ALBERT

Notes: When a rather extensive network of short distance refraction profiles was shot the following two observations were made. Firstly, the wave velocity in the weathered layer showed a quite considerable fluctuation in horizontal direction, the extreme values being of the order of 300 and 700 m/sec. A practical result of this scattering of the velocities is that an uncertainty of about 10% is introduced in the computation of the weathering corrections. The second observation is that, in the majority of cases, the travel time curve does not pass through the origin. It could be ascertained that this observation was not caused by errors in the method of observation. A probable explanation of the phenomenon is found in a theory that has been developed by Gassmann, who derived the velocity distribution for a hexagonal packing of spherical solid bodies. According to this theory extremely low velocities would occur in the first few centimeters of the crust of the earth. Qualitatively, our observations are in agreement with the theory of Gassmann.

Notes: The geophysicists who attempted to evaluate elastic anisotropy of some bedded formations most often gave but little information about recording and interpretating the measurements.May be they did not lay enough stress on the fact that any determination of the anisotropy factor is a critical operation and that, to have some certainty. it must be made under good conditions and then discussed.Due to the very favourable conditions offered: undisturbed tectonics and topography, relatively regular series the Berriane district in Northern Sahara, is rather well suited to accurate measurements and to an anisotropy study down to 1,250 meters. Since measurements have been carried out in the wildcat drilled at Berriane by S. N. Repal, it seems interesting to communicate the results obtained and to discuss them according to the influence of high velocity layers.It can be noted that in the clay and sand series which have been investigated, anisotropy coefficient amounts to 1.09 or so.To conclude, it seems desirable that determinations made by numerous operators should allow a more accurate knowledge of the anisotropy factor in the main types of rocks.

Notes: The aim of the present investigation is to examine the significance of the second derivative for the purpose of the prospective determination of the geological properties of the district of Offenburg, which are relatively wellknown as a result of both reflection seismic and bore profile findings.The calculation of the second derivative is carried out by means of three approximation formulae, which are compared with each other. In contrast to the isogam map the second derivative shows some additional characteristics, whose structural significance illuminates the comparison with the results of reflection seismics.A geological profile constructed on the basis of 6 wells completely confirms the geophysical findings.

Notes: The widespread use of common depth point techniques has emphasized the need for accurate static corrections. Manual interpretation methods can give excellent results, but a computer technique is desirable because of the great volumn of data recorded in common depth point shooting. The redundancy inherent in common depth point data may be used to compute a statistical estimate of the static corrections. The corrections are assumed to be time-invarient, surface-consistent, and independent of frequency. Surface consistency implies that all traces from a particular shot will receive the same shot static correction and all traces from a particular receiver position will receive the same receiver correction.Time shifts are computed for all input traces using crosscorrelation functions between common depth point traces. The time shift for each trace is composed of a shot static, a receiver static, residual normal moveout if present, and noise. Estimates of the shot and receiver static corrections are obtained by averaging different sets of the measured time shifts. Time shifts which are greatly in error are detected and removed from the computations.The method is useful for data which has a moderate to good signal to noise ratio. Residual normal moveout should be corrected before estimating the statics. The program estimates the statics for correctly stacking common depth point traces but it is not sensitive to constant or very slowly changing static errors.

Notes: The 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.

Notes: The 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.

Notes: The author proposes the parameter Δ2/ΔT1 for possible application in aeromagnetic surveying making use of already available gradiometer systems equipped with sensors separated vertically.

Notes: Geophysical field equipment has undergone rapid changes in the past decade; from simple AGC amplifiers and galvo cameras to binary gain switching amplifiers and digital recorders, all in an attempt to keep pace with the new geophysical interpretive methods developed, and the growing acceptance of the terminology, methods, and philosophy of communication theory.The additional tools of the digital recorder and digital computer make it possible to utilize these new techniques in geophysical processing. Accomplishing these new techniques demands severe requirements on the digital field recording process in handling the decreasing energy return from the seismometer, and to fully realize the capabilities of digital techniques in reducing data. Simple automatic gain control may be used. However, in the more sophisticated interpretive methods, such as autoregression and deconvolution, it is necessary to reconstruct the actual energy levels in the computer. Recording the control signal used in master AGC or programmed gain control may prove satisfactory; however the accuracy of control versus gain is limited to I% for such analog instrumentation.To utilize the computer to its fullest extent, and to accurately perform these new techniques, requires an accuracy of I% or better. This accuracy is obtainable by using a step gain control where the gain is increased by fixed steps in which each step represents a gain in amplification by a constant factor. The accuracy in this case can be made dependent only on the tolerance of resistors used as attenuators or feedback elements. Preferably the constant factor of gain steps should be a number easily handled by the computer. By using 6 db steps it becomes a simple matter to shift binary numbers, such as multiplying or dividing by 10 in the decimal system.The requirements or parameters for such an amplifier system, and the elements of the amplifier necessary to achieve these requirements are presented.

Notes: Spurious reflections showing a residual move-out are generally present on both corrected seismic cross-sections and common depth point composites.We propose to determine a space-time filter satisfying the following conditions: to attenuate as much as possible reflections presenting a given move-out, to retain intact reflections whose time gradient is zero (or has a predetermined value), to be applicable efficiently even to a small number of traces, not to amplify random noise unduly.After briefly indicating the design principle of these filters, we shall give the results of their application to the theoretical examples, in order to bring out: the influence of sampling interval and filter length (possibility of achieving efficient filtering using an apparatus with a small number of terms), the effect of filtering on dipping reflections (reduction in amplitude and distortion increasing with the time gradient), the range of reflection move-out that can effectively be filtered with the same apparatus, the disturbing influence of random noise.〈section xml:id="abs1-2"〉〈title type="main"〉RESUMEOn constate généralement, tant sur les films sismiques corrigés que sur les résultats de couverture multiple, la présence de réflexions parasites présentant une courbure résiduelle d'indicatrice.Nous nous sommes proposé de déterminer un opérateur de filtrage spatio-temporel satisfaisant aux conditions suivantes: filtrer le plus possible les réflexions présentant une courbure donnée, conserver intégralement les réflexions dont le gradient temps est nul (ou a une valeur déterminée), pourvoir être appliqué efficacement à un petit nombre de traces, ne pas amplifier outre mesure les bruits inorganicés.Après avoir indiqué brièvement le principe du calcul de ces filtres, nous présenterons les résultats de leur application à des exemples théoriques, afin de mettre en évidence:ľ'influence du pas d'échantillonnage et de la longueur du filtre (possibilityé d'obtenir un filtrage efficace avec un opérateur comportant un petit nombre de termes),ľ'effet du filtrage sur les réflexions pentées (réduction d'amplitude et distorsion croissant avec le gradient temps),ľ'ouverture de ľ'éventail des réflexions courbes que ľ'on peut filtrer efficacement avec un même opérateur,ľ'influence perturbatrice de bruits inorganicés.

Notes: An iterative process is proposed that computes a distribution of masses giving rise to a certain gravitational field. The possibility of applying a similar procedure to magnetic and electric fields is also discussed.

Notes: The method presented takes the influence of refraction rigidly into account. All travel-times available are used in an application of the method of least squares. The solution is illustrated by a computer flow diagram.

Notes: Charts are presented for the computation of the vertical component of the attraction of horizontal laminas and of horizontal cylinders bounded by irregular w-sided polygons. Contrary to older methods no restricting conditions are made for the directions of the sides of the polygons.

Notes: It was found in Part I of this paper that approximating the sharp cut-off frequency characteristic best in a mean square sense by an impulse response of finite length M produced a characteristic whose slope on a linear frequency scale was proportional to the length of impulse response, but whose maximum overshoot of ±9% was independent of this length (Gibbs' phenomenon). Weighting functions, based on frequency tapering or arbitrarily chosen, were used in Part II to modify the truncated impulse response of the sharp cut-off frequency characteristic, and thereby obtain a trade-off between the value of maximum overshoot and the sharpness of the resulting characteristic. These weighting functions, known as apodising functions, were dependent on the time-bandwidth product Mξ, where 2ξ, corresponded to the tapering range of frequencies.Part III now deals with digital filters where the number 2N–1 of coefficients is directly related to the finite length M of the continuous impulse response. The values of the filter coefficients are taken from the continuous impulse response at the sampling instants, and the resulting characteristic is approximately the same as that derived in Part II for the continuous finite length impulse response. Corresponding to known types of frequency tapering, we now specify a filter characteristic which is undefined in the tapering range, and determine the filter coefficients according to a mean square criterion over the rest of the frequency spectrum. The resulting characteristic is dependent on the time bandwidth product Mξ= (N–1/2)ξ up to a maximum value of 2, beyond which undesirable effects occur. This optimum partially specified characteristic is an improvement on the previous digital filters in terms of the trade-off ratio for values of maximum overshoot less than 1%. Similar to the previous optimum characteristic is the optimum partially specified weighted digital filter, where greater “emphasis is placed on reducing the value of maximum overshoot than of maximum undershoot”. Such characteristics are capable of providing better trade-off ratios than the other filters for maximum overshoots greater than 1/2%. However these filters have critical maximum numbers 2.NC–1 of coefficients, beyond which the resulting characteristics have unsuitable shapes. This type of characteristic differs from the others in not being a biassed odd function about its cut-off frequency.

Notes: In Part I of this paper, we examined the properties of the best mean square approximation to the sharp cut-off frequency characteristic by an impulse response of finite length. It was found that the sharpness of cut-off for the resulting frequency characteristic depended on the length of the impulse response–but because of the discontinuous nature of the specified frequency characteristic, this best mean square approximation always had a maximum overshoot of ± 9%, independent of the length of the impulse response (Gibbs phenomenon).In Part II, we investigate ways of reducing this ± 9% overshoot at the expense of a reduced sharpness of cut-off. The discontinuous frequency characteristic is first approximated by a continuous characteristic with linear or cosine frequency tapering. The impulse response for such tapered characteristics consists of the impulse response of the discontinuous frequency characteristic weighted by a certain function corresponding to the type of tapering employed. The best mean square approximation to the tapered characteristic by an impulse response of finite length M will produce a frequency characteristic whose properties are now dependent on the time-band width product Mζ, where 2ζ is the tapering range.A trade-off exists between the maximum overshoot and the sharpness of cut-off for the resulting characteristic for both forms of frequency tapering. Instead of considering other forms of tapering in the frequency domain, we now investigate arbitrarily chosen weighting functions in the time domain to determine the minimum length of impulse response for a minimum value of maximum overshoot and a maximum value of sharpness of cut-off.Part III will discuss the digital realization of the above finite length impulse responses together with the optimum partially specified digital filter approximation to the desired frequency characteristic.

Notes: Book reviewed in this article:Le Filtrage en Sismique, Tome IJ. AUBOUIN “Geosynclines” (Developments in Geotectonics 1). Elsevier Publishing CompanyEarth and Planetary Science Letters Vol. 1. Nr. 2H. Ramberg Gravity, Deformation and the Earth's Crust Academic Press“Potassium Argon Dating” Compiled by O. A. Schaeffer and J. Zähringer

Notes: Deep seismic sounding was performed along two profiles which cross at the Dinarides area right angles. One of the profiles goes far into the Adriatic Sea.Besides considerations on the lithophysical conditions, characteristics of the registered waves are analysed. The amplitude curves and curves of amplitude ratios are shown. Special attention was paid to the frequency of the registered waves.In order to obtain a better knowledge of the registered wave pattern three-component recordings of waves were carried out. The analysis of the records obtained is given, with particular regard to the possibility of creating converted waves.The Earth's crust structure along the profiles II and III is given.

Notes: Nomograms for solving equations in multilayer and dipping layer cases are presented. The nomograms constructed are used to solve the following equations: I. Intercept-time formula. 2. Critical distance formula. 3. Critical angle formula. 4. Critical angle and dip angle formula. 5. Vertical depth formula.

Notes: Consideration 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.

Notes: A large self-potential anomaly was outlined in 1963–64 at Tantahuatay near Hualgayoc in the Andes of northern Peru. Peak value recorded was–1842 millivolts–thus making it one of the strongest, or perhaps the strongest, SP anomaly ever measured. A lack of detailed geological data precludes the formulation of an adequate explanation for the Tantahuatay anomaly, but geological and mineralogical similarities with the well-documented Venencocha anomaly near Cerro de Pasco, Peru (Kruger and Lacy, 1949), suggest that the anomaly arises from sulfuric acid associated with the mineral alunite. The anomaly obviously cannot be explained by the half-cell mechanism of Sato and Mooney (1960), who place a limit of 700 millivolts on self-potential anomalies over sulfide bodies. Further study of the Tantahuatay anomaly would be of interest in understanding self-potential mechanisms in general.

Notes: Book review in this articleF. S. Grant and G. F. West, Interpretation Theory in Applied Geophysics, McGraw-Hill Comp., New York, 1965, 583 pp., price $ 17.50.Archaeo-Physica. Technische und naturwissenschaftliche Beiträge zur Feldarchäologie. Mit Beitragen von E. Le Borgne, I. Scollar, J. D. Mudie, J. Görier, H.-J. Appel, G. Strunk-Lichtenberg, Böhlau Verlag, Köln, Graz, 1965, 202 pp., 124 fig.H. Takeuchi, Theory of the Earth's Interior, Blaisdell Publishing Company, Waltham (Mass.), Toronto, London, 1966, 131 pp.G. D. Garland, The Earth's Shape and Gravity, The Commonwealth and International Library, Geophysics Division, Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfurt, 1965, 183 pp., price: 17s 6d.

Notes: Using a comprehensive theory of the vertical force variometer, it is shown that the mean of the two readings taken in azimuths 180 degrees apart only eliminates the error of misorientation and of inclination of the knife edge if these factors are sufficiently small. The necessary accuracy in the 180 degree rotation and in the readjustment of the levels are investigated and a practical test is developed to allow the initial adjustments to be determined. Finally, a brief description of a new variometer tripod is given.

Notes: It is known that good use can be made of calculating the second vertical derivative of gravitational and magnetic fields. The first derivative, or Vertical Gradient, has the same properties, Like the second derivative, it does not depend on the locally linear regional anomaly. Moreover, the gradient is less affected by experimental errors.The report gives a practical method of calculating the vertical gradient. Its application is identical to that in general use for calculating the second derivative, except that the numerical coefficients are different. The method also allows the establishment of formulae for downward extension of the field and its derivatives.

Notes: According to a study of seismic velocities in the Alpine Foreland of Eastern Switzerland, the initial velocity is rather high in comparison with other Tertiary basins and shows an exceptionally high increase rate. When analysing the average and the interval velocities, especially of Tertiary strata, and when comparing them with velocities of strata of the same age and a very similar facies of the Northern Rheintalgraben, it has been found that the increase of velocity is closely related to the distance to the Subalpine Molasse. The conclusion is that the velocity of the Tertiary strata is strongly influenced by the folding pressure of the Subalpine Molasse or of the Alps. The same method has been applied to a relatively large number of wells in the area of the “German Molasse”. Not only the results in Eastern Switzerland have been confirmed, but also it has been proved that the diagenesis of the Tertiary strata and, hence, their velocities are influenced only partially by the specific depth of the basin. Velocities increase towards the Folded Molasse or the Alps. Consequently they depend on lateral folding pressure, which decreases from west to east with the increasing width of the basin. The tertiary strata of the basin have been affected by lateral folding pressurefrom south to north. However, structures with lateral compression have not been discovered yet in the German Alpine Foreland.

Notes: In a paper by Koefoed and Kegge (1968), which was based on previous work of Wesley (1958), the electrical current pattern has been derived that is induced by an oscillating magnetic dipole in a semi-infinite thin plate of infinitesimal resistivity.In the present paper, the range of validity of the assumptions, on which the work of Wesley is based, is subjected to a theoretical analysis. It is found that the decisive factor for the validity of Wesley's derivation is the quotient of the square of the penetration depth of the electrical current over the product of the thickness of the plate and a distance that is indicative of the size of the current loops in the plate. Wesley's derivation is shown to be valid only when this factor is negligible. It is also shown that in this condition the imaginary component of the anomaly must be negligible.Model experiments are described in which the electrical current pattern is studied also in the range in which the derivation of Wesley is not valid. The procedure used in these model experiments was to measure the tangential component of the magnetic field strength very close to the metal plate that simulated the conductive dyke.In order to express the results of the measurements in terms of the imaginary to real ratio, these results are compared with an interpretation graph for field measurements that was published by Hedström and Parasnis (1958). It is found that the current pattern in the plate is essentially the same as that which follows from Wesley's derivation, provided that the imaginary to real ratio is less than one third. The measurements do not permit to draw conclusions regarding the current pattern in the plate in conditions that correspond to larger values of the imaginary to real ratio.

Notes: Electrical resistivity anomalies of a symmetrical four-electrode co-linear system across a single vertical discontinuity are treated in relation to: a) the ratio of potential electrode separation to the current electrode separation that are employed in the system and b) the angle which the electrode alignment makes with the discontinuity. Several conclusions are extracted from this treatment and methods for obtaining an optimum sensitivity of the system, with respect to these parameters, are shown. Disadvantages of special arrangements, such as the Wenner configuration, are indicated. Methods are outlined to utilise variations in the apparent resistivity plot for determining the angle between the electrode alignment and the discontinuity, quantitatively or qualitatively. These variations include certain deviations from the standard curves obtained in longitudinal traverses made at right angles to the discontinuity. Also, a comparison is made between longitudinal and cross traverses, in relation to the discontinuity.

Notes: When, in a two-layer earth, the substratum is insulating or infinitely conducting, the thickness of the top layer can be determined from surface potential measurements along a radius from a single point power electrode. The observed potential needs to be numerically integrated in a direction perpendicular to the said radius, and Figure 4 can then be used to find the thickness. A field example is included.

Notes: In order to increase the seismic efficiency of the Sparker-system developments were made in 1966/67. Results illustrating the main steps of this development are discussed. A new type of electrode called Transploder electrode was field-tested and proved to be promising.

Notes: The theory of electrical dipole soundings proved that this method can produce resistivity measurements, which are comparable with those obtained by electrical soundings of the Wenner or Schlumberger type. Their main advantage is the use of short cable lengths, which is important if the depth of penetration should be large.A considerable disadvantage of the dipole method is the great sensitivity to lateral discontinuities. Though these have an influence on the Schlumberger arrangement as well, they can disturb a dipole sounding to such an extent than an interpretation based on a horizontal layer case is no more possible.There are six different dipole arrays, which differ from each other with respect to the angle enclosed by the two dipole orientations-the current dipole AB and the measuring dipole MN. The theoretical comparison of the dipole arrays with the Schlumberger array concerning their sensitivity to lateral discontinuities is a useful basis for the choice of the most suitable configuration.Considering geological subsurface conditions the right choice of a dipole array can give an optimal result, i.e. a dipole sounding for which the sensitivity to lateral discontinuities is as small as possible under the given circumstances.

Notes: Deconvolution and deringing are well known subjects and it is not necessary to state again their objectives nor the basical methods used to reach them. Let us just remember that, generally, among many others, the two following assumptions are made for simplification purposes:〈list xml:id="l1" style="plain"〉—for deconvolution, it is assumed that the recorded seismic signal is constant, meaning that its shape is the same all along the time interval during which the trace is to be deconvolved;—for de-ringing, it is assumed that the ringing period is constant and that the intensity of the ringing phenomenon is independant of the time.With these two assumptions, a single constant operator can be applied for deconvolving, deringing or both. In most cases, the time variations of the signal or of the ringing are small enough and the error resulting of the application of a constant operator is acceptable. It results into a slight increase of the noise level or into a small residual ringing in the processed trace.When this noise or the residual ringing are too important, the assumption of a constant signal and ringing period must be rejected. This is the case that is examined here according to the following steps:〈list xml:id="l2" style="plain"〉—short definition of the problem;—fast evaluation of some possible solutions;—the selected solution: resulting approximations and how to obviate them, computing method and a remark about the operators;—theoretical example: the efficiency of the process used is evaluated on data in which the results aimed at are known; the influence of the selection of numerical values to be assigned to the parameters is examined;—real cases: comparison of results obtained with the Protee process and with more conventional processes assuming a time invariance or including a weighted composition of several conventional processes each with a different operator.

Notes: Sharp cut-off frequency filtering is carried out in the discrete time domain on digital computers. A convolution of the digital filter impulse response with the sampled input yields the output. For practical reasons, the length of the filter inpulse response, corresponding to the number of filter coefficients, is limited, and consequently the resulting frequency characteristic will no longer be identical to that originally specified. This is analogous to synthesising some specified frequency characteristic with a finite number of resistive, capacitative and inductive components.In Part I of this paper, we examine the effect of approximating the sharp cut-off frequency characteristic best in a mean square sense by an impulse response of finite length. The resulting frequency characteristic corresponds to the truncated impulse response of the specified frequency characteristic. It has a cut-off slope proportional to, and a mean square error inversely proportional to, the length of the impulse response, and is a biassed odd function about the cut-off frequency point. Because of the Gibbs phenomenon for discontinuous functions, the resulting frequency characteristic will always have a maximum overshoot with respect to the specified characteristic of ± 9%, regardless of the length of the corresponding impulse response. Equal length truncated impulse responses of specified filters with different cut-off frequencies yield frequency characteristics which are almost identical about their respective cut-off points. Now on a log frequency scale (as against a linear frequency scale implied previously) such characteristics may be made almost identical about the respective cut-off points by having the truncated impulse responses composed of an equal number of zero crossings. Results for the low-pass filter are applicable to the high-pass and band-pass characteristics.In the latter case, the mean square error is double that for a single slope characteristic (low-pass or high-pass) and the slopes at both edges of the passband are approximately equal in magnitude to the length of the impulse response (linear frequency scale).Part II of this paper is concerned with reducing the ± 9% overshoot that results from the discontinuous nature of the sharp cut-off frequency characteristic and which is not dependent on the length of the truncated impulse response. The reduction is achieved, at the expense of the steepness of cut-off for the resulting frequency characteristic, by the use of functions which weight the truncated impulse response of the specified frequency characteristic. These functions are called apodising functions. Among other variables, the length of the truncated weighted impulse response will determine the amount of maximum overshoot since the effective frequency characteristic being approximated is no longer a discontinuous function. The digital realization of the finite length impulse responses of Parts I and II is discussed in Part III, together with the optimum partially specified digital filter approximation to the desired frequency characteristic.

Notes: The purpose of this report is to show a method of determining the top of a refractor departing from the times and slopes of the direct and inverse dromocrones. The method does not need topographical correction and can be applied without knowledge of the distance between the geophone and the shot point.These results having been obtained, the commonly accepted point of view is upset: instead of looking for two points on the surface corresponding to one point of the refractor, we try to etablish, starting with only one point from the surface, the two corresponding points from the top of the refractor.This method can be applied to isolated points and does not demand interpretative hypotheses of any kind, excluding the velocity evaluation of the overburden and of the refractor.The necessary calculations can be easily executed by means of a digital computer to which the dromocrone times and the distances between the geophones must be given. These calculations can also be executed by a person having no knowledge of refraction seismology.This report also examines the validity of the approximations involved in the method proposed.

Notes: Determining the shape of a pulse generated by an explosion solely from the data provided by the recorded seismic trace is a difficult and even ambitious task.Knowledge of parameters such as length and number of “arches” of the pulse under study is, in fact, indispensable in solving this problem.These parameters cannot be found directly in the seismic trace, which nevertheless contains a great amount of information. Autocorrelation, with its mathematical and statistical properties, is an efficient way of making the best of this information.We compute all the autocorrelations of reflections having a given number of arches which fulfil certain conditions determined in advance. Then, after statistical testing of some parameters pertaining to the autocorrelations (abcissae of zeros, of extrema …), we select only those with a maximum likelihood. It is sufficient to consider only the reflections whose autocorrelations have been selected and to arrange them in groups according to their shape and arch number in order to obtain average pulses.In so doing several solutions are arrived at, but when considering a given number of traces, a single record for instance, it is possible by comparing these results with each other to considerably reduce their number.In the last part of the paper the nature of the impulse obtained with our method is examined in order to find out whether it is “minimum phase” for carrying out deconvolutions.

Notes: In recent years considerable work has been done to devise a satisfactory non-dynamite seismic system that would replace dynamite in offshore areas. Prior to the advent of digital recording and processing, the non-dynamite sources have generally not provided the depth of penetration or the resolution required for satisfactory seismic interpretation.More recent developments in non-dynamite offshore marine sources include adaptation of the Vibroseis from a land unit to a marine unit, and adaptation of the Dinoseis unit from a land to a marine unit. The SUE (Seismic Underwater Explorer) system is a thermodynamic non-dynamite source utilizing a mixture of propane and oxygen detonated in a special chamber approximately 15 feet below the water surface. This source gives penetration to more than 4 sec in areas typified by Gulf of Mexico type geology and shows deeper penetration than had previously been obtained by dynamite along the western United States in areas with 20 lb charge limitations. A pneumatic source, the airgun, has been in production use in the United States since June 1966. This non-dynamite source provides an intriguing amount of versatility and can be expanded to provide additional energy as necessary to obtain the penetration desired. Tests using systems comprised of from eight to twenty-three airguns show penetration in excess of 5 seconds in many areas. Power spectra comparisons both in amplitude and frequency content demonstrate that this is a controlled source generating a controlled seismic wavelet and a controlled frequency spectrum that can be tailored to fit requirements of particular areas. Sample sections obtained in the Gulf of Mexico and the Pacific Ocean offshore California show adequate penetration to 5.0 seconds reflection time.Quantitative measurements with the airguns demonstrate the effect of:〈list xml:id="l1" style="custom"〉1Variation of the number of guns in the system;2Shaping the frequency spectrum by using different sizes of airguns in the system;3Effects on signal-to-noise ratios as a result of stacking several small energy sources together;4Reproducibility of the initial pulse wavelet from shot to shot.The improvement in record quality as a result of advanced digital processing with non-dynamite sources is comparable to that obtained with dynamite sources. Non-dynamite sources make additional improvements possible where high source multiplicity is advantageous. Excellent dynamic correlations yield accurate velocity control as well as definitions of apparent velocities attributable to multiples and primary-to-multiple amplitude relationships.Non-dynamite sources are being used more and more extensively in offshore exploration. The advent of digital recording and processing provides a means for improving depth of penetration and resolution of many non-dynamite sources.

Notes: The electromagnetic field radiated from a magnetic dipole lying on the ground is considered, in the extremely low frequency range (DC to 20 000 Hertz).Theoretical and experimental data are given on the characteristics of the surface wave (vanishing wave) generated at the air-ground interface, in the case of an homogeneous subsurface.The case of a subsurface with electrical resistivity varying with depth is considered.It is shown how the above-mentioned characteristics may be applied in the quantitative investigation of the electrical resistivity of the subsurface as a function of depth, in a method using the measurements on the ground of all the components of the radiated field: horizontal electrical components, vertical and horizontal magnetic components.

Notes: Book review in this articleHandbuch der Physik/Encyclopedia of Physics, Ed.: S. FlüggeThe Aurora. By S.-I. Akasofu, S. Chapman and A. B. Meinel.Time-Variations of Cosmic Rays. By S. E. Forbush.Magnetic Properties of Rocks and Minerals. By T. Nagata.

Notes: A theory is developed to predict the amplitude and velocity of the first arrival produced by a thin solid refractor embedded in a solid environment. Laboratory experiments on a three dimensional model substantially confirm the theory. The essential conclusion may be found in Figure 8 where it is shown that for a constant wavelength, and for thicknesses up to about one half a wavelength, the attenuation per unit distance decreases monotonically with increase of refractor thickness.The assumption is made that the amplitude, A, attenuates as (x)-n exp(-βx), where x is horizontal distance and n and β are constants. It is emphasised that it is difficult to obtain reliable values for n and β from the initial amplitude measurements.

Notes: Book reviewed in this article: State of Stress in the Earth's Crust, Proceedings of the International ConferenceF. A. Vening Meinesz, The Earth's Crust and Mantle (Development in Solid Earth Geophysics)

Notes: A 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.

Notes: Book review in this articleN. A. Ogil'vi, D. I. Fedorovich, Groundwater Seepage Rates. English translation by N. H. Choksy, Consultants Bureau, New York 1966, 33 pp., 12 fig.

Notes: Mapping 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.

Notes: To be able to make use of all existing probe interpretation techniques, it is desirable that field resistivity observations be conducted in such a way that it is possible to construct an equivalent curve for the surface variation of potential about a point source. Further, the usual parallel layer interpretation will only be justified in as much as the observed potential curve is compatible with such a subsurface geometry. Thus, whilst a potential curve may be constructed from suitable finite potential differences obtained using a Wenner configuration of electrodes, it can be shown, using the tri-potential technique of measurements, that these potential differences may arise partly from lateral resistivity variations.In this paper, a ladder network technique is employed to display these lateral effects and an adjustment method proposed to reduce them. The adjusted potential differences obtained form a consecutive series suitable for summation to give the potential function. These values are subject to further minimum adjustments required for them to comply with slope and curvature conditions for a layered medium. After forming the potential curve by summation, a final numerical smoothing process is carried out. From this smoothed potential curve, corresponding Wenner and Schlumberger curves can readily be derived for interpretation.The method proposed thus attempts to extract from the observed data the maximum part which can be reconciled with a purely depth variation of resistivity. A method is also proposed for compounding the ‘errors of closure’ of the network to provide a Lateral Inhomogeneity Index which gives a measure of the departure of the observed data from the basic interpretation requirements.The method involves no great labour, but can readily be programmed for a computer if desired. Examples are given of the application of the method to field observations. In the interest of objectivity, the final smoothing has been confined to a single stage but in certain very extreme examples a further stage may prove desirable.

Notes: Book reviewed in this article:M. R. J. Wyllie, The Fundamentals of Well Log Interpretation.

Notes: Proton precession magnetometers usually operate discontinuously since thy rely one intermittent impulses. The aerial versions of these magnetometers suffer from relatively high background noise. The type of magnetometer discussed in this paper has solved the two problems of discontinuity of measurements and reduced sensitivity due to background noise.Comparative texts with an established flux-gate apparatus have given significant and convincing results.

Notes: Book reviewed in this article:S. I. Kuznetsov, M. V. Ivanov and N. N. Lyalikova, Introduction to Geological Microbiology Organic Geochemistry, Editor I. A. Breger

Notes: The formula for the Bouguer anomaly contains the density of the masses above the datum plane. If we use a wrong value for the density we obtain on the Bouguer map additional anomalies which coincide with the topographic features.If we do not know the Bouguer density we can compute several Bouguer maps based on different arbitrary densities. Then we select that map which shows the least correlation with the topography and obtain in this way a reasonable value for the density. This method has been found by Nettleton.Several authors have formulated this process mathematically and have elaborated numerical methods. This paper will present such a method. It differs from the former methods by the following:〈list xml:id="l1" style="custom"〉1A general formula for the Bouguer density is presented, using a non-specified linear operator. By choosing special definition for this operator, we can obtain the formulae of several of the known methods.2It is shown that the determination of the density by “Nettleton Profiles” gives less reliable results than the statistical investigation of the whole area covered by the gravity survey.3The known methods do not consider the variations of the vertical gradient. It is shown that in areas with a regional gravity anomaly or an extended topographic feature the known methods yield poor results.4It is shown that the vertical gradient of gravity used as operator gives a most exact and simple formula.5It is shown how the electronic computer—after reading the Bouguer values based on an arbitrary initial density—can compute the residuals, derivatives etc., which are based on the corrected Bouguer density.

Notes: An electronic analogue was used to obtain geophone distortion of typical seismic pulses. Some of the results were checked by computation and in all cases agreement was extremely close. For late arrival events estimates of attenuation and phase shift may be made from the steady-state response curves. It is explained why these curves are not applicable to the first peak, for which one must use the results in Table III.Ground-geophone coupling introduces the same distortion as a very lightly damped galvanometer with a natural frequency usually in the range 100c/s—200c/s. In swampy terrain this frequency may reduce to 30c/s—40c/s and coupling effects may be severe.An electronic unit whose characteristics are the inverse of those of a geophone has been used to improve the first peak amplitude of a seismic refraction record. Since 1c/s geophones are often desirable in refraction survey it may well be more economic to use higher frequency geophones followed by their inverse filter.

Notes: The paper describes a new method for the calculation of standard-graphs i.e. resistivity-curves for assumed resistivity profiles. It starts from the integral of Stefanesco and arrives at a system of image poles, similar to, but simpler than earlier developed systems. The advantages of the new method are described, the accuracy is discussed and it is indicated how the accuracy can be improved by a simple artifice.

Notes: In the present study an attempt is made to relate the general pattern of reflection seismograms obtained over a coal basin to the acoustical properties peculiar to the Coal Measures. The Carboniferous is characterized by a very rapid succession of distinct lithological units, resulting in a surprising variability in their physical properties. Coal seams in particular are conspicuous by their low density and velocity and they produce acoustical contrasts of 35–50 % with respect to country rock. The resulting heavy shielding action prevents the seismic energy from penetrating deeply into this type of formation.With the aid of synthetic seismograms, arranged into synthetic profiles, it is shown that only a minor part of the Coal Measures reflections is of primary origin. The majority has a secondary character brought about by reverberations inside the weathering zone. Thus the conclusion is reached that reflection shooting allows of mapping only the structure of the top section of the Carboniferous, which is sufficient for the purposes of the coalmining industry.

Notes: In the region covered by the paper, electrical methods have been applied in four different zones:〈list xml:id="l1" style="custom"〉a) Ales-Maruejols Basin (resistive lower Oligocene blanketed by conductive Upper Oligocene);b) Ledignan and Vaunage-Lunel anticlines (faulted structures in the marly and limy Cretaceous, with different resistivities;c) Camargue (thick series of conductive sediments);d) Beziers Basin (highly complicated structures in the Mesozoic, widely blanketed by conductive Miocene).It may be assumed that electrical methods can yield valuable information enabling one to define the rugged subsurface topography of resistive strata burried under a reasonably thick cover of conductive sediments especially when a part of the lower formation outcrops even if the part exposed be small. Faults may be delineated and much, more information is obtainable than can be expected from gravity meter survey at a price not very much higher.

Notes: For the treatment of the problems involved in the interpretation of gravity pictures this paper gives a formula that holds generally for any potential function. It provides an extended applicability of the relation used by Elkins for the computation of the second derivative, and also yields an analogous relation to derivatives of higher order of the gravity field.This relation has not been utilized to determine in details the course of the derivatives of higher order in a plane, but is merely applied to points of comparatively extreme curvature of the isogams where the differential values present a ratio favourable to the “noise level”. By this method the values of the derivatives of higher order will not be determined themselves but only the ratio's responsible for the depth of divergence in comparison with the course of an anomaly of masses replaced by points.It is shown by examples of intercalated masses that the divergence points are important and by law related to the form and position of the density contrasts themselves.An analysis of the total gravity picture is made possible by progressing from elements close to the surface to deeper ones. In this way the fundamental features of the earth's crust will be obtained. The application of the analysis process to a gravity anomaly actually measured in Northwest Germany is given.

Notes: When refraction time signals are transmitted over a radio link between shooter and observer there is a serious risk of interference from electrical storms. This risk can be minimised by sending a series of signals at fixed time intervals and the paper describes a simple device which will do this with the required accuracy.

Notes: Seismic reflection, telluric and gravity results are given for the lifted area of Ferrara, in Northern Italy. The agreement is shown between the available shallow seismic data and the gravity evidences. For a portion of the above area where seismic results are particularly poor the vertical gradients method gives a resolution of a gravity anomaly and confirms the telluric information. The residual gravity values, the vertical gradients and the telluric data along a seismic line crossing the zone are compared with seismic results and with evidences from adjacent wells.

Notes: Investigations into reflection seismic on the salt structure of Heide raised the following questions:〈list xml:id="l1" style="custom"〉1) How can the different directions of trend of a series of layers be established?2) How are the contour maps of reflecting horizons to be constructed if there is no general trend of the layers?To answer these questions, the case of the subsoil consisting of a series of layers with plane reflecting beds and constant layer-velocities is treated strictly. The strike lines of the reflecting planes may be at any angle whatever. However, formulas for constructing contour maps of the reflecting planes have been derived. With these formulas, the problem quoted under 1) has also been solved.The construction of contour maps is given.For special cases, formulas are obtained which have already been proved by others.

Notes: The triple integral for the attraction of a mass on a point is transformed in a double sum. This double sum serves to construct a graph for the rapid determination of the gravimetric influence of structures given by depth contours. The influence of topography can also be computed with this graph.

Notes: The formulas derived by the author in a preliminary paper for taking into consideration refraction when dealing with the problem of a vertical plane are extended to the three-dimensional case. Vector analysis is extensively applied. Among others it is shown that in the general case the 3 horizontal twodimensional vectors, i.e.〈list xml:id="l1" style="custom"〉1) the gradient of the time of reflection2) the direction of true dip3) the vector from the shot point to the projection of the reflecting point, point into 3 different directions.

Notes: The dependence of the apparent resistivity on the distance between the potential electrodes is examined and a numerical method is described permitting quantitative calculations. Such a numerical relation is also established for the transformation of Wenner graphs into Schlumberger graphs.In addition it is shown, in which manner the jumps in observed Schlumberger curves, that result from changing the probe spacing, must be smoothed out.

Notes: The luni-solar corrections are considered under the three following aspects:Quality of results: the application of tidal corrections to all stations is pointless as long as the operations do not substantially exceed two hours.Working conditions: it seems possible to increase the duration of programs without any loss of precision, but operating in such a way requires particular care.Behaviour of gravity meters: the introduction of tidal corrections allows to separate three kinds of instrumental drifts; a good knowledge of the mean operational drift enables to appreciate the quality of a given set of measurements.An example is given to show the possibility in some cases to detect small errors which are close to the limit of precision of the instrument.

Notes: Exploration of the Catania region was carried out for over a year by means of electrical soundings. The thickness of the overburden (lava and alluvium) was thus computed and the contour map of the blue clays basement shows the existence of several buried channels where new wells were drilled, all of them successful.

Notes: The paper consists of an account of a resistivity investigation into an old river valley in Coal Measure strata. This valley denuded several of the upper coal seams leaving behind unconsolidated material and it was the purpose of the work to be described to investigate how far the extent and nature of this material could be determined by resistivity methods conducted at the surface.As such the survey fits into a wider programme of research instigated by the National Coal Board.The feature, which is quite well known geologically, was surveyed by conventional methods and the results obtained are discussed in relation to the above project.Thus, the investigations succeeded in tracing the approximate centre line of the feature and in yielding some information on the nature and order of thickness of the deposits. Limitations of the method and its future application are also discussed.

Notes: The use of MKS system units in preference to the cgs system facilitates accurate numerical calculation in magnetostatic problems in geophysics and the practice of stating the precise dimensions of every unit guards against confusion. Suggestions are made for the unique definition of quantities such as magnetic potential, etc. for which the undesirable circumstance of arbitrary alternatives still persists.

Notes: The Fourier transform formula for a two-dimensional fault truncating a horizontal bed at an arbitrary angle of inclination is derived. The amplitude spectrum of the Fourier transform is found to give information about the depth to the top of the upper part of the faulted bed and the inclination of the fault-plane. Under suitable conditions the thickness and the displacement of the bed involved can be obtained. With actual field data, these transforms can be obtained at discrete points by a Fourier analysis of the gravity anomaly. A field example from the Logan fault area near Montreal, Que., Canada, is given.

Notes: Die Interpretation magnetischer Anomalien durch Modellkörper geschieht bevorzugt nach der indirekten Methode (trial und error). Dieses von Hand aufwendige Verfahren läβt sich mit Hilfe der Ausgleichsrechnung nach der Methode der kleinsten Quadrate Rechenautomaten übertragen.Die allgemeinen Grundlagen des Verfahrens werden beschrieben. Wesentliche Voraus-setzungen sind:〈list xml:id="l1" style="custom"〉1)die Annahme bestimmter Körperformen2)das Vorhandensein von Näherungswerten der Unbekannten (Lage, Magnetisierung etc.)3)eine genügend groβe Anzahl von Meβwerten, um den Ausgleichsprozeβ durchführen zu können.Die Vorteile der Methode sind:〈list xml:id="l2" style="custom"〉1)weitgehende Automatisierung und schnelle Arbeitsweise bei Verwendung von Rechenautomaten2)Ermittlung der Fehler der UnbekanntenDie Methode wurde angewandt auf die Interpretation 2-dimensionaler ΔZ- und ΔT-Anomalien. Drei Körpertypen werden dem Rechenprogramm zugrunde gelegt, und zwar die unendliche und endliche diinne Platte und der Kreiszylinder. In die Maschine ein-gegeben werden nur die Meβwerte. Die Interpretation erfolgt im einzelnen in folgenden Schritten:〈list xml:id="l3" style="custom"〉1)Ermittlung von Näherungswerten2)Bestimmung der Körper bester Annäherung3)Iteration für den Körper bester Annäherung.Die Maschine gibt die Endwerte der Unbekannten (Lage, Einfallen, Magnetisierung etc.) mit Angabe der mittleren Fehler sowie die hierzu gehörigen Modellanomalien aus. Diese Endwerte werden einem Zeichenautomaten übergeben, der die gemessene Kurve, die theoretische Kurve und die gesuchten Modellkorper zeichnet.Interpretationsbeispiele werden vorgeführt.

Notes: In one geophysical survey over a salt dome in the Gulf of Mexico, data taken from a single magnetic and seismic shipborne traverse demonstrated significantly the importance of magnetic measurements. The reduced magnetic and seismic profiles were integrated with gravity measurements from an earlier survey demonstrating the value of obtaining simultaneous geophysical data. The traverse was approximately 25 miles in length, 135 miles southeast of Galveston, Texas. The observed gradient averaged approximately 2 gammas per 1000 feet and crosses the southwest corner of a large shallow salt dome called the Way Dome. The recorded magnetic profile over the salt dome shows a negative magnetic anomaly extending for approximately 12 miles with a maximum amplitude of approximately 20 gammas. This negatively anomaly is due to the negative susceptibility contrast between the salt and cap rock that truncates the surrounding parent sediments. The shape of the negative anomaly correlates well with the continous seismic record and clearly delineates the topographical and structural features of the salt dome. The recorded analog magnetic profile was replotted, with both the regional gradient and time variations removed, which makes the observed anomaly much sharper than is noticeable on the original recorded strip chart record. A theoretical magnetic anomaly was calculated using a computer program for comparison to the observed anomaly. The results showed good correlation.

Notes: The auto-correlation function of a seismic trace contains information on all the multiple reflection activity present in the trace.The interpretation of this information is facilitated by the arrangement of autocorrelation functions in cross-sectional form, in the manner of a normal record section. This is the concept of the Sectional Auto-Correlogram.Specifically, the Sectional Auto-Correlogram will…Show if the record section does not include significant multiples, thus allowing confident picking of the primary reflections.Show if the record section does include significant multiples, giving their travel times and inclinations (and, under certain circumstances, their reflection coefficients).Indicate by what process the multiples should be treated.Yield an authoritative measure of the success of a multiple-attenuating treatment.Delineate shallow horizons, even those whose primary reflections are too early to be recorded satisfactorily.Give the true travel time of a primary reflector, and the sign of its reflection coefficient.The Sectional Auto-Correlogram allows the study of primary reflectors by consideration of the multiples generated by them, and in this sense may be said to turn multiple reflections to advantage. Thus a primary reflection at a certain time is defined if we find that every reflection on the record is followed by a multiple after this certain time. Alternatively, a primary reflection at a certain time is defined if, after that certain time, we can find a repetition of the entire record.The Sectional Auto-Correlogram also has secondary uses in fault identification, crustal studies and weathering problems.

Notes: The development of optically pumped and monitored “atomic” magnetometers has allowed the application of greater resolution in geomagnetic measurements for exploration purposes. This paper presents a survey of instrumentation in use, the variety of exploration techniques that are being used in practice, and an estimate of their state of development.Alkali metals (rubidium and cesium) and helium have been used as active elements to obtain the magnetic-field dependent Larmor frequency. Each of these instruments is capable of obtaining high resolution data (data with sensitivity numerically smaller than one-tenth gamma). They have been adapted for airborne, land, and marine usage.Such sensitivity has enabled the rapid development of geomagnetic gradiometers, high sensitivity aeromagnetics, diurnally reduced ground surveys, broad-band magneto-telluric surveys, susceptibility measurements, and convenient magnetic search and location techniques. Outlines of each procedure and an example of its application are given.

Notes: The efficient production of “Geophysical Prospecting” depends upon the co-operation of the individual authors and this paper serves as a guide for them. Some suggestions are also made on the presentation of papers at meetings in the hope of promoting successful discussions.

Notes: A process is described whereby the interpretation of seismic reflection data is carried out by a preliminary two-dimensional plotting procedure followed by a three-dimensional migration. The concept of a surface of maximum convexity is introduced as an integral part of the process of migration. The procedures for deriving the necessary charts of curves are considered and a number of serviceable charts presented.

Notes: In the first part of the present paper we shall investigate the possibility of localising highly situated inclined faults with the aid of the vertical gradient and the second derivative in the direction of the vertical. Since these quantities have been computed from gravity values by means of formulae of approximation we shall have to study the question as to their applicability for possible quantitative interpretation. Particular caution should be exercised when making the usual comparison with theoretical test examples. For three effects have to be taken into account which result from the application of the formulae of approximation:〈list xml:id="l1" style="custom"〉1) The extreme values appear more or less smoothed out2) Extremal abscissae are being displaced3) The results are influenced by the orientation of the grid which forms the basis of the calculation.For a practical instance it was possible to locate a well under troublesome circumstances. This well is situated on the downthrown side of an inclined fault, the depth of the upthrown side being known as a result of another well.We shall show in the second part of the present paper how small, deeply situated structures may be recognised in the diagrams of the vertical gradient and of the second derivative. In the case of two practical instances the effect of these structures is rendered unrecognisable in the isogam map in view of regional influences. The results according to the formulae of Baranov, Elkins and Rosenbach are contrasted with each other.

Notes: Studies made on head waves in a large number of two-dimensional horizontal and inclined layer seismic models are described. The assumption that the amplitude of head wave decreases exponentially with distance is found to be valid in horizontal layers. For the correct estimation of the head wave decay coefficient, the decrease of amplitude due to the divergence of wave energy should always be considered.The variations of head wave amplitude at large distances from the source appear to follow the theory of Heelan (1953). It is, however, concluded that the theory can only be verified from the measurements in models which have large velocity contrast and thick layer at the top.A prominent interference phenomenon between the direct and head wave has been observed near the critical distance. This is more marked for up-dip profile in the case of inclined layer models. The rate of head wave amplitude decrease with distance beyond the zone of interference is found to depend on dip angle, direction of the dip, and velocity contrast.

Notes: Velocity Spectra which were originally developed for the optimum stacking of seismic data have been found to give considerable information concerning lithologic and stratigraphic changes in the geologic section. In the Gulf of Mexico shale sections and sand bodies have been recognized on the Velocity Spectra display, and in the Caribbean last year a first attempt was made to utilize Velocity Spectra information for the determination and mapping of lithology. Since that time, a new program has been developed which takes dip into account when computing the interval velocity. This program has been applied to a seismic section in the North Sea which has resulted in a geologic model derived from interval velocities which were found to be quite consistent. Such a model can be of great value in geological interpretation.

Notes: This new method of calculation, of the second vertical derivative of gravity or magnetic fields is appreciably different from the classical methods because it is based upon the variations of the distance between the isogams rather than a regular grid with “constant spacing”. In a certain way, it is a method of “constant interval”. A number of practical advantages are inherent to the method, among these, the possibility to use the cartesian charts with bi-logarithmic scales which make the calculation much easier, and the creating of iso-error maps which are indispensable for the interpretation of the derivative maps. Three examples of practical application are given, two of them pertain to gravimetry, the third to aeromagnetism. These results are compared with second derivative maps obtained with other methods.

Notes: A description and classification is given for those later events in seismograms of refraction–and wide angle reflection shooting which travel nearly parallel and at constant time intervals behind the first arrivals and which are frequently observed in field surveys. Multiple events with the velocity V1 of the uppermost layer may be caused by multiple P-reflections and certain velocity conditions or by PS-conversions. In addition to these types multiple events with the velocity V2 or Vn may be caused by reflected refractions or by reflected diving waves. The different types will be distinguished mainly by means of travel time–and amplitude-considerations.

Notes: Electronic circuits are described which simulate the effects of galvanometers and geophones. By placing these circuits in the feedback loop of an operational amplifier it is possible to obtain transfer functions which are the inverse of those of the transducers. That is, they will remove the distortion on the signal which was produced by the geophone or the galvanometer.Both a geophone simulator and its inverse filter have been built and used (O'Brien, 1965). The simulator is accurate over at least seven octaves and the inverse filter restores the ground signal to what it would have been if the recording geophone had had a natural frequency √n+1 times that of the actual geophone, where A is the gain of the operational amplifier used in the circuit.

Notes: Uphole recordings in sediments very often reveal shear waves. With their velocity and that of the P-waves Poisson's ratio may be determined, this usually has unexpectedly high values.A number of up-hole shots were recorded with a linear spread of geophones and with constant gain amplifiers. Calculations were made to show the effect of the free surface and ray divergence (the spread factor). The theoretical, relative amplitudes of the ground motion were plotted together with the observed values. In general, there is good agreement between theory and observation which is better for the P-waves than for the S-waves. The reasons for this difference are discussed.Finally, an absorption coefficient is calculated from the amplitudes measured at the surface.

Notes: The transient fields from a finite horizontal loop excited by a half sine wave current pulse have been computed numerically for a particular source receiver configuration at a height of 100 meters above a layered ground. The amplitude of the vertical component of the magnetic field has been chosen for the interpretation. Curves of apparent conductivity vs. time, plotted during the off-time of the signal, show that layering is easily resolved, that resonance effects are present and that polarization effects are detectable for certain types of polarization.

Notes: In the first part, the author, recalling the principle of d/c current measurements, shows by means of some examples, different experimental results relative to the induced polarization phenomenon. He presents the case of the negative induced polarization which can be explained by geometric effects. He gives some examples of saturation curves and discusses the problem of the linearity of the I.P. phenomenon. Then he shows some aspects which demonstrate that I.P. decay curves do not always conform to the general law. He concludes by showing the influence of the current electrodes, the position of which, relative to the polarizable bodies, may alter the shape of the I.P. anomalies.In the second part, the author presents different case histories of I.P. mineral surveys where I.P. is compared to other geophysical methods and drilling results.

Notes: Magneto-telluric measurements were carried out at a group of eight sites, from Braunschweig to Lübeck, to determine the resistivity values associated with the North German conductivity anomaly. The data were analyzed for scalar and tensor apparent resistivities over the period range 5–2000 seconds. The results in general indicate very conductive (˜I Ω-m) sediments overlying a resistive basement which is strongly lineated.Interpreted basement depth (˜6 km) is compatible with published seismic refraction data. Principal conductivity axes in the basement appear to be directly related to trends of salt domes and major troughs. A major change in axis direction occurs near the center of the North German anomaly.

Notes: Attenuation caused by transmission is known to be the greater the closer the samples are taken together. As a result, the amplitudes of seismograms with multiple reflections can be expected to be negligible within a more or less brief time interval, as is the case for seismograms without multiple reflections with attenuation. This paper examines the process by which multiple reflections regenerate these greatly attenuated reflections. It is also ascertained that a sampling interval of one ms for continuous velocity logs is valid for any survey. For economic reasons, we recommend the selection of a larger interval without, however, overdoing things and thus losing too much information.

Notes: Amplitudes of the vertical ground motion are larger in the critical angle region than in the near vertical region, especially amplitudes coming from deeper boundaries or interfaces with small velocity contrast. Four basic boundary models are used to derive specific travel time patterns for first order and higher order interfaces. The transition from reflected waves to diving waves in the supercritical angle region is shown for the different models.Examples from wide angle surveys in Bavaria and in the Buchara region in the USSR have many characteristic similarities. Travel time patterns and asymptotic velocities are almost identical. The most important boundaries of the continental crust - the Mohorovč Ić discontinuity and the top of the crystalline basement - correspond to two boundary models mentioned before. Amplitude and frequency investigations have been used to derive items of the M-discontinuity. It is certainly a gradient zone and seems to have a lenticular structure with material of stepwise different velocities.

Notes: When a small, transparent replica of a seismic section is illuminated by a homogeneous beam of coherent, monochromatic parallel light a diffraction pattern is created that is representation of the double Fourier spectrum of the recorded seismic waves, i.e. their spectrum in terms of frequency, f, and apparent wave number, k.Masking selected parts of this diffraction pattern causes the spectrum to be filtered: the recomposition of the filtered spectrum then provides a filtered section.The ideal seismic section for this purpose would be a continuous variable density section obtained from recording made at every point of the seismic line. The light transmission coefficient (in terms of light amplitude) at each spot of the replica should be linearly related to the instantaneous seismic signal strength at the spot on the seismic section to which it refers.Unfortunately we cannot make recordings at every point of a seismic line and in our practically realisable recordings we have to be content with sampling in the direction of the location coordinate x. This means that with variable density recordings aliasing will be present and evident in the spectrum obtained in the direction of k; furthermore, the aliased spectrum is also multiplied by a sine function of k because the recording obtained at a given station is not presented on the seismic section as a single line along the time axis, but occupies the entire width of the trace.The diffraction patterns created by variable density recordings of dipping sine waves, including clipped recordings, and of the effect of dip filtering in such sections are discussed. The efficiency of dip rejection is shown to decrease with increasing dip.The diffraction pattern of a variable density recording is found to be characterised by a relationship between point pairs in the pattern.No such simple relationship has been found for the diffraction pattern of a variable area section; the spectra of such VAR sections belong to a very special class, because the amplitude transmission coefficient has only two values, viz. 0 and 1.Consequently, selective masking of the diffraction pattern of a VAR section may give rise to a filtered profile that does not look like a VAR section at all.General statements about the diffraction pattern of VAR sections are hard to give, because the transmission coefficient at a given point in the replica is not proportional to the signal level in the seismic section at the relevant point.In the case of VAR presentation of harmonic waves it was found that, as well as the aliasing effect in the k direction, higher harmonics of the frequency are also introduced.Some synthetic examples are given that show dip filtering to be less effective with VAR than with variable density recordings.Some arguments are advanced in favour of the opinion that high-pass filtering of VAR sections will have less success than low-pass filtering. This is demonstrated by two synthetic examples.

Notes: The 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.

Notes: For 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.

Notes: A nomogram is presented which enables evaluation of the components of magnetic attraction of a homogeneous finite rectangular prism, and of gravitational attraction due to a uniform rectangular lamina.In practice any three-dimensional body could be approximated by a number of right rectangular prisms of varying dimensions governed by the shape of the body. The magnetic attraction of the whole body is then obtained by numerical summation of the effects of the constituent prisms.For evaluating the gravitational effect, the cross-section of the body corresponding to each elevation contour is approximated by a number of rectangular laminae (or by a stepping polygon) the attraction of which can be determined with the aid of the same nomogram. The total gravitational attraction of the body is obtained by a process of graphical integration along the vertical axis.

Notes: In [50] and [51] a theory has been developed relating formation factor, permeability and porosity of porous sedimentary rock by means of statistical parameters of the pore system, and further, tying those statistical parameters to other macroscopically measurable quantities like capillarity, capillary retention, flow dispersion etc. This paper deals with experimental methods and apparatus for checking the theoretically derived relations using columns of packed loose or artificially consolidated sands or other granular matter. Some initial experiments, mainly intended for checking out equipment and methods are reported. The discussion of the results so far shows good agreement with the theory in most cases, except for the irreducible water saturation. However, for a definite statement on the general validity of the theory more data must be accumulated.

Notes: Some 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.

Notes: Integration of the continuous seismic reflection profiler with the marine refraction method on engineering surveys offers a solution to hidden layer problems, allowing both layer velocity and thickness to be computed.

Notes: This paper is the follow-up of an earlier paper by the same author on the calculation of standard-graphs for horizontally stratified subsoils. The method which was developed in that earlier paper was destined for handwork; it was laid down in master-tables. The present paper deals with the presentation of similar methods to the computer expert in purely mathematical denotation. Two different denotations are described for the calculation of the image pole strengths involved. The first denotation is an improved version of Watsons formulae; it gives the total strengths. The second denotation preserves the character of successive approximations as described in the previous paper. Both denotations have been worked out until a six layer resistivity profile, but actually there is no limitation to the number of layers. There is no restriction to the resistivities of any layer. The only condition is now that all interface depths must be integers.This paper is followed by a paper on the relevant computer program by Argelo in this same issue

Notes: Book review in this articleJ. Frihagen, Electron Density Profiles in Ionosphere and Exosphere, North-Holland Publishing Company, Amsterdam, 1966, price N. fls. 60,–.J. A. E. Allum, Photogeology and Regional Mapping, Pergamon Press, London, 1966, 107 pages, 16 plates, 23 figures, price 17 s 6 d net.

Notes: The common depth point method of shooting in oil exploration provides a series of seismic traces which yield information about the substrata layers at one location. After normal moveout and static corrections have been applied, the traces are combined by horizontal stacking, or linear multichannel filtering, into a single record in which the primary reflections have been enhanced relative to the multiple reflections and random noise.The criterion used in optimum horizontal stacking is to maximize the signal to noise power ratio, where signal refers to the primary reflection sequence and noise includes the multiple reflections. It is shown when this criterion is equivalent to minimizing the mean square difference between the desired signal (primary reflection sequence) and the weighted horizontally stacked traces.If the seismic traces are combined by multichannel linear filtering, the primary reflection sequence will have undergone some phase and frequency distortion on the resulting record. The signal to noise power ratio then becomes less meaningful a criterion for designing the optimum linear multichannel filter, and the mean square criterion is adopted. In general, however, since more a priori information about the seismic traces is required to design the optimum linear multichannel filter than required for the optimum set of weights of the horizontal stacking process, the former will be an improvement over the latter. It becomes evident that optimum horizontal stacking is a restricted form of linear multichannel filtering.

Notes: Book review in this articleW. L. RUSSELL, Principles of Petroleum Geology, McGraw-Hill Publishing Company