OF THE PRIMARY SEISMIC PULSE *
Authors R. E. WHITE and P. N. S. O'BRIENAbstractA seismic trace after application of suitable amplitude recovery may be treated as a stationary time‐series. Such a trace, or a portion of it, is modelled by the expression
where j represents trace number on the record, t is time, αj is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and nj is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto‐correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time‐domain pulse itself is then reconstituted under the assumption of minimum‐phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z‐transform, (C) a fast method based on inverting the least‐squares inverse of the wavelets, i.e. inverting the normal time‐domain deconvolution operator. Problems associated with these three methods are most acute when the z‐transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace‐to‐trace, from shot‐to‐shot, and from one shot‐point medium to another. There is reasonable agreement between the minimum‐phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge‐factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.
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CANCELLING MULTIPLE REFLECTIONS BY FEEDBACK *
Authors K. KOEHLER, TH. KREY and H. WACHHOLZAbstractFor horizontal layering and plane horizontal impulsive wavefronts it is theoretically possible to get rid of multiple reflections by a feedback procedure which can easily be derived using raypath philosophy. To reduce the increase of noise inherent in the method the precise theoretical formulae are altered in such a manner that a practical application becomes possible. For this purpose the autocorrelation will be used.
Application of the new process to a CRP section where the shot geophone distances in the field had not been long enough to attenuate multiple reflections effectively gave favourable results.
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A HIGH RESOLUTION MARINE SEISMIC SURVEY *
By A. L. LUCASAbstractSub‐bottom profilers achieve high resolution but limited penetration beneath the seabed. Marine seismic surveys with long streamers and conventional sources suffer from an incomplete CDP stack and an unnecessarily low signal frequency in the early part of the section. Consequently there is a depth interval over which the optimum resolution of the seismic reflection method is not achieved. This paper describes the design, conduct, and results of an experimental survey made to obtain high resolution sections (predominant frequency about 200 Hz) with reflection times up to one second in the northern North Sea. The prime motivation for the experiment was to assess the possibility of mapping a shallow gas sand which had been encountered by the drillers.
The design concept of the survey was to keep all the benefits of conventional marine seismic data gathering and processing, but to reduce their dimensions and time scales by a factor of five to ten. The survey in 1972 recorded a total of twenty‐four lines using twenty‐four fold cover with 5 m spacing between the reflector points, and a separation of 50 m between adjacent lines. Multi‐electrode sparkers were used with a shallow purpose‐built twenty‐four channel 240 m hydrophone streamer. The recording sample interval was 1 ms. The final sections, obtained after conventional data processing, were of good quality. The results of velocity analysis helped to distinguish primary and multiple energy. Reflections with large negative reflection coefficients were seen in some parts of the survey area, and these are thought to indicate thin gas sands.
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RELATED PROPERTIES OF MINIMUM‐PHASE AND ZERO‐PHASE TIME FUNCTIONS *
More LessAbstractIn this paper properties of the discrete zero‐phase time function are derived and compared with related properties of the discrete minimum‐phase time function.
The two‐sided minimum‐length signal is introduced and it is derived that, for any given amplitude spectrum, the two‐sided minimum‐length signal and the signal with zero‐phase spectrum are identical signals. A comparison is made between the one‐sided minimum‐length signal (minimum‐phase signal) and the two‐sided minimum‐length signal (zero‐phase signal).
A computational scheme is discussed which determines the zero‐phase correspondent of a given signal.
A method is proposed to compute zero‐phase least‐square inverse filters. The efficiency of minimum‐phase and zero‐phase least‐square inverse filters is shown on signals with different phase properties.
A criterion is derived which determines whether a symmetric time function has the zero‐phase property. The close relationship with the minimum‐phase criterion is discussed.
Finally the relationship between signal length and resolving power is illustrated on numerical examples.
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STRESS WAVE VELOCITY AND CRACK SYSTEM OF A MEDIUM *
Authors V. SCHENK and Z. SCHENKOVÁAbstractTwo in situ measurements of stress wave velocity in a granodiorite massif were made. Firstly, the velocities close to the source were investigated (for elimination of the influence of cracks), and secondly, the velocities in different horizontal directions over a large area were studied from the viewpoint of their dependence on the crack system of the medium. A correlation between the mutual orientation of the cracks and the maximum or minimum values of the stress wave velocities was obtained.
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STACKING FILTERS AND THEIR CHARACTERIZATION IN THE (f—k) DOMAIN *
By P. HUBRALAbstractThe implementation of a stacking filter involves the filtering of each trace with an individual filter and the subsequent summing of all outputs. The actual position of a trace in space as well as certain simultaneous shifts of traces and filter components in time do not influence the process. The resulting output is consequently invariant to various arbitrary coordinate transformations. For a certain useful class of ensembles of non‐linear moveout arrival times for signals a particular transformation can be found which transforms a given ensemble into one consisting only of straight lines. It is thus possible to reduce, for instance, the analysis of a stacking filter designed for hyperbola‐like moveout curves to the analysis of a velocity filter with linear moveout curves. As the (f—k) transform is a very useful concept to describe a velocity filter, it can consequently be applied to characterize a stacking filter in regard to its performance on input signals with non‐linear moveout.
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THE INTERPRETATION OF GRADIENT ARRAY CHARGEABILITY ANOMALIES *
By D. H. QUICKAbstractEmpirical equalities derived from time domain induced polarization scale modelling with the gradient array over simple geometries, and from the potential field functions for equivalent simple charge configurations are similar. The function for the dyke like body is analogous to the magnetic case allowing both total and vertical magnetic field interpretation techniques to be applied to gradient array chargeability anomalies.
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AN EXAMPLE OF THE APPLICATION OF AUTO‐CORRELATION AND SPECTRAL ANALYSIS IN MINING EXPLORATION *
By D. D. SARMAAbstractThis paper deals with a case study on the application of auto‐correlation and spectral analysis methods to mineral assay data taken along seven drives and two winzes concerning the McTaggart's (West) lode of Kolar gold fields. The general model conceived in this study is: measured (estimated) ore grade at jth location =true value + error at jth location. Employing an auto‐correlation function of the form C e‐ a |k| for signals, the respective contributions of signals and noise to the total logarithmic variances for the data along drives and winzes are analysed. Smoothed spectral density estimates and their 90% confidence limits are computed for the series of data.
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TWO DIMENSIONAL MASS DISTRIBUTIONS FROM GRAVITY ANOMALIES: A COMPUTER METHOD *
By D. J. JINAbstractQureshi and Mula have suggested a computer method for the calculation of the shape of a two dimensional body from the gravity anomaly profile associated with it. The application of the method, however, was restricted to those bodies which have their top or base horizontal and end sides vertical. In this paper study has been made to investigate the possibility of eliminating the above mentioned restrictions and has arrived at the affirmative conclusion.
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THE DETERMINATION OF FILTER COEFFICIENTS FOR THE COMPUTATION OF STANDARD CURVES FOR DIPOLE RESISTIVITY SOUNDING OVER LAYERED EARTH BY LINEAR DIGITAL FILTERING *
Authors U. C. DAS and D. P. GHOSHAbstractThe technique of linear digital filtering developed for the computation of standard curves for conventional resistivity and electromagnetic depth soundings is applied to the determination of filter coefficients for the computation of dipole curves from the resistivity transform function by convolution. In designing the filter function from which the coefficients are derived, a sampling interval shorter than the one used in the earlier work on resistivity sounding is found to be necessary. The performance of the filter sets is tested and found to be highly accurate. The method is also simple and very fast in application.
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COMPATIBILITY OF EM AND IP SURVEYS *
By D. VOGELSANGAbstractMethods and typical case histories of EM and IP surveys are compared in order to check their compatibility for the investigation of large areas for base metal sulphides. It is demonstrated that the fast, low cost EM may miss sulphide concentrations which cause no reduction of apparent resistivity, or which act like horizontal slabs, where EM anomalies occur marginally. In such cases only IP can recognize the whole extent of the mineralization. The misleading role of graphite exists for both methods.
The conclusion is that EM remains the only economical method to survey whole ore districts, but that the shortcomings should always be taken into account in the interpretation. They can be overcome by employing geological, geochemical or other geophysical indicators in selecting promising targets for follow‐up IP. Even if less than 20% of the area is covered by the expensive IP, there is a fair chance that all sulphide bearing rocks will be found. Therefore, the question is not whether to apply EM or IP methods, but how to combine them best.
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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)