ALBERT

Notes: For horizontal layering and plane horizontal impulsive wavefronts it is theoretically possible to get rid of multiple reflections by a feedback procedure which can easily be derived using raypath philosophy. To reduce the increase of noise inherent in the method the precise theoretical formulae are altered in such a manner that a practical application becomes possible. For this purpose the autocorrelation will be used.Application of the new process to a CRP section where the shot geophone distances in the field had not been long enough to attenuate multiple reflections effectively gave favourable results.

Notes: Two in situ measurements of stress wave velocity in a granodiorite massif were made. Firstly, the velocities close to the source were investigated (for elimination of the influence of cracks), and secondly, the velocities in different horizontal directions over a large area were studied from the viewpoint of their dependence on the crack system of the medium. A correlation between the mutual orientation of the cracks and the maximum or minimum values of the stress wave velocities was obtained.

Notes: The technique of linear digital filtering as developed for the direct interpretation of Schlumberger and Wenner soundings (Ghosh 1971) has been applied here for the derivation of the resistivity transform function from the field dipole measurements as the first step in directly interpreting dipole data. Filter coefficients for this transformation have been worked out for the radial-polar, perpendicular and parallel (30°) arrays of dipole sounding. The procedure combines speed with accuracy.

Notes: Dipole soundings are more sensitive to noise caused by lateral and superficial inhomogeneities than Schlumberger soundings. However, the former are preferable for deep explorations in view of the relatively short cables required. The simple solution of carrying out the field work by means of dipole spreads, and to transform the dipole resistivity diagrams into Schlumberger ones by means of proper formulae would be valid only for smooth and regular curves; but often, owing to the presence of lateral noises, the dipole data show a considerable scatter. For such cases a “continuous dipole sounding” method is proposed for which all successive dipoles are contiguous, so that all parts of the profiles are covered and interpolation is not necessary. Obviously the moving dipoles have lengths proportional to their distances, so that they appear equal in the usual bilogarithmic scale. It follows that only polar-dipole arrays may be used. The transition from a dipole to the corresponding Schlumberger apparent resistivity diagram requires an integration constant which is not unequivocally determined. Therefore, the solution is not unique, but all possible derived Schlumberger diagrams have a common part. Similarly, they have some common interpretative results, which may be referred to the original dipole diagram obtained in the field.A special measurement technique is required since the dipole-dipole voltages to be determined are noticeably smaller than the Schlumberger ones. This is true also because dipole soundings are used for great depths and for long distances between the two dipoles.

Notes: Basic requirements for a seismic reflection system using a moderate-power controlled source are discussed. General considerations and computer modelling show promise for geophysical prospecting, especially at low penetration and very high noise level. For many applications, ranging from mineral and water prospecting, to civil and military engineering, and even archeology, a relatively cheap, small and portable device of this kind might be more convenient than conventional explosive sources or sophisticated controlled sources of the vibroseis type. The use of a simple, low frequency periodic signal facilitates rapid data processing procedures and suggests that the mechanical generator will be very simple and cheap.

Notes: A method is described to transform a dipole sounding curve, obtained with any one of the common dipole arrays over a horizontally layered earth, to the form of a Schlumberger sounding curve. Starting from the general expression which relates the dipole apparent resistivity to the Schlumberger apparent resistivity and its derivative with respect to the spacing, it is possible with some approximations to derive an easy numerical computation procedure in order to perform the transformation. The applicability of the method is discussed briefly.

Notes: Approximate deconvolution by means of Wiener filters has become standard practice in seismic data-processing. It is well-known that addition of a certain percentage of noise energy to the autocorrelation of the signal wavelet leads to a filter that does not increase, or even reduces, the noise level on the seismogram. This noise addition will, in general, cause a minimum phase signal to become mixed phase. A technique is presented for the calculation of the optimum-lag shaping filter for a contaminated signal wavelet. The advantages of this method over the more conventional approach are that it needs less arithmetic operations and that it automatically gives the filter with the optimum combination of shaping performance and noise reduction.

Notes: A set of parabolae is defined to approximate the observed gravity profile for specifying the lateral density variation in a two dimensional causative body. This variation separates the “biased” as well as “unbiased” residual anomaly structure. The method may be directly incorporated into existing numerical and graphical techniques of interpretation for subsequent delineation of structural configuration. The simple relations derived by inspection of the observed gravity profile permit universal application of the technique and in particular for the determination of the size and shape of sub-shelf structures. The suitability of the method in various problems of two dimensional interpretation has been indicated through an illustration of the Godavari Basin (India).

Notes: Decomposition of IP discharge curve into a sum of exponentials yields more information than present practice does. Such a work was performed, as a beginning, by hand, plotting the ordinates on semi logarithimic paper. It gave, according to the cases, two or three exponentials, each with an amplitude Ai and the time constant τi.Three examples of ground prospection are given, the third of which shows an anomaly, unnoticed with present technique but obvious on a profile curve with A1/A2 in ordinates.A computer processing technique is described which yields directly the time constants τi by seeking a differential equation which the IP voltage satisfies; the order of the equation is set arbitrarily. On a practical prospection record with only two exponentials, the assumption that the differential equation does not depend on charge duration (everything else being equal) has been checked (the shape of the curves would depend on boundary conditions). The assumption roughly holds for charge durations from 5 seconds to 40 seconds. We hope that a larger number of exponentials will yield better results.〈section xml:id="abs1-2"〉〈title type="main"〉SommaireLa décomposition de la courbe de décharge en une somme d'exponentielles permet d'en tirer plus d'information que la pratique actuelle. Un tel travail a été fait, pour commencer, à la main en portant les ordonnées sur papier logarithmique; il a fourni, suivant les cas, deux ou trois exponentielles avec, pour chacune d'elles, le coefficient Ai et la constante de temps τi.On donne trois exemples de prospection sur le terrain, dont le dernier comporte une anomalie, inaperçue avec la technique actuelle, mais bien mise en évidence en traçant la courbe de A1/A2 le long du profil.On donne ensuite une technique de calcul sur ordinateur des τi, en recherchant l'équation différentielle à laquelle obéit la tension ΔVPP enregistrée, l'ordre de cette équation étant fixé arbitrairement. On a cherchéà vérifier sur un enregistrement de terrain, avec. deux exponentielles seulement, l'hypothèse suivant laquelle l'équation différentielle ne dépend pas de la durée de charge (toutes choses égales d'ailleurs). L'hypothèse se trouve grossièrement vérifiée pour les durées de charge allant de 5 secondes à 40 secondes, et nous espérons qu'un plus grand nombre d'exponentielles donnera de meilleurs résultats.

Notes: The conventional seismic technique is subject to a recording time following each transmission of energy, in which it is forbidden to release any new pulse. The recording time depends on the deepest reflection of interest, and is often 10 seconds or more in actual practice. To each transmission corresponds one record, i.e. a fixed amount of data which cannot be increased in a given time.Pulse coding allows us to go beyond this limit, by transmitting several times during the normal recording time. The procedure gives as many records as there are pulses, but they overlap, each event being repeated every time there is a pulse. It is possible to process the composite record back to its usual appearance with all events in their proper place if the time breaks are accurately known and make up a code such that the unavoidable noise generated by the process be kept, on the final section, below the ambient noise. The processing is quite similar to that of records made from vibrating sources, though faster in practice.The additional information can be devoted to a saving of time and money as the same profile may be recorded in a shorter time; or to an improvement of quality of the section due to a higher order of coverage, a multiplication of the ray paths and a closer sampling of the reflectors. It is also possible to record information in several planes at the same time, and to work out a 3-dimensional restitution, without loss of production.The process applies to all kinds of sources provided they can be triggered according to the code with sufficient accuracy. Depending on the source and conditions of implementation, the method benefits from other advantages such as better resolution, increased flexibility, and better coupling.Two different names have been given to the process, Sosie and Seiscode, which apply to slightly different parameters for the sequence of pulses. Sosie is more useful at sea, while the normal scope for Seiscode is onshore. Both names are trademarks for SNPA.

Notes: Master diagrams for electromagnetic responses of nine dipole dipole systems are presented for various depths of a vertical infinitely conducting vein. The YY system gives the minimum anomaly for both the inline and broadside arrays. Among other inline systems, it is difficult to decide the clearcut superiority of one system over the other, whereas the XX system in broadside array gives maximum anomaly.

Notes: The interpretation of Turam data is treated by means of a development of the conventional approach to this type of data. The development consists of a curve matching technique based upon a line current approximation to the true induced current pattern.The technique requires computation facilities which are readily available in modern programmable calculators.Practical examples of the use of the method illustrate that it can reveal information concerning the geometry of a conducting body which would not be gained by the conventional approach.

Notes: Two-layer type curves of apparent frequency effect for the Wenner configuration are presented. The formulation is based on the normal definition of frequency effect in terms of resistivities measured at different frequencies plus the definition of apparent resistivity over two horizontal layers as a function of first and second layer resistivities. The use of these type curves in the interpretation of multilayer apparent frequency-effect curves is described and some field examples are given.

Notes: In this paper properties of the discrete zero-phase time function are derived and compared with related properties of the discrete minimum-phase time function.The two-sided minimum-length signal is introduced and it is derived that, for any given amplitude spectrum, the two-sided minimum-length signal and the signal with zero-phase spectrum are identical signals. A comparison is made between the one-sided minimum-length signal (minimum-phase signal) and the two-sided minimum-length signal (zero-phase signal).A computational scheme is discussed which determines the zero-phase correspondent of a given signal.A method is proposed to compute zero-phase least-square inverse filters. The efficiency of minimum-phase and zero-phase least-square inverse filters is shown on signals with different phase properties.A criterion is derived which determines whether a symmetric time function has the zero-phase property. The close relationship with the minimum-phase criterion is discussed.Finally the relationship between signal length and resolving power is illustrated on numerical examples.

Notes: Empirical equalities derived from time domain induced polarization scale modelling with the gradient array over simple geometries, and from the potential field functions for equivalent simple charge configurations are similar. The function for the dyke like body is analogous to the magnetic case allowing both total and vertical magnetic field interpretation techniques to be applied to gradient array chargeability anomalies.

Notes: “Remote sensing” techniques have been used for many years as an exploration tool; broadly speaking, any method using sensors not directly connected to the earth's surface falls into this group.It is preferable, however, to use the term solely with reference to a number of new sensors which have recently become available to earth scientists for the detection of various radiations of the electromagnetic spectrum in the wave length range from 0.1 micron (UV) to some centimeters including the visible and infrared regions.Radiations artificially induced in the earth (active sensing) or spontaneous radiations (passive sensing) can be detected. Some of the bands investigated seem promising for application to geological surveys, especially using sensors on aircraft and satellites, which allow synoptic and large scale investigations.A brief account is given of the results already achieved and of future developments such as the ERTS and manned satellite (post Apollo) “earth observation” programmes.The potential role of Europe in the field is discussed.Details are given of some applications of thermal I.R. imagery to geological and vulcanological problems, with special emphasis on the research carried out in Italy.

Notes: A simple calculation procedure that gives the equilibrium temperature in geothermal measurements reduces the reading time in field work from reported 60 minutes to about 10 minutes.

Notes: Boundary-value problems in steady-state current flow were solved numerically in bispherical coordinates for a sphere of arbitrary conductivity in a half-space. Solutions for the potential on the surface of the half-space were examined for the cases where both current sources were on the surface, one source on the surface and the second between the surface and the sphere, and one source on the surface and the other in the sphere. Results show a great similarity with the layered case when the buried electrode is placed between the surface and the conducting region. Such a buried electrode configuration makes it possible to obtain an accurate measurement of the depth to the conductor in both cases. A model with the current electrode placed in a conductive sphere is compared with a three-layered model with the source in a conductive intermediate layer, and results indicate that the lateral extent of a finite anomalous zone can be estimated using these limiting curves. The validity of these theoretical calculations for buried spheres was confirmed experimentally by tests conducted on an analog model.

Notes: A checking method of digital multiple elimination and of deconvolution processing using computers and based on optical autocorrelation is first presented. Comparison between autocorrelograms before and after a single or several processing steps allows to estimate, on one hand, the strength of the deconvolution obtained, known by the study of the central parts which is in fact the signal autocorrelation, on the other hand, the multiple elimination given by the study of side parts of the autocorrelogram.Further, an optical deconvolution procedure, is presented. For this, it is supposed that the signal is known and optically reproduced in the same way as the one of a trace. This is achieved by sphero-cylindrical optics allowing trace to trace processing. Deconvolution is carried out in the spectral domain by inserting a filter in the Fourier plane of the optical unit, the transmission law of which expresses the Fourier transform of the antisignal. This filter device introduces a holographic technique called Fourier holography, in such a way phases as well as amplitudes are preserved.Several results are presented from a synthetic section and also from field sections.

Notes: The separation of regional from local gravity anomalies by means of the application of two-dimensional linear filters is analyzed. It was found that optimization of the filter in the least squares sense leads to filters that produce strong localized concentrations of the error, which may erroneously be interpreted as anomalies. For this reason the maximum absolute value of the error is a more important criterion for the quality of the filter than the root mean square error. This maximum absolute error is minimized by the minimax filter. Intermediate filters are derived which give a transition zone which comes appreciably closer to that of the optimal filter at only a small price in terms of increase of the maximum absolute error.

Notes: The Laboratory of Geophysics of the University of Arizona was presented with an exploration problem by Falconbridge, Ltd. of Canada. Massive mineralized hemispherical “pods” are in the vicinity of a tuff layer of high conductivity and induced polarization response, covered by large thicknesses of resistive volcanics. The initial approach was to utilize electrolytic tank modeling. The extreme resistivity and IP contrasts proved to be difficult to recreate. Two dimensional modeling was attempted next with conductive paper, using copper and silver paint for anomalous masses. This method also proved inadequate. Finally, mathematical equations were solved which could model any arbitrary anomalous body in any steady state electrical field. Plane waves as well as point current sources producing non-plane waves are possible. Finite difference equations were derived for the non-linear partial differential equations under consideration. The equations were solved using a digital computer. Initially, the boundary conditions had to be satisfied at the boundaries of resistivity changes, severely restricting possible geometric shapes for anomalous bodies. The final and successful solution was to apply numerical techniques to obtain solutions of equations which require only that the relative resistivities through the area be specified. The Falconbridge problem and its solution are analyzed.

Notes: For the two and three layer cases geo-electrical sounding graphs can be rapidly and accurately evaluated by comparing them with an adequate set of standard model graphs. The variety of model graphs required is reasonably limited and the use of a computer is unnecessary for this type of interpretation.For more than three layers a compilation of model graphs is not possible, because the variety of curves required in practice increases immensely. To evaluate a measured graph under these conditions, a model graph is calculated by computer for an approximately calculated resistivity profile which is determined, for example, by means of the auxiliary point methods. This model graph is then compared with the measured curve, and from the deviation between the curves a new resistivity profile is derived, the model graph of which is calculated for another comparison procedure, etc. This type of interpretation, although exact, is very inconvenient and time-consuming, because there is no simple method by which an improved resistivity profile can be derived from the deviations between a model graph and a measured graph.The aim of this paper is, on the one hand, to give a simple interpretation method, suitable for use during field work, for multi-layer geo-electrical sounding graphs, and, on the other hand, to indicate an automatic evaluation procedure based on these principles, suitable for use by digital computer.This interpretation system is based on the resolution of the kernel function of Stefanescu's integral into partial fractions. The system consists of a calculation method for an arbitrary multi-layer case and a highly accurate approximation method for determining those partial fractions which are important for interpretation. The partial fractions are found by fitting three-layer graphs to a measured curve. Using the roots and coefficients of these partial fractions and simple equations derived from the kernel function of Stefanescu's integral, the thicknesses and resistivities of layers may be directly calculated for successively increasing depths.The system also provides a simple method for the approximative construction of model graphs.

Notes: The theoretical horizontal resistivity profiles over an outcropping vertical dyke for various parameters-electrode spacing, vein-width and resistivity contrast—with inline alpha, beta and gamma-Wenner electrode systems are described. The resistivity profiles present a most bewildering variety of shapes as compared to those in resistivity soundings. The analysis of type curves suggests suitable electrode configuration for detection of wide, moderately wide, and thin veins. The negative apparent resistivity values on the gamma anomalies for resistive vein over certain vein-widths of higher positive values of resistivity reflection factor contradict the concept of apparent resistivity hitherto held.

Notes: Il est maintenant courant d'employer l'ordinateur pour interpréter les sondages électriques. Cependant, le problème à résoudre en prospection électrique n'admettant pas une solution unique, le but des traitements automatiques consiste simplement à fournir plusieurs hypothèses qui aident à bâtir une interprétation géologique des mesures géophysiques. C'est, d'ailleurs, ce qu'on recherche aussi par la comparaison visuelle des courbes de terrain avec des abaques précalculés. Mais, tandis que l'interprétation manuelle, pour conduire à des solutions qui respectent les mesures faites sur le terrain, exige un temps très long, le traitement automatique fournit immédiatement des solutions compatibles avec les courbes àétudier.Les procédés employés s'adaptent aux divers besoins de la prospection: ils peuvent traiter aussi bien la station isolée que les profils de sondages électriques. C'est ce qu'on se propose de montrer, à l'aide de quelques exemples tirés d'études récentes.

Notes: Various experiments are described in designing two-dimensional magnetic interpretation algorithms using computer curve fitting techniques.For a single anomaly the position of the anomaly maximum and the half-width of the anomaly give good initial estimates of the plate position and thickness. A nomogram and formulae for improving these estimates is given. Curves and estimates for the effects of finite depth extent of a plate show the limits, when the lower surface of the plate can be neglected in curve fitting.The combined anomaly of two parallel plates can be separated into partial anomalies with no common points using the horizontal derivative of the anomaly. The changes of the anomaly maxima and changes in anomaly half-widths are studied as a function of plate separation. The position of the maxima and the half-widths can be corrected before applying the one-plate procedure for obtaining initial estimates of plate positions and thicknesses.The performance of standard optimization methods of Powell, Davidon, and Marquardt in improving the values of the plate parameters are compared. The Powell method seems to be the most reliable for both single and multi-plate anomalies. All methods become unacceptably slow when the number of plates is greater than 2 or 3. In these cases feasible interpretation times are obtained using the partial anomalies and sequential parabolic search of the parameter values as tailored specially to the thick plate model.Experiments with three different error norms, the classical least squares, weighted least squares and minimax, show that the first norm gives the best overall performance in automatic interpretation. The behaviour of the classical least squares norm as a function of the plate parameters is also briefly described.

Notes: The growing awareness of the significance of three-dimensional interpretation of seismic reflection data carries with it a need for better understanding of the role of the velocity configuration in the production of reflection patterns. Modeling the reflection responses of a simple dipping plane reflector through velocity models of various degrees of complexity demonstrates the importance of overlying velocities in determining the reflection pattern.Modeling is accomplished using a raytracing technique which determines total travel time of the normal incidence raypath through an arbitrary iso-velocity layer model.

Notes: In a previous paper it has been shown that we can relate the transient IP electric field Ep, existing in a rock after a step wave of polarizing current, with the steady-state current density Jss during the current step wave as follows: Ep=ρ'Jss.This relation may be interpreted as a generalized Ohm's law, valid in linear cases, in which ρ’(fictitious resistivity) is defined as the product of the true resistivity ρ with the chargeability m.Supposing Ep=—grad Up and applying the divergence condition div Jss= o, one can, for a layered earth, obtain a general expression for the depolarization potential Up as a solution of Laplace's equation ∇2Up= o.Since the mathematical procedure for the solution of this last equation is identical to that used in resistivity problems, we propose now the introduction of an apparent fictitious resistivity ρ'a (defined as the product of the apparent resistivity ρa with the apparent chargeability ma) as a new parameter for the interpretations of IP soundings carried out over layered structures with a common electrode array.The most general expression of ρ'a as a function of the electrode distance turns out to be mathematically identical to the general expression of ρ'a. Therefore it is possible to interpret a ρ'a field curve using the same standard graphs for resistivity prospecting with the usual method of complete curve matching.In this manner a great deal of work is saved since there is no need to construct proper ma graphs for the interpretation of IP soundings, as it has been done up to now.Finally some field examples are reported.

Notes: Dipole sounding resistivity measurements over layered earth can be interpreted directly by adapting the procedure given by Koefoed (1968) for Schlumberger system. To carry out the first step of the interpretation leading to the determination of the raised kernel function, partial resistivity functions for the dipole method are derived and given in the form of standard curves. The second step involving the derivation of layering parameters from the kernel being independent of the electrode configurations remains unaltered. The applicability and limitations of the method are discussed.

Notes: Computations have been made for the effect of ground slope in combination with transmitter coil misorientation on different electromagnetic depth sounding systems and sets of frequency sounding master curves are presented for different angles. The effect of a thin air layer due to the elevation of coils above ground surface has been studied for different systems. Also discussed are the effects due to an error in transmitter-receiver coil separation.

Notes: Cable feathering is defined as the angle between a line connecting the cable end points and the line of the seismic profile. It is shown that an average reflection point map is more accurate than a shot point location map for geologic interpretation. Geologic resolution is degraded by feathering and this degradation is a function of the number of channels recorded. Feathering in areas of dipping reflectors produces non-standard normal move-out because the depth points are not common, and the perpendicular distances to the reflecting surfaces vary among traces in the c.d.p. gather. An example of a profile shot across a large river is discussed.

Notes: First, we review briefly the principle of the method, the computation of theoretical curves for a layered earth, and the recording technique in use in our surveys.The case history deals with an area covered with overthrust nappes (marls of Miocene age), which had slid on a Triassic sole, obscuring the geological picture.The magnetotelluric survey followed those of gravity and aeromagnetics and preceded the seismic one from North to South, it displayed a shallow and gently dipping basin, a major fault system, and a deep basin with a thick resistive layer, often underlying a conducting one.The seismics, and later the drilling of a well East of the profile, confirmed these features; in particular, the thick resistive layer was revealed to be Jurassic; only its thickness had been slightly overestimated. This fact lead the people in charge of the operations to ask for a reinterpretation synthesis of magnetotellurics, seismics and gravity, the results of which are also presented.

Notes: When the fixed-source electromagnetic method is applied the quantities measured are influenced by the resistivity of the whole environment. This occurs mostly in the cases of measurements in areas with prevailing high resistivities, and if a weathered layer with considerably lower resistivity than that of the original rock has been formed near the surface. For this reason it is important to be acquainted with the properties of the two-layer ground with an overlying conductive layer.In the present paper attention will be drawn to theoretical calculations connected with the field of the homogeneous ground and that of the two-layer ground.

Notes: In mathematical statistical filtering the deconvolution problem can be solved by two different methods:〈list xml:id="l1" style="custom"〉1by inverse filtering2by calculating the prediction error.Both methods are well known in the theory of Wiener filters.If, however, the generating process of the signal is known and can be described by a set of linear first order differential equations, then the Kalman filter can also be used to solve the deconvolution problem. In the case of the inverse filtering method this was shown by Bayless and Brigham (1970). But, while their method can only be used if the original signal is a colored random process, this paper shows that in the case of a white process the prediction error filtering method is a more appropriate approach. The method is extremely efficient and simple. This can be demonstrated by an example which maybe of special interest for seismic exploration.

Notes: The use of the electrical image method in calculating the potential of a source in the presence of a buried conductive sphere proves to be difficult because of the great number of terms making up the potential formula. The disadvantages contained by this method are avoided here by resorting to the theory of graphs. In view of this aim the “propagation” of the electrical images due to the sphere has been represented by an infinite graph to which an infinite matrix has been attached.Taking this as a basis several FORTRAN IV programs for the computation of resistivity pseudo-sections for various electrode configurations have been coded, and a great deal of such pseudo-sections have already been calculated with an IBM-360 computer. Using these results, recommendations regarding both the methodology of the geoelectrical prospecting of spherical shaped conductors and the most suitable way of building resistivity pseudo-sections are developed.

Notes: An account is given of the use of the square array technique in investigating the surface effects of rotational anisotropy when the axes of anisotropy are inclined to the surface. It is shown that, as with other arrays, two anisotropy parameters 〈inlineGraphic alt="inline image" href="urn:x-wiley:00168025:GPR249:GPR_249_mu1" location="equation/GPR_249_mu1.gif"/〉 and n can be derived by varying the array orientation.On the basis of these considerations, the effects of such anisotropy on the values of the mean apparent resistivity and azimuthal inhomogeneity ratio normally obtained in square array measurements is reviewed.Particular attention is paid to the variation of resistivity with orientation and it is noted that, in areas of moderate anisotropy, this variation is lower for the square than for the Schlumberger array.In addition to this advantage, the azimuthal inhomogeneity ratio obtained from square array measurements may be used to indicate the severity of anisotropy in an area and two field examples of this use are given.Where anisotropy is severe, gross variations of apparent resistivity with orientation are obtained with either square or collinear arrays. In these circumstances, the use of crossed measurements is considered and the particular stability of the crossed square array demonstrated.

Notes: Electrical resistivity sounding was attempted with success in 1960 on the surface of the Nile water in Khor Kundi El-Bahari, the starting place for the construction of the offset channel of the High Dam. The method was applied to determine the depth to the upper surface of the granite below the alluvium and Nile water. The success of the method conducted at two stations in the Khor is attributed to the favourable geological conditions of the section which consists of nearly homogeneous layers besides the good earthing conditions of electrodes dipped in water. The high resistivity contrast between water and granite facilitates interpretation of sounding curves. Factors interfering with the results of interpretation are mentioned.

Notes: This paper presents a dot chart for calculating gravity effects from two-dimensional bodies with the addition of a supplementary set of curves which can be used to determine the “end corrections” to modify the calculated effects when the length of the body is not relatively long with respect to the horizontal dimensions of the cross-section. The use of the chart is demonstrated by different examples. The results of theoretical cases amenable to mathematical treatment and computer results both compare favorably to those computed using the present chart.A fundamental incentive of constructing this chart, in a final form ready to use, is to make it available to gravity interpreters for utilization. Future effort in chart construction is thereby avoided.

Notes: By applying dynamic corrections a seismic trace recorded at a distance x from the energy source should be varied in such a way as to obtain a trace which would be recorded at zero-distance, i.e. at the source itself. Only such a zero-offset-trace contains the correct sequence of reflection coefficients (reflectivity function), whilst all other traces contain a distorted reflectivity function. In the simplest case, the reflectivity function is compressed over a shorter time whereas in more complicated cases a partial inversion of the reflectivity function results. This happens when some of the reflection hyperbolae intersect one another.The reconstruction of the true zero-offset reflectivity function by the application of dynamic corrections can only be an approximative process. In the first case mentioned we must expect a decrease in accuracy of the corrected trace in comparison with a zero-offset-trace. In the second case, where intersections of the hyperbolae occur, accurate reconstruction is clearly impossible.The problems are discussed with the help of theoretical and practical examples.

Notes: Fourier transform techniques have been used to calculate the theoretical filter (amplitude) response function of Nth order vertical derivative continuation operation. The amplitude response functions of the vertical gradient and its continuation follow from the same. These response functions are subsequently used to calculate the weighting coefficients suitable for two dimensional equispaced data. A shortening operator has been incorporated to limit the extent of the operator. For comparative study, some of the developed coefficient sets and the one presented in this paper are analysed in the frequency domain and their merits and demerits are discussed.

Notes: Creation of antifiltrational cementation curtains needed to prevent increased seepage from water reservoirs is a rather labour-consuming and costly measure. High cost of such curtains necessitates careful checking of the quality of cementation as well as the strength and stability of the solidified cement which is being formed in the pores and fissures of injected rocks.The traditional methods of control are rather labour-consuming and do not allow observations during process of cementation. The advantage of electrometric observations of cementation curtains lies in the possibility of making measurements on the surface from the moment of pumping slurry into a borehole up to the termination of cement hardening.The laboratory investigations carried out by the authors demonstrate an increase in the specific electrical resistivity of a cement in the course of hardening as well as the existence of a functional dependence between the electrical and strength parameters which allows to use the resistivity method for checking the cement strength.Methods of electrometric observations of cementation curtains are dependent on the particular features of cementation and the curtain dimensions. The observations are usually conducted in a network of profiles parallel to the curtain axis. The cement slurry spreading in the space is studied on the maps of ρa and geoelectrical sections obtained at different distances from the feed line. Zones of the strongest absorption of cement slurry are indicated by resistivity minima. The electrometric observations should be compared with the data on cement expenditure in the boreholes.The cement strengthening is monitored by comparing the results of control observations consecutively conducted in 1-2 months following the cementation, with utilization of the ρa maps and graphs. If the specific resistivities of the skeleton of the enclosing rocks and the filler of cavities are known, one can approximately evaluate the changes in the cement strength in absolute units (kg/cm2).By way of example, the authors give the results of electrometric observations conducted to evaluate the quality of an antifiltrational curtain on one of the high-mountain water reservoirs in Armenia.

Notes: The paper presents the method and algorithm for computing the time-distance curve for head waves in the case of a dipping refractor and velocity increasing with depth in the overburden. The method is illustrated by an example.

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 comparison of a group of continuous total field stations in Ireland with the record of the total field from Valentia Observatory enables the errors which would be involved in using the Observatory as a diurnal correction base to be examined. For the most part, for a single correction, these errors lie between ± 2 and ± 6 gammas. However, they have three notable characteristics: (i) they are not closely dependent on the magnetic ‘noisiness’ of the day, (ii) they are only marginally reduced by the application of station-base time differences and (iii), they are strongly related to differences between the amplitude of the daily magnetic variation at the station and at the base. A permanent geographical basis for the latter differences enables a system for the estimation of the errors to be proposed.

Notes: The automatic picking of seismic sections becomes delicate with the presence of blind zones breaking up the continuity of horizons. This makes it difficult to establish correlations between reflections coming from above and below these blind zones.With the help of a certain number of characteristic parameters, a computer capable of storing a great quantity of data makes it possible to identify the horizons bounding a blind zone. Once this investigation has been made, the coherence between these horizons still has to be measured by making a factorial analysis of these different parameters. The statistical decision functions involved in this analysis are well adapted to computer logic. They enable the probability to be given with which the horizons located above and below blind zones correspond.A program has been worked out to provide the degree of coherence between such horizons.

Notes: An operative technique is described along with a method of representation of Induced Polarization values obtained over homogeneous rocks against the electrical power per unit volume.The results of similar experiments over two-layer ground, are shown according to the same operative technique and method of representation.With the method of representation suggested in this paper it is possible to distinguish discontinuities and to get information about the thickness of the upper medium.

Notes: Nomograms are presented for the purpose of rapid computation of the apparent resistivity functions from the field data for symmetrical and unsymmetrical linear electrode arrays.

Notes: Apparent resistivity measurements with the square array technique in the vicinity of a dipping interface have the advantage over collinear array methods that they are less dependent on orientation of the array.In order to exploit this, existing potential solutions for the dipping interface problem have been adapted for the computation of apparent resistivities over such a feature using a square array.Comprehensive interpretation techniques covering this problem are given and the limitations imposed by residual array orientation effects are discussed.

Notes: L'onde amortie de type Rayleigh à l'interface de deux milieux solides à fort contraste de densités et de vitesses est étudiée théoriquement et expérimentalement sur un modèle à deux dimensions plexiglas-laiton.

Notes: In the interpretation of anomalies obtained with moving source-receiver dipole electromagnetic surveys, use is frequently made of the so-called phasor or vector diagrams. Most such diagrams are based on model experiments or theoretical calculations on bodies of simple geometry. If the anomaly at some given coil-separation and frequency is known it is possible to predict the anomaly at some other separation and frequency. While the results of such predictions often agree admirably in the laboratory experiments, wide, systematic discrepancies are observed in full-scale field work. Some of the discrepancies can be explained by various phenomenological arguments and in this respect the effect of overburden conductivity appears to be more serious than is generally supposed. The effect of phase rotation due to the overburden is discussed in detail.The paper is mainly a cautionary note based on some full-scale data of multi-frequency, multi-separation surveys against the blind use of vector diagrams, but it also discusses the extent of the extra information and interpretation aid provided by such surveys.

Notes: The considerable increase of sensitivity of new magnetometers allows the elaboration of magnetometric maps with contour intervals of fractions of one gamma. On these maps, small anomalies appear which had never been visible before. They are caused by susceptibility contrasts within the sediments.The areal distribution of these small undulations of the magnetic field depends on tectonics, therefore their analysis can give useful information about the tectonic pattern of the sediments. This paper discusses the automatic transformation of these small anomalies into tectonic units. The problem is solved by a method called Digital Template Analysis which has already yielded very useful results in gravity interpretation.The application of the method described is restricted to surveys executed by high sensitivity magnetometers. Therefore it is supposed that in most oil exploration problems these magnetometers will replace instruments with lower sensitivity. The improved magnetometer surveys in combination with the interpretation method described represent a most efficient, fast and unexpensive reconnaissance method.

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: In this paper it is shown how one may obtain a generalized Ohm's law which relates the induced polarization electric field to the steady-state current density through the introduction of a fictitious resistivity defined as the product of the chargeability and the resistivity of a given medium.The potential generated by the induced polarization is calculated at any point in a layered earth by the same procedure as used for calculating the potential due to a point source of direct current.On the basis of the definition of the apparent chargeability ma, the expressions of ma for different stratigraphie situations are obtained, provided the IP measurements are carried out on surface with an appropriate AMNB array. These expressions may be used to plot master curves for IP vertical soundings.Finally some field experiments over sedimentary formations and the quantitative interpretation procedure are reported.

Notes: The interface phenomena for low periods, i.e. the initial oscillations, and the cut-off periods are two characteristic features in Magnetotelluric Sounding curves. A method is proposed to distinguish between transitional and homogeneous layered earth by means of these two features.

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: In the linear filter method of interpreting resistivity sounding data, as developed by Ghosh (1971), it appears that the filter function in the x-domain approaches an oscillating function for both large positive and large negative abscissa values. In the present note the reason for this oscillating behaviour is derived, and a possible practical application is indicated.

Notes: Amplitude spectra of input FM signals used in the vibratory source method of seismic exploration often show undesirable oscillations near the initial and terminal frequencies. These oscillations have an effect on the correlation background and distort the output signal. Considerable improvement in reducing the amplitude of these oscillations is obtained using a proper taper fuction. Attention is given to the relation between the tapering time and bandwidth of the spectrum.Analyses of the spectra of the received data from vibratory sources show considerable attenuation in comparison with the original field sweep. Since the matched filtering process will result in a series of waveforms which have the shape of the autocorrelation of the input signal, consideration is given to the autocorrelation function and its zero-lag coefficient of the FM signal in the presence of attenuation. A method has been developed which compensates for the attenuation and recovers the distortion of waveforms when the received data is correlated.The design of a waveform shaping filter for vibratory source data is given to reduce the influence of phase distortion on the received waveforms as well as to increase S/N ratio resolution. Parameters used for this filter are based on the properties of the FM signal and its autocorrelation function.Several examples from field data are presented to illustrate the methods. The results indicate that the use of the above techniques yields sections with good frequency resolution and improved S/N ratio.

Notes: Reddy, I. K., D. Rankin, 1971, Magnetotelluric Effect of Dipping Anisotropies, Geophysical Prospecting 19, 84–97.A solution is obtained for the magnetotelluric effect in the case of multi-layered earth, each layer containing dipping anisotropy, with the strike of anisotropy oriented at an arbitrary angle to the measuring directions. A technique to compute tensor impedances and tensor apparent resistivities is presented and the importance of anisotropies in magnetotelluric interpretation is discussed.

Notes: Results of rock magnetic investigations and magnetic field measurements in the Logar Valley, Afghanistan, are presented. Rock magnetic investigations on samples of the ore and the country rock have demonstrated that the chromite is strongly magnetic, whereas the country rock has proved predominantly non-magnetic, partly weakly magnetic. The isanomalic maps show strong anomalies of some 1000 γ above the known chromite occurrences. Anomalies of the country rock amounting to some 100 γ have been observed only above basic dikes. The measured anomalies have been interpreted quantitatively by 2- and 3-dimensional models. This interpretation is demonstrated and the question of chromite detection discussed. Model graphs are used to investigate in detail whether the extension in depth of ore bodies can be estimated.

Notes: This work deals with a theoretical investigation of the magnetotelluric sounding where the horizontal layers of a geological section do not have a sharp but a transitional boundary. The ratio of the horizontal electric to the horizontal magnetic components gives a measure of “Cagniard impedance”, which together with the phase relationship between them, enables one to determine the subsurface geometry and the true resistivities.Utilising the principle of similitude a set of Resistivity Master Curves and the corresponding phase relationships are presented here for the case where the lower half-space is infinitely resistive. The relation between the relative transition thickness and the cut-off period is illustrated.

Notes: A point source or a dipole source of electric current, placed on a randomly layered semi-infinite medium, produces an inhomogeneous random potential field on the surface. The variance of the random potential, normalized with reference to the normal field (that is, a field due to a point source or a dipole source on a homogeneous medium), falls off inversely as the distance from the source. The conductivity of the layers is assumed to vary randomly about a mean value (unity) such that the variations can be represented by a zero mean homogeneous random function. Further the variations are assumed to be small compared to the mean so that the first order perturbation is adequate. The analysis shows that the dipole field is more sensitive than the single pole field to the conductivity variations.

Notes: Book reviewed in this article:F. Link, Eclipse Phenomena in AstronomyMarine Geophysical Researches–an International Journal for the Study of the Earth Beneath the SeaM. K. Polshkov (editor): Exploration Geophysics, Vol. 48

Notes: The relationship between porosity and formation factor in unconsolidated homogeneous and anisotropic sediments without granule-liquid interaction is investigated by introducing a parametric model that simulates a variable cellular structure.In this hypothesis, porosity φ and F-factor are calculated for some fixed values of the parameter, solving numerically two integral expressions.From these calculations the form of the function φ=f(F), corresponding to the proposed model, has been deduced. This relation is in very good agreement with Archie's empirical law for unconsolidated sands which requires that F=φ--1,3. Therefore it seems that the validity of Archie's law is theoretically confirmed for the unconsolidated sediments considered in this paper.

Notes: In a previous publication (Koefoed 1968) a function called the “raised kernel function” has been introduced as an intermediate function in the interpretation of resistivity sounding data, and methods have been described both for the determination of the raised kernel function from the apparent resistivity function, and for the determination of the layer distribution from the raised kernel function.In the present paper a procedure is described by which the second step in this interpretation method–i.e. the determination of the layer distribution from the raised kernel function–is considerably accelerated. This gain in interpretation speed is attained by the use of a standard graph for a function which defines the reduction of the raised kernel function to a lower boundary plane.

Notes: Despite the use of CDP and digital methods the Zechstein base is still the deepest horizon in the vast salt-dome basin of Central Europe for which continuous information can be obtained by reflection seismics. Thus in North-western Germany, in addition to reflection seismics, the refraction seismic method has been increasingly used for a reliable survey of deeper horizons.The first part of the paper deals with the investigation of the various possibilities and limitations of refraction seismics with regard to the investigation of Pre-Zechstein layers in a basin with a tectonically very complicated overburden. The recording techniques specially developed for continuous profiling of the desired refraction seismic arrivals and the data processing methods are described.The main problems of interpretation are then discussed, in particular with regard to depth representation. The advantages and disadvantages of the various methods, e.g. Gardner's, Hales' and Wyrobek's, and of the wave-front method, are compared. On account of the tectonically complicated overburden Thornburgh's wave-front method proved to be the most useful.In a further section the various possibilities for velocity determinations are mentioned, e.g. Wyrobek's determination of the overburden velocity, for which the wave-front method automatically furnishes the necessary corrections to a deep datum.Finally, some examples are given for the results obtained, including some incidental information on the deeper crust.

Notes: Two alternative types of diagrams are shown which allow the direct conversion of readings taken by certain types of proton magnetometers into magnetic field strength. The accuracy of these diagrams is discussed and found to satisfy the requirements.

Notes: Boundary-value problems in steady-state current flow were solved numerically for one and two layers over a half-space. Solutions were obtained for layers of various resistivities where one of the current sources was placed below the surface and the second kept at some finite distance from the drill hole. When a fixed surface dipole receiving pair was used, it was found that as the buried source approached a conductive region, quite good determinations of the depth to the conductor could be made, hence reducing the possibility of extended drilling in “dry” holes resulting from poor surface data and/or interpretation. Numerous models were generated to find the optimum positioning of the two current electrodes for different field situations of this type. It was also found that by placing a current source in the conductive region, better resolution of the lateral extent of a possible ore zone could be obtained, due both to the more rapid convergence of the apparent resistivity to the resistivity of the conductor, and the fact that a smaller separation in the receiving dipole could be used. Numerous analog models were constructed to verify the digital results. Surface and down-hole resistivity field data are compared to show the strength of this technique in delineating structure.

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: For almost two years, satellite navigation has been used in reconnaissance exploration. However, only in the last six months has it been demonstrated that an “integrated” system provides navigational accuracy for all geophysical prospecting. This paper describes the accuracy of the integrated system and illustrates its merits.The primary objective of the integrated system is to provide continuous, accurate, geodetic position information. This is accomplished by integrating instantaneous position, velocity and heading from outputs of the Doppler sonar, gyrocompass, velocimeter, vertical references with periodic updates obtained from the Navy Navigation Satellite System. Each of the subsystems, their operations and functions will be discussed.Satellite navigation offers many advantages for marine surveys. Features for point-to-point automatic steering, onboard plotting of shotpoint data, firing of seismic energy source as a function of exact distance and real-time data logging onto digital tape have been implemented. With the onboard computer all navigation, gravity and magnetic information is recorded on tape and some preprocessing and filtering of gravity and magnetic data may be accomplished.

Notes: As an extension of the eddy current pattern computed by Koefoed and Kegge (1968) for a thin vertical infinitely-conducting half-plate in presence of oscillating magnetic dipoles, this paper computes the contribution to the (electro-) magnetic anomaly at the receiver by each element of the vein separately. Twelve contour diagrams for such elemental contributions are presented as samples. Two points of general interest stand out: (1) The contributions from different portions of the vein are not all of one sign; the contribution from one part may cancel that from another; and (2) The portion of the vein nearest to the transmitter-receiver system does not necessarily make the largest contribution to the total measured signal.

Notes: Koefoed has given practical procedures of obtaining the layer parameters directly from the apparent resistivity sounding measurements by using the raised kernel function H(λ) as the intermediate step. However, it is felt that the first step of his method—namely the derivation of the H curve from the apparent resistivity curve—is relatively lengthy.In this paper a method is proposed of determining the resistivity transform T(λ), a function directly related to H(λ), from the resistivity field curve. It is shown that the apparent resistivity and the resistivity transform functions are linearily related to each other such that the principle of linear electric filter theory could be applied to obtain the latter from the former. Separate sets of filter coefficients have been worked out for the Schlumberger and the Wenner form of field procedures. The practical process of deriving the T curve simply amounts to running a weighted average of the sampled apparent resistivity field data with the pre-determined coefficients. The whole process could be graphically performed within an quarter of an hour with an accuracy of about 2%.

Notes: Fontanel, A., G. Grau, 1971, Corrélation optique en lumière cohérente, Geophysical Prospecting 19, 98–117.This paper describes a general bidimensional two-step method of correlation (or convolution) making use of the theory of holography.In the first step the light diffracted by one of the two plane transparent objects to be correlated interferes with the light diffracted by the other one. The hologram thus generated is photographed in the focal image plane of a convergent lens. Owing to the quadratic detection property of the photographic emulsion, the square of the modulus of the product of the spectra of the two objects considered is recorded on the photographic plate.In the second step the convolution product of the two objects appears when the hologram is illuminated with a beam of coherent light.In its geophysical application this optical method of convolution makes it easy for us to obtain the autocorrelogram of a seismic cross-section. This method also makes it possible to correlate each of the seismic traces by special precalculated optically-recorded filters.

Notes: In order to locate relatively optimum sites for drilling exploratory holes for fresh water, an electrical resistivity survey was conducted along the new Mahukona-Kawaihae Road on the west flank of the Kohala Mountain. Two resistivity soundings made at the same stations, using the Schlumberger electrode configuration, determined an a spacing of 275 feet for horizontal profiling with the Wenner array.The correlation coefficient of the elevation to profile data was 0.41. A procedure for removing elevation effect from observed apparent resistivity was developed. Based on the reduced resistivity profile, four relatively optimum sites for additional exploration, such as by drilling, are specified. There is no specific interpretation of the data that can definitely indicate the occurrence of large underground reservoirs of fresh water anywhere along the profile. This is because the interpretation of horizontal profiling data is essentially relative and not absolute.

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: 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.