ALBERT

Notes: The decay rate of gamma radiation emitted by a Jamaican mineral spring was measured using portable rate meters. The results of these experiments, supported by auxiliary tests, suggested that the main radioelement causing the radioactivity was radon 222. Fluctuations in the intensity of the radiation were studied in situ. An inverse relation between the intensity and the discharge rate of water was established and the effect of rainfall and of earthquakes was investigated. Some suggestions are made concerning the possible source of radon.

Notes: The iron ores of the Siegerland-district are found in lodes occurring in schists of Lower Devonian age. In the course of the geophysical exploration for these ores, an attempt was also made to clarify the structure and the tectonics of the substratum of the sedimentary rock formations by seismic reflection measurements from the surface. Reflections were recorded in great numbers from layers of Silurian and Devonian age. The form of the folding of the strata derived therefrom corresponds well with that deduced from geological investigations. Beyond that, correlatable reflections were recorded from horizons down to a depth of nearly 25 000 m. It turned out that the iron ore lodes known from the mine workings occur almost vertically above those places where greater dislocations appear in the deepest substratum, and which geologically could be interpreted as fracture zones. The results so far obtained seem to be indicative of the fact that the tectonics of the deepest substratum and the occurrence of ore deposits are related to each other.

Notes: Precision calibration tests carried out with a Worden gravimeter in environment conditions as varied as possible have led to the following conclusions. The secular variation curve of the calibration shows that the secular relative variation has been very appreciable in the first year of life of the instrument, precisely of 1.3 × 10−3 in 13 months, while it has been practically zero in the second year. This must be ascribed to the fact that at the beginning of the operations the gravity-meter had just arrived from the factory with its measuring body renewed.On the other side the effect of 24°C of temperature difference between two series of determinations reveals itself in a variation of 0.0022 of the value of the calibration, so that it can be established that the variation of the calibration is I‰ for each 10°C of temperature variation.

Notes: Due weight must be given to three factors (1) its purpose, (2) the limitations imposed by nature, industry and environment, (3) the effect of errors in auxiliary measurements. Together the last two factors give an estimate of the accuracy which can be achieved. If this is sufficient for the instrument to fulfil its purpose design and construction can proceed. If it is not, a detailed survey of the last two factors is necessary in order to estimate the research effort that will be required when directed into the most effective channels. If the project is considered worth the effort it can proceed. These factors are discussed in relation to a borehole gravimeter. It is shown that the purpose will be served only if the accuracy is comparable with the best surface gravimeters. Borehole versions of some surface instruments are considered and it is concluded that none is suitable without considerable modifications. A successful borehole gravimeter is likely to be a completely new instrument.

Notes: Recently, quite good determinations of interfaces have been made by means of seismic well surveys. These were carried out for various oil companies in Northwest Germany, especially on salt-domes, and in Southern Germany, and in the area of the Upper Rhine Valley. It was the purpose to determine the configuration and position of salt-flanks and important planes of stratification in the neighbourhood of deep wells, and thus to reduce the risk of expensive wells.For the delineation of the boundary surfaces the method described by Gardner in “Geophysics 1949” was applied.The problems arising and the results obtained are discussed in connection with some interesting examples. From them we see, above all, that a knowledge as precise as possible of the seismic velocities of all media involved in the measurement is very important. A good idea of the general stratification in the area of deep wells seismically surveyed will make possible a rational and adequate planning of the survey program and will facilitate the interpretation.

Notes: A method is described in which the major part of gravimetric terrain corrections may be estimated by digital computing methods.

Notes: The electric and magnetic field of a direct-current element, embedded in a space consisting of two halfspaces differing in conductivity and permeability, is given in a form suitable for integration along a cable. From these formulae is obtained the field when one end of a D.C. cable is grounded in a highly conducting, pencilformed ore body, considered as a line electrode with uniform current leakage. Numerical examples are given for a horizontal line electrode. The formulae should be useful as a first approximation to the A.C. case. The validity of this is shortly discussed.

Notes: An analogy is established between the propagation of an electromagnetic field in a horizontally stratified conductive medium and that of currents in a linear electric network. This analogy will allow us to know in which case measurements executed at the surface of the ground can provide information about the properties of deeper layers. The situation is the same as when one tries, by means of impedance measurements at the input terminals, to know the properties of electric lines or lumped networks.A symmetrical linear network establishes between:Voltages V1 and V2 (respectively at input and output terminals)Currents I1 and I2 (respectively at input and output terminals), the relationship 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR77:GPR_77_mu1"/〉 is called the “phase constant” and Z the characteristic impedance The table 〈displayedItem type="mathematics" xml:id="mu2" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR77:GPR_77_mu2"/〉 is called “characteristic matrix”If one then takes the horizontal components of an electromagnetic field, one can compare the voltage V with the horizontal electric field E (in volts m-1) and the current I with the horizontal magnetic field H (in Amp m−1)For plane waves in vacuum, one gets (Schelkunoff) Z=C (velocity of light)A layer whose thickness is D has a phase constant⌈= 2 πD/λ (λ= wavelength)For plane waves in a conductive, non magnetic medium whose conductivity is δ, one gets 〈displayedItem type="mathematics" xml:id="mu3" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR77:GPR_77_mu3"/〉 For the system of waves created by a point-source one expresses the solution, since it is classical, as a sum or integral of different modes. For each of these modes, one can still write a bilinear relationship similar to (1), and calculate Z and ⌈.A generalization of this result is given.Boundary conditions that exist at the surfaces of separation are met by writing the continuity of E and H. This condition exactly corresponds to the fact that there one V and one I at the junctions of various sections of lines, or networks.The characteristic matrix of a cascade of networks-or here that of a horizontally stratified ground– is the product of the matrixes of each network. If, in addition, one knows the end impedance–here the conductivity λn of the last layer, supposed to be infinite–one can compute the input impedance Re of the whole system. In electromagnetic prospecting, it is Re that conditions the observable field.Inversely, if measurements were infinitely accurate, the. knowledge of the surface field would give all the thicknesses D and conductivities δ of intermediate layers, in the same way that impedance measurements at the input terminals of a cable would allow to locate any failure. The imperfection of measurements causes the elements located too far away (from the point of view of wave attenuation) to escape detection.

Notes: The iron ores of the Siegerland district are found in lodes occurring in schists of Lower Devonian age. These lodes, normally dipping almost perpendicularly, could be traced only by seismic reflection measurements underground, up to distances of approximately 500 m. The geophones were attached to the walls of the galleries. The frequencies of the recorded longitudinal and transverse waves ranged from 200 to 500 c.p.s. By this method a new siderite lode was discovered.

Notes: Book Reviewed in this article:Lehrbuch der angewandten Geophysik, Teil II, H. Haalck.

Notes: A series of repeat observations during a period of 5 years reveal a variation with time of the Worden gravimeter No. 142 small dial spring system. A possible change in the gravity difference concerned is ruled out. It is shown that the small dial scale factor has diminished by about 0.25 % within the last two years against about 0.5 % four to five years ago. The ratio of L.D. to S.D. has been analysed and the results obtained show confirmation of the change in the small dial system and prove a consistency in the large dial system.

Notes: A study is made of the possibility of calculating electric potentials, and therefore of interpreting apparent resistivity measurements, when the ground presents structural conditions more complicated than plane, parallel stratification.For this work a schematic type of structure has been chosen, in which the discontinuity planes for electric resistivity are both parallel and perpendicular to the level of the ground.The problem has been examinated in its general aspect, and then some criteria for the numerical calculation have been indicated.Some calculated examples are presented, relevant to vertical electric soundings accomplished by conventional technique, for particular types of structure.

Notes: The elastic impulse-from an explosion is propagated through the earth as an expanding shell bounded by the wavefront. This wavefront and its motion are a physical reality while rays or trajectories are much less sharply defined and cannot actually be observed because the wavelengths involved in seismic processes are too long. This means that the visualization and the interpretation of seismic processes can be carried out in a more satisfactory, simple and comprehensible way with wavefronts than with rays.H. R. Thornburgh (1930) introduced the very lucid and simple method of interpreting seismic refraction sections, using Huygen's principle to construct wavefronts from two symmetrical shotpoints by working back from their observed arrival times at the surface. The depths are found first with only a knowledge of the velocities down to the refractor and after that the velocities in the refractor can be determined.The pattern of the two wavefronts at equal time intervals, obtained when carrying out Thornburgh's construction, leads to the very simple, approximative “Plus-Minus” method. The additions of the travel times from two symmetrical shotpoints to-each geophone give the relative depths and their subtractions give the velocities of the refractor. The method extrapolates exact quantities from the refractor boundary up to the surface by the “Plus”- and “Minus” lines. This extrapolation introduces errors that can, more or less, be corrected for. A number of hypothetical cases are presented to give an insight into the applicability and reliability of the “Plus-Minus” method. Its main applications are for fairly shallow refraction investigations and for determining weathering corrections for refraction and reflection work.

Notes: Major savings for operators of seismic parties have been achieved by the use of prilled ammonium nitrate as a substitute for gelatin dynamite in areas where shot holes are dry. Pound for pound, the prills appear to have the same energy yield as 60% gelatin dynamite, and some improvement of records has been noted where prills are used. Safety problems are less with ammonium nitrate than with dynamite, and the development of efficient field handling techniques prevents the loss of production.

Notes: Some mathematical inequalities are proved and their relevance to the interpretation of local magnetic and gravity anomalies is discussed. They can be applied to the readings of either a vertical magnetometer or a total field magnetometer or a gravimeter and yield a maximum possible value for the depth below the earth's surface of the top surface of the body producing the anomaly.

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: 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 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: 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: 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: 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: A new logging method, which makes use of specific chemical reactions to locate petroleum or other minerals has been developed. The method has been named “Differential Electric Log” (CED).In this paper the application to the CED method of redox (reduction/oxidation) reactions is discussed. A series of organic oxidants was found, capable of undergoing reaction with crude oil, sulphur, mineral sulphides, lignite. A small amount of an oxidant of this type is added to the drilling fluid and pumped into the borehole where reaction takes place in correspondence with layers containing oxidizable minerals. Two SP logs, recorded before and after the oxidation, are compared and the presence of such minerals is thus detected.A theoretical hypothesis explaining the mechanism of the potential change due to the chemical reaction is proposed both in the case of electronically conducting and non conducting minerals. The influence of redox potential on SP is discussed.The results of laboratory experiments on several different oxidizable ores and those of field tests performed on pyrite, lignite, and oil wells are reported on and discussed on the basis of the theoretical hypothesis proposed.

Notes: It has been customary in geothermal studies to assume the surface to be an isothermal plane, though difficulties existed to explain the magnitude of thermal anomalies observed in the field under this assumption. Detailed investigations of temperatures at depths between 5 cm and 230 cm show that—after removal of the strong diurnal variations—sizeable anomalies persist right to the surface. Thus, the effective heat transfer (coefficient) at the surface might be lower than commonly assumed.

Notes: The application of automatic methods to the processing of potential field survey results has led to the need for the development of special procedures for the interpolation and extrapolation of such data. A method is proposed which utilizes the mathematical properties of potential field data to achieve a minimum distortion solution to the interpolation/extrapolation problem. The proposed method is suitable for use with any data point distribution. Digital computer programs have been prepared using the method; results obtained through the use of the programs are presented.

Notes: La sismique réflexion a été mise en œuvre dans des galeries de mines avec un appareillage nouveau: dispositifs appropriés, géophones spéciaux, chaîne d'enregistrement haute fréquence (30–2000 hertz).Des réflexions à des fréquences de l'ordre de 600 à 1200 hertz ont été obtenues dans les cas favorables sur des couches de charbon de l'ordre du mètre situées jusqu'à une soixantaine de mètres sous la galerie.Une bonne compacité des terrains situés autour de la galerie est une condition nécessaire à l'obtention de réflexions. Les accidents affectant les couches peuvent alors être visibles.

Notes: At the EAEG meeting in Venice (May 1969) Linsser presented a new method for the interpretation of seismic measurements (“Transformation of Seismic Data into Geological Models by Digital Template Analysis”). First results were presented during the S.E.G. convention in Calgary (September 1969). Meanwhile some experience concerning the possibility of the application of this method is available.Starting from the fact that the computer is able to store several physical parameters (amplitude, wave-length, direction of the seismic event, coincidence with a template and the beginning and the end of each reflection), the importance of these data for the investigation of special geophysical questions will be discussed.This method has been tested with several examples on the following problems:〈list xml:id="l1" style="custom"〉1Proving and exact localisation of faults.2Investigation of velocities of interesting layers.3Additional information for the geological interpretation of seismic sections.4Picking of weak reflections in the “Pre-Zechsteinian” in Northern Germany.Finally the possibilities of further applications and developments are discussed.

Notes: The deposits of the central sector of the Labrador Trough are magnetite-rich iron ores subjected to enrichment by the process of leaching. In spite of the fact that some ore types are porous and low in density, most of the ore zones have undergone a net increase in density brought about by enrichment. In the course of their formation, the magnetic characteristics of the rocks have changed and a great deal of the magnetite was altered to relatively non-magnetic iron oxides and hydrous iron oxides. Consequently, induced as well as remanent magnetization decreased, but the ratio of the latter with respect to the former increased substantially. All drift-covered areas underlain with iron-formation are potential ore producing areas. From measurements of the first two physical properties and determination of the thickness of overburden by means of a combined gravity-magnetic-seismic or resistivity survey, it is possible to detect and distinguish the iron formations and potential ore zones from the country rocks.In spite of the fact that the iron formations are a complex assemblage of rock types, each having different physical and chemical properties, a qualitative and semi-quantitative correlation between the results of the surveys and the geology as well as the structure of the area could be established. Consequently, in order to increase the chances of success, first a mathematical correlation of the amplitude of the gravity anomalies with the specific gravity, the iron content, the silica content, the porosity factors and the dimensions of the underlying orebodies, and secondly, a quantitative correlation of the ground magnetic intensity relative to the reference lithologie unit with the percentage of Fe3 O4 recovery and the volume magnetic susceptibility were done for many deposits.A few discoveries were made with this method. Finally, a fully quantitative interpretation of the geophysical data using a multimodeling analysis led to the discovery of additional direct-shipping iron ore deposits in the Schefferville mining district of Canada.

Notes: A gravity anomaly profile, considered to be associated with a two-dimensional mass distribution of constant density contrast, may be interpreted with the help of a digital computer. Using the infinite slab formula and anomaly values at selected points of the profile, an initial model of the anomalous mass is built. The gravity effect of the model is computed with a simplified version of the formula derived by Talwani, Worzel and Landisman (1959) for line-integration. After the effect is computed at a point, the model is adjusted depending upon the residual anomaly. The effect of the adjusted model is computed at the following point. Within one cycle of computation the model is adjusted as many times as the number of the selected points. Five such cycles are sufficient to minimize residuals in most cases. A final cycle is computed without adjustment.Local anomaly profiles have been interpreted to obtain the shape of a sedimentary basin and of a faulted block. A regional anomaly profile has been interpreted to obtain crustal structure.

Notes: Optimum filters can be computed using orthogonal coordinates obtained from the eigenvalues and eigenvectors of the autocorrelation matrix. The method is used to obtain unit distance prediction error filters. The output of a unit distance prediction error filter when applied to the input wavelet is an impulse at zero time. The effect on the output of added white noise is easily obtained using the approach through the orthogonal coordinates. The added white noise results in output wavelets which are no longer impulses at zero time. The decrease in time resolution gives a filter that does not increase undesirable high frequency noise as much as filters computed without white noise.Orthogonal coordinates with little signal energy can be omitted from the filter computation resulting in output wavelets resembling those computed using added white noise.

Notes: The increasing use of velocity analysis programs in seismic processing in addition to direct application to normal move out corrections often makes it possible to study the variation of the average velocity versus time and distance. Usually, it is even feasible to compute interval velocities with a good accuracy.We intend to use these velocities to convert the usual time domain displays to the depth domain.An exact conversion requires the knowledge of all interval velocities and all the velocity interfaces.However, when the dips are small, the conversion can be done without considering the dip of all these interfaces, and in some cases migration can even be completely neglected.Three different programs will be described and their use discussed in view of the type of problems to which they are applied.Practical examples of the various methods will be presented.

Notes: In magnetic routine interpretation the comparison of two-dimensional model curves with measured magnetic anomalies is widely used for an approximate evaluation of the position and depth of magnetic models.Before starting an interpretation of a survey by means of two-dimensional models, it is very useful to have an idea of the shape of anomalies caused by extended but finite bodies, taking into account various strike directions: Three sets of anomalies of thin plates (horizontal length 19, downward length 9, width 1) dipping 30°, 60°, and 90° resp. for various strike directions and an inclination of 20° were computed. Some of these anomalies, e.g. those with nearly N-S strike direction look rather complicated, and at the first glance one would not expect that they are caused by such simple bodies.Several profiles crossing the computed anomalies perpendicularly were interpreted two-dimensionally. For less extended anomalies the depths determined for the top of the plates are 10-20% too small, the magnetization amounts to 50–75 % of the value of the finite bodies. The interpretation of the profiles covering more extended anomalies gave very accurately the same values for the position, depth and magnetization for the two-dimensional body as for the original three-dimensional model.Anomalies of vertical prisms with varying extensions in the y-direction were computed. Their differences in amplitude and in the distance maximum-minimum show that interpretation of short anomalies by two-dimensional methods yields depth errors of up to 20 percent.To see the possibilities of the separation of superimposed anomalies dike anomalies were added to the anomaly of a broad body in great depth and several attempts were made to interpret parts of the composite anomalies. The interpreted bodies lie too deep. In complicated cases the depth values can have large errors, but experienced interpreters should be able to keep the errors in the range of one third of the depth values.

Notes: Carborne gamma radiation surveys over petroleum reservoirs and faults in the glaciated Michigan Basin suggest that this mobile technique may be useful in reconnaissance subsurface exploration, especially in fault detection. This conclusion assumes favorable surface conditions, as well as proper instrumentation, field procedures, and interpretive techniques. Glaciated regions are relatively undesirable terrains for gamma radiation surveys. Thick deposits of glacial drift appear to repress the detection of subsurface features. Furthermore, extremely heterogeneous soil conditions, which are characteristic of many glaciated regions, result in excessive radiation interference. The operational conditions which produced optimum results consisted of continuous profiling on unconsolidated roads, employing two simultaneously operated scintillation counters. Optimum detection was obtained during relatively cool nighttime traverses.

Notes: Cancelling of multiple reflections by CDP stacking is generally incomplete. When the order of coverage is low, an improvement may be obtained by the use of special filters (e.g. Schneider et al: Geophysics 1965; D'Hoeraene: Geophysics 1966). But when the order of coverage is high, the efficiency of these filters is less obvious. On the other hand, the higher the order of coverage, the higher the efficiency in the solution presented.Schematically, our method includes three steps:Firstly: Searching for the multiple reflections.For this purpose Move Out corrections corresponding to the multiples are applied to each individual record, then CDP stacking is carried out.Secondly: Cleaning up of the individual records.“Decorrections” are firstly applied, then multiples are subtracted. For this, subtraction is weighed versus the energy of the multiples, that is to say versus the correlation between the original record and the pure multiple reflections.Thirdly: Normal processing with the cleaned records which have been obtained.The different steps of this method are illustrated with the help of theoretical examples. Its efficiency improvement in regard to normal CDP stacking is then demonstrated by means of true examples.

Notes: One of the problems in signal processing is estimating the impulse response function of an unknown system. The well-known Wiener filter theory has been a powerful method in attacking this problem. In comparison, the use of stochastic approximation method as an adaptive signal processor is relatively new. This adaptive scheme can often be described by a recursive equation in which the estimated impulse response parameters are adjusted according to the gradient of a predetermined error function.This paper illustrates by means of simple examples the application of stochastic approximation method as a single-channel adaptive processor. Under some conditions the expected value of its weight sequence converges to the corresponding Wiener optimum filter when the least-mean-square error criterion is used.

Notes: In well velocity surveys made to calibrate Sonic (CV) Logs the calibration survey uses frequencies around 50 Hz whereas the Sonic Logging tool uses frequencies around 20 kHz. There thus exists the possibility of making a direct measure of velocity dispersion. In any one survey the disturbing factors, both instrumental and operational, will often mask any dispersive effect that might exist. Consequently this paper reports on a statistical analysis of the velocity differences resulting from calibration surveys and Sonic logs. Only Borehole Compensated Sonic Logs were used. Four areas were investigated: the North Sea, Abu Dhabi, Libya and Alaska. After rejecting logs and calibration records which were obviously in error there remained 424000 feet (about 130 km) of usable log distributed throughout 66 wells. The four areas were analysed separately and in no case was the estimated dispersion significantly different from zero. However, the mean values did correlate with lithology from (− 0.17 ± 0.18)% for the essentially carbonate section in Abu Dhabi to (+ 0.45 ± 0.25)% for the sand-shale section in Alaska, a positive sign meaning that the higher frequencies travelled faster. Except for Alaska the calibration surveys were made with a wall-clamp geophone, and for these areas amplitude measurements were made. After suitable corrections estimates of the absorption parameter Q were obtained. These varied from 20 to 200 with mean values of 63 for Libya, 70 for Abu Dhabi and 88 for the North Sea (excluding the Tertiary). If, as is usually assumed, the absorption mechanism is linear and is described by a Q which is independent of frequency, then these values would necessarily imply dispersion of several percent. As instanced above no such dispersion was observed. It is possible that the expected dispersion was compensated for by invasion of the mud filtrate into the borehole walls, but it is more likely that the absorption mechanism was substantially non-linear.

Notes: In recent times, velocity surveys at marine well locations have been performed using non-explosive energy sources such as air-guns and gas guns. In addition, surveys in land wells have been successfully carried out using a modified version of the air-gun. This paper illustrates some of the characteristics of these devices and compares the data obtained from typical surveys with conventional dynamite surveys.Since data obtained from well velocity surveys using non-explosive sources are now commonly recorded on tape, they lend themself to further digital processing and interpretation techniques that were not previously so conveniently available. Some examples of these processes, e.g. the examination of attenuation, frequency and energy content of the recorded well geophone signals, are given in the paper. Examples of some other digital processes, using calibrated Acoustic logs, whether recorded digitally in the field or subsequently converted from analogue recordings, are also given in the paper. These include the construction of an Acoustic log in the vertical axis from logs obtained in deviated wells.

Notes: Anisotropy measurements were carried out in two wells 300 km apart in the Northern Sahara, in order to improve the interpretation of seismic refraction surveys.These measurements were based on; the shortening of experimental oblique travel-times with respect to theoretical, travel-times computed by disregarding anisotropy. A perfect knowledge of the velocity distribution is required in order to eliminate all influence of refraction; therefore a continuous velocity log is indispensable.The results in the two wells are in agreement, and show that anisotropy is essentially a function of lithology. The following values were obtained: 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR202:GPR_202_mu1"/〉 Consequences pertaining to seismic refraction are as follows:— Depths computed without anisotropy are too small by 8 % to 9 %, i.e. about 300 meters.— The error on offsets reaches 70 %.— Depth computations carried out by assigning anisotropy factors at the sight of lithology gave very satisfactory results.— High velocity, highly anisotropic formations such as anhydrite play a very important part in the propagation of refracted waves and in interpretation.Consequences pertaining to seismic reflection are as follows:— Velocity profiles yield velocities closer to horizontal velocities than to vertical velocities.— Depth and migration computations are significantly influenced by high velocity, highly anisotropic formations such as anhydrite.

Notes: Book Reviewed in this article:Handbuch der Physik. Herausgegeben von S. Flügge.Der geologische Bau des Untergrundes von Schleswig-Holstein und seine Erdöllager-stätten.

Notes: Conventional or continuous velocity logging generally fail to solve the problem of velocities in the whole area of a seismic survey. Surface measurements often bring a large amount of additional information: effect of shallow layers, change of facies, correlations. The authors present a theoretical view on the physical meaning of interval velocities. After a short synthesis of the diverse formulae formerly proposed (Faust, West), the practical manner of using these formulae and the accurate interpretation obtained with the help of geological and geophysical data are shown. Several characteristical examples are finally explained and commented on.

Notes: A uniform field of the normal geomagnetic vertical intensity and its normal dependence on the first and second powers of latitude and longitude are derived for Europe and represented by sketches. The epochs of 1938.5, 1941.5, 1944.5, 1947.5, 1950.5, 1953.5, and 1956.5 have been chosen.It is suggested that anomalies of the vertical intensity should be given according to this field in order to obtain, in course of time, a coherent image of the magnetic effects of the European continent.

Notes: Solutions for the propagation of elastic waves at the surface of a cylindrical hole of infinite length are derived from the wave equation for a perfectly elastic and isotropic medium. It is found that the phase and group velocities depend on the ratio between the wave length and the circumference of the cylindrical hole. These surface waves can be classified into different orders. They differ in the calculated dispersion curves, in the range of possible wave lengths (cut-off-frequencies), and in the amplitude proportion of the components of the displacement vector. For very short wave lengths these waves converge to normal Rayleigh waves.These results are used to explain some of the multiple onsets and disturbances on seismograms, obtained in practical seismic investigations in the mines of Siegerland.The conformity of theoretical and practical results is limited, because the idealised suppositions on which the computation is based, such as perfect elasticity, homogeneous and isotropic medium, and circular cross section of the mine gallery are met only approximately in practice.

Notes: Two distinct filters are developed in the frequency domain which represent an attempt to increase the resolution of fine structure contained in the signal whilst keeping the expected filtered noise energy within reasonable bounds. A parameter termed the White Noise Amplification is defined and used together with a measure of the deconvolved pulse width in order to provide a more complete characterisation of the filters. Each of the two main types of frequency domain filters discussed varies in properties with respect to a single adjustable parameter. This may be contrasted with a time domain Wiener filter which in general has three variables: length, delay and an adjustable noise parameter or weight. The direct frequency domain analogue of the Wiener filter is termed a gamma-Fourier filter, and is shown to have properties which span the range from those of a spiking filter with zero least square error at one extreme, to those of a matched filter at the other extreme of its variable parameter's range. The second type of filter considered—termed the modulated Gaussian filter—is similarly shown to be a perfect spiking filter at one extreme of its parameter range, but adopts the properties of an output energy filter at the other extreme.

Notes: A review of the most significant mathematical properties of digital operators and an introduction to their important applications to seismic digital filtering is given.Basic definitions in the time-series field and the principles of digital filtering are introduced starting from the Z-transform domain.Predictive decomposition for stationary stochastic processes and inverse operators are also discussed.Applications of digital filtering to seismic signal concern the predictive deconvolution, characteristics of dispersive and recursive operators, matched filters, and multichannel operators.A brief discussion on frequency, wave number, and velocity filtering phylosophy is given at the end of the paper.

Notes: The general use of continuous CDP seismic lines means that the neighbourhood of each depth point can be considered according to two sets of co-ordinates:— the co-ordinates of the abscissa on the seismic lines and the reflection time, which allow investigation of the local dip of coherent events;— the co-ordinates of the reflection time and the move out, which allow investigations of the average velocity for these same events.The combination of both investigations for each coherent event is a very convenient operation for the seismologist, and can provide some useful interpretation aids such as velocity profiles, or information on the interval velocities.The principles which we use consist in the examination of a large range of possibilities, of which only the most coherent are chosen.Some examples are shown.

Notes: Harmonic steady-state solutions for magnetic and electric vector components are obtained for a layered transitional earth in a vertical magnetic dipole field. The conduction currents dominate the displacement currents. The time factor eiωt is implied. MKS units are used.

Notes: Modern seismic recording instruments allow precise measurements of the amplitude of reflected signals. Intuitively we would expect that this amplitude information could be used to increase our knowledge of the physical properties of the reflecting earth.The relevant factors defining the amplitude of a reflection signal are: spherical divergence, absorption, the reflection coefficient of the reflecting interface, the cumulative transmission loss at all interfaces above this, and the effect of multiple reflections.Of these factors, three—spherical divergence, the reflection coefficient and the transmission loss—are reasonably clear concepts (though the estimation of transmission loss from acoustic logs caused some difficulties in the hey-day of synthetic seismograms). Absorption still presents considerable problems of detail, but our understanding has increased significantly in recent years.The factor least well understood is undoubtedly the effect of multiple reflections. Multiple paths having an even number of bounces can have the effect of delaying, shaping and magnifying the pulse transmitted through a layered sequence. Simple demonstations of this phenomenon can be made using elementary thin plates, and these can be presented for various synthetic and real sequences of layers. Such demonstrations lead one to explore the relation between the spectrum of the transmitted pulse and the spectrum of the reflection coefficient series.If it were possible to isolate the amplitude and shape variations imposed by absorption within a layer, there would be a chance that this measure of absorption would be useful as a correlatable or diagnostic indication of rock properties. If it were possible to isolate the amplitude and shape variations imposed by multiple reflections, there would be a chance that this measure would be useful as an indication of cyclic sedimentation and of the dominant durations of the sedimentary cycles. However, the separation of these two effects constitutes a formidable challenge. The very difficulty of this separation suggests that it may be opportune to review the quantitative estimates of absorption made by field experiments.

Notes: The first part of the contribution deals with the generalization of the solution given by Sharpe and states the elements of the mathematical model of the explosion generating longitudinal waves. The generalization of Sharpe's solution consists in finding out the response of the medium to a pressure p(t) applied at the source, for any value of the ratio K=Vp/Vs covering the range √2 ÷∞.The second part contains the results of the calculation and design of three electronic analog models of the explosion process in rocks. The first is represented by electrical circuits separated by emitter follower circuits. The scheme of the second model has electrical circuits and elements of operational calculus (integrator, summation instrument). The electrical circuits are represented by the two filters simulating the selective effect of the explosion in rocks. The third model is a logical programming scheme of the problem on an analog computer.For the calculus of the electrical parameters of the three schemes we have taken into account scaling of the physical and geometrical parameters of the medium and of the explosion which should ensure the simulation of the explosion process in rocks of all kinds of importance in seismic prospecting.

Notes: The gravitational attraction produced by a geological body of irregular shape can be easily determined by dividing it into cubes of small size. The exact expression of the effect of a cube is very complicated, but it can be calculated by using an electronic computer.4851 values of the gravitational attraction were determined for different positions of a cube with the side of 2l and the center in M(x0, y0, z0), for x0∈[0;20], y0∈[0;20] and z0∈[0;10]. Using these values, templates in double logarithmic representation were drawn, with x0 and z0 as parameters and y0 as abscissa, and with x0 and y0 as parameters and z0 in abscissa; this double set of templates permits a good interpolation for all cubes in the considered domain of M.The use of templates was tested to approximate the effect produced by a theoretical model of spherical shape and in a real case of a three-dimensional salt body of known shape based on a large number of boreholes. In both cases very good results were obtained.

Notes: A precise method of gravity interpretation is described which uses tables for the attraction of rectangular prisms in all positions relative to a given point. Hence the attraction of any body or combination of bodies may be assessed without complicated mathematical procedures.

Notes: Large memory computers create new possibilities for seismic interpretation in well-drilled areas, and more generally in problems involving deep sources.Records obtained by well-to-surface, surface-to-well and/or well-to-well propagation contain a large amount of information, owing to the great number of seismic rays travelling throughout the subsurface.This paper considers two successive steps:— direct case: computation of the first arrival times of seismic rays propagating through a two-dimensional subsurface with given vertical and horizontal velocity variations;— inverse case: computation of a two-dimensional velocity distribution, knowing the travel times of seismic rays through the subsurface.A computer program has been elaborated to solve both direct and inverse problems. There are no difficulties with the direct case; a certain number of uncertainties remain with the inverse case.

Notes: Simultaneous observations of electrical earth-potentials along parallel measuring lines offer a simple but useful method to study telluric and stray-current potentials. Different correlation-factors between the records of both observation points can help to separate telluric from industrial stray-current potentials. A method is suggested to eliminate disturbing impulses of stray currents from continuous telluric current recordings as those made at observatories.The influence of stray currents can also be eliminated from potential readings of an artificial current as applied in geoelectric measurements with the four-point-method. The elimination is possible by a simultaneous observation of the stray-current potentials on an equipotential line of the artificially generated field. The recording examples show an appreciable improvement of the signal-noise ratio without increase in the current. The method is useful for geoelectrical prospecting in areas which are contaminated by industrial noise.

Notes: Computer-Graphics, the visual display of data in digital and analog form, allows immediate interaction between man and machine. This interaction facility is valuable when the user is engaged in model design. By using such a device in gravity interpretation, the geophysicist can overcome the slow process of model simulation constrained by the conventional input/output devices, also maximum control over running programmes can be exerted if needed.