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- Volume 15, Issue 3, 1967
Geophysical Prospecting - Volume 15, Issue 3, 1967
Volume 15, Issue 3, 1967
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PRINCIPLES OF DIGITAL WIENER FILTERING*
Authors ENDERS A. ROBINSON and SVEN TREITELABSTRACTThe theory of statistical communication provides an invaluable framework within which it is possible to formulate design criteria and actually obtain solutions for digital filters. These are then applicable in a wide range of geophysical problems. The basic model for the filtering process considered here consists of an input signal, a desired output signal, and an actual output signal. If one minimizes the energy or power existing in the difference between desired and actual filter outputs, it becomes possible to solve for the so‐called optimum, or least squares filter, commonly known as the “Wiener” filter. In this paper we derive from basic principles the theory leading to such filters. The analysis is carried out in the time domain in discrete form. We propose a model of a seismic trace in terms of a statistical communication system. This model trace is the sum of a signal time series plus a noise time series. If we assume that estimates of the signal shape and of the noise autocorrelation are available, we may calculate Wiener filters which will attenuate the noise and sharpen the signal. The net result of these operations can then in general be expected to increase seismic resolution. We show a few numerical examples to illustrate the model's applicability to situations one might find in practice.
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A METHOD OF TACKLING SOME SEISMIC PROBLEMS AND ITS APPLICATIONS *
By L. ALFANOABSTRACTThe theory is explained and practical applications are shown for a numerical procedure in seismology. Particularly the problems concerning the generation of waves under the action of external pressures, and their propagation, in non‐homogeneous, both elastic and absorbing media, have been carried out. These problems have been assumed mono‐dimensional and refer to plane and spherical waves.
The procedure is based on the solution, by means of series, of the wave differential equation, non‐homogeneous, and with non‐constant coefficients. It is a direct numerical method whose advantage is, mainly, the possibility of tackling, without great difficulties, problems regarding non‐homogeneous elastic and absorbing media.
On the contrary the methods which require the theoretical expression of the solutions by means of formulae, generally, present conceptual and numerical difficulties.
As examples of application of this procedure, the following cases have been carried out by means of numerical calculations.
a) Propagation of a wave, initially of symmetrical shape, in a viscoelastic medium; from the results it appears that the wave propagates without losing its symmetry, i.e. without sensible dispersion. A theoretical analysis has been carried out to justify this result, showing that the dispersion in viscoelastic media is noticeable only for relatively high frequencies. It seems that the practical absence of dispersion in field experiments do not exclude necessarily the viscoelastic character of absorption.
b) Generation of plane waves under the effect of a uniform pressure distributed on the plane surface of a medium. The way the length and the shape of the generated wave depends not only on the type of pressure acting on the surface but also on the near surface impedance variations has been studied.
c) Generation of a spherical wave under the action of a pressure in a spherical hole.
The examples treated show how the length and shape of the wave depends on the radius of the hole. Particularly the frequencies of the wave spectrum are proportional to this radius, for a given type of pressure acting in the hole.
The characteristics of this procedure would also permit the study of media for which the stress‐strain relations are not univocal and linear (non linear absorption). This study, interesting for the wave propagation in rocks, is worth while to be carried out in a special paper.
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THE ANALYSIS AND DESIGN OF TWO‐DIMENSIONAL FILTERS FOR TWO‐DIMENSIONAL DATA *
Authors E. K. DARBY and E. B. DAVIESABSTRACTSome of the methods such as regional removal and second derivative calculations which can be used to outline anomalies on potential data maps can be thought of as a filtering operation. The analysis and design of such two‐dimensional filters by means of direct and inverse two‐dimensional Fourier transforms have been considered.
An analysis of several published sets of second derivative coefficient sets indicates that, in general, they are not a good approximation to the theoretical second derivative filter. Alternate methods of designing regional removal and second derivative filters are discussed. The properties of various two‐dimensional filters are further illustrated by means of maps obtained from the convolution of several of these filters with a set of observed field data. These maps show the large changes in anomaly shape which can result from the inclusion or rejection of various wavelength components.
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THREE‐DIMENSIONAL ELECTRIC MISE‐A‐LA‐MASSE SURVEY OF AN IRREGULAR LEAD‐ZINC‐COPPER DEPOSIT IN CENTRAL SWEDEN *
More LessABSTRACTThe principle of the mise‐á‐la‐masse method is to earth one current electrode of a pair in a conducting mineral show (in a borehole, in an outcrop etc.) and measure the resulting distribution of electric potentials. The distribution will, to some extent, reflect the geometry of the ore mass of which the mineral show forms a part.
In a mise‐á‐la‐masse survey of a lead‐zinc deposit in Central Sweden electric potentials were measured on the surface of the ground as well as in some 25 drillholes, in either case with earthings (successively) in three different parts of the irregular ore deposit. Besides this, measurements were made in drillholes with earthings in two further drillholes.
Geologic correlation between the drillholes is difficult in the present case on account of the irregular geometry of the ore deposit. However, the mise‐á‐la‐masse measurements clearly showed the dip and the pitch of the ore body, established connections between the different ore widths encountered in the various holes, and yielded information about the shape of the ore mass.
In particular, the survey showed that the ore lenses must be crescent‐shaped rather than tabular, and the dip was indicated to be westerly, instead of easterly as originally presumed.
Three‐dimensional models of equipotential surfaces were constructed from the observed drillhole and surface potentials (using transparent plastic sheets and thin copper wire) and these helped to elucidate the mass geometry further.
The surface and underground potential data collected in the present case should be of nterest to geophysicists working on analytic continuation problems.
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RESPONSE OF A TWO‐LAYER GROUND TO AN INFINITE CABLE CARRYING ALTERNATING CURRENT WITH REFERENCE TO TURAM ANOMALIES *
More LessABSTRACTA formula is developed for the vertical magnetic field due to an alternating current passing through a long horizontal cable placed on a two‐layer ground. The variations of the phase and amplitude ratio of the vertical field, along profiles perpendicular to the cable line are investigated. Within the limits encountered in practice, it is found that if the upper layer is conductive, as compared to the lower layer, the phase may vary appreciably whereas the amplitude ratio changes as in the case of vacuum.
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THE USE OF A SQUARE CONFIGURATION IN RESISTIVITY PROSPECTING *
Authors G. M. HABBERJAM and G. E. WATKINSABSTRACTConsideration is given to the use of a configuration of four electrodes set in a square array for resistivity measurements.
It is found that, by passing current successively between different pairs of electrodes, an apparent resistivity can be determined which is both more sensitive to the position of the array centre and less dependent on orientation than the measures usually obtained with colinear arrays of electrodes. At the same time the observations made enable the degree of the departure of local conditions from conditions of lateral homogeneity to be assessed.
Theoretical and practical examples of the use of this electrode system are given and the use of the system both as a tool in mapping and in depth investigations is considered.
It is shown that provided electrode spacings are suitably arranged the results of a probe carried out using the square array can be interpreted by conventional methods.
The system is shown to have particular advantages in the investigation of lateral resistivity variations and the reduced dependence on orientation makes possible the recasting of interpretation data in an orientationally invariant form with a consequent drastic reduction in the number of type curves required for a particular problem.
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THE VERTICAL MAGNETIC FIELD OF AN ALTERNATING CURRENT DIPOLE FOR HORIZONTALLY STRATIFIED MEDIA *
By E. MUNDRYABSTRACTFor the computation of the vertical component Hz of the magnetic field of a horizontal A.C. dipole lying on the earth's surface, a recurrence formula is presented for a horizontally stratified half space, to obtain the (n+ 1)‐layer case from the w‐layer case.
By means of several computed diagrams for the two‐layer case, Hz can be determined for different ratios of conductivity of the subsoil and that of the overburden. Thereby the distance from the dipole as well as the layer thickness h are expressed in terms of the wave length A of a plain wave in the overburden. Assuming a sufficiently large conductivity difference, the results show that evidence about the subsurface conditions can be obtained if the distance between the measuring coil and the dipole is of the order of A/3, and if the thickness h of the layer varies within the range A/100 < h < A/6.
As an example for the 3‐layer case, a nonconducting intermediate layer is assumed.
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NVESTIGATION OF TECTONICS BY GRAVITY DETAILING*
More LessABSTRACTMapping of fault patterns is an important part of geophysical exploration. A computerized digital template analysis method is described which tests gravity maps for the effects of faults by comparing measured gravity data with calculated master curves. The interpreted gravity data are incorporated in a tectonic map using geological symbols and units, for ready use by the geologists.
Tectonics can be investigated by gravity detailing if the smallest undulations on the Bouguer map are taken into consideration. Up to now, residual and derivative gravity maps have explained gravity effects by assuming spherical bodies which are almost unknown in geology. The method discussed here uses tectonic elements, such as fault‐blocks and dikes as a basis of interpretation instead of the spherical bodies of the conventional interpretation methods.
Gravity data can be easily and relatively cheaply obtained in the early phases of exploration by area wide spot coverage following lines of easy access such as roads, etc. Seismic studies, by contrast, have the disadvantage of being executed along predetermined profile lines. Only after sufficient detailing do seismic profiles permit‐if at all ‐an areal mapping of faults. Thus a tectonic map is obtained only at the end of a geophysical survey instead of being available prior to the planning of costly seismic profiles. The use of gravimetric data and their interpretation by the suggested method provides tectonic detail maps in the early phases of geophysical studies.
In addition, this article discusses a general geophysical interpretation method, using the investigation of faults by gravity as an example. Applications of this method for different gravity and magnetics problems as well as for combined interpretations are outlined. Detailed case histories will be published in later articles.
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TOPICS ON SEISMIC RESEARCH AT THE MONACO OCEANOGRAPHIC MUSEUM *
More LessABSTRACTThe author comments the techniques and methods used in continuous seismic profiling by the Monaco Oceanographic Museum during the last five years.
Pinger probe give informations on the Mud layering and thickness. On the shelf or in abyssal plains, boomer and sparker are employed and allow to rise various geological conclusions. South coast of France, continental shelf in the Gulf of Lion, abyssal plain of the Ligurian Sea and Lake of Geneva are the areas concerned to with the results.
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BOOK REVIEW
Book review in this article
N. A. Ogil'vi, D. I. Fedorovich, Groundwater Seepage Rates. English translation by N. H. Choksy, Consultants Bureau, New York 1966, 33 pp., 12 fig.
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