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: 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: 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: 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: Qureshi and Mula have suggested a computer method for the calculation of the shape of a two dimensional body from the gravity anomaly profile associated with it. The application of the method, however, was restricted to those bodies which have their top or base horizontal and end sides vertical. In this paper study has been made to investigate the possibility of eliminating the above mentioned restrictions and has arrived at the affirmative conclusion.

Notes: Consideration is given to the form of apparent resistivity sections obtained by varying electrode array position and spacing over two dimensional features.Since basic solutions exist for horizontally layered media and for vertical or dipping single interfaces, simple rules are proposed whereby these solutions can be directly combined to give solutions for more complex sections. Substantial approximations may be involved as the rules do not fully allow for interactions between the constituents.The range of error incurred in application of the rules is explored, with particular reference to the square array system of resistivity measurement. The two extremes- of orientation of the square array with respect to the line of section are separately considered in this survey.Within appropriate limits, the rules appear extendable to a wide variety of simple structures for which rigorous solutions would be formidable. The rules are finally discussed in relation to practical applications.

Notes: In modern oil exploration layers of prospective interest with rather simple structural features are often overlain by very complicated bodies as e.g. saltdomes or other kinds of diapirs, olistostromes, or front zones of overthrusted blankets. In all these cases normal reflection seismic investigations, where downgoing and upgoing rays are rather close to each other, mostly fail, either because no reflections from underneath the complicated bodies are obtained, or because a reliable migrated depth presentation becomes practically impossible due to the inhomogeneity of the overlying bodies.The undershooting technique avoids these difficulties by using ray paths which do not traverse the complicated bodies e.g. by shooting on one side of a saltdome and recording on the other side. On account of the large shot-geophone distances in this method special considerations and computer processes were developed concerning moveout corrections for common depth point stacking and migrated depth presentation.In many cases the location of the disturbing complicated bodies is known in advance. The shooting and recording program can then be adjusted to this knowledge and thereby kept to a minimum. If the location of the complicated bodies is unknown a more extended seismic program has to be carried out encompassing a great variety of shot-geophone distances. But in this case the approximate location of the complicated bodies can be deduced from the survey too.Results are presented in order to give an idea of the efficiency of the new seismic tool.

Notes: This paper describes the procedure for interpreting the apparent resistivity data measured with the two-electrode array directly with the help of kernel function. The calculation of kernel function from the observed resistivity curve is done by the method of decomposition. In the method of decomposition the resistivity curve is approximated by a sum of certain functions, whose choice is only restricted by the requirement that the contribution to the kernel function corresponding to them should be easily computable. A few such functions are classified. These, and the standard curves for corresponding kernel functions obtained by utilising an integral expression for two-electrode array expressing the kernel explicitly in terms of the apparent resistivity functions, are plotted on log-log scale. The determination of layer parameters, that is, the layer resistivities and thicknesses from the kernel function can be carried out by a method proposed by Pekeris (1940).

Notes: A six-channel wide-band digital system for magnetotelluric measurements is described The system is designed to operate in the frequency band 10-.0001 Hz. The recording is made on a 7 track tape in an IBM compatible 12 bit format. The amplitude and phase responses of the system and sample records are presented.

Notes: Several types of multichannel filters have been introduced in the past with the purpose of rejecting, in a seismic section, coherent noise having a slope different from that of the signal.These filters, generally, tend to introduce a certain amount of mixing and therefore the output trace shows increased horizontal coherence. This is due to the model on which these filters are based, since the hypothesis is posed that the reflectors are continuous. This may be dangerous since it could lead to mistaken interpretations, for example when small faults or breaks are made to disappear in the output section.Other problems that could arise in the application of multichannel filters after-stack are space-aliasing and high-pass filtering. The former occurs when coherent noise is rejected with apparent Velocity V and frequency fa=V/X, where X is the distance between traces. In this case, the signal also is distorted since it is rejected in the same frequency range. The high pass filtering effect occurs when the multichannel filter is designed to remove low coherent noise with high apparent velocity.In the paper a family of multichannel filters is presented based on a model of the seismic section such that minimum mixing effects appear. The filters are designed to give good results even in the case of low frequency and high velocity coherent noise.Some practical examples are shown.

Notes: Sub-bottom profilers achieve high resolution but limited penetration beneath the seabed. Marine seismic surveys with long streamers and conventional sources suffer from an incomplete CDP stack and an unnecessarily low signal frequency in the early part of the section. Consequently there is a depth interval over which the optimum resolution of the seismic reflection method is not achieved. This paper describes the design, conduct, and results of an experimental survey made to obtain high resolution sections (predominant frequency about 200 Hz) with reflection times up to one second in the northern North Sea. The prime motivation for the experiment was to assess the possibility of mapping a shallow gas sand which had been encountered by the drillers.The design concept of the survey was to keep all the benefits of conventional marine seismic data gathering and processing, but to reduce their dimensions and time scales by a factor of five to ten. The survey in 1972 recorded a total of twenty-four lines using twenty-four fold cover with 5 m spacing between the reflector points, and a separation of 50 m between adjacent lines. Multi-electrode sparkers were used with a shallow purpose-built twenty-four channel 240 m hydrophone streamer. The recording sample interval was 1 ms. The final sections, obtained after conventional data processing, were of good quality. The results of velocity analysis helped to distinguish primary and multiple energy. Reflections with large negative reflection coefficients were seen in some parts of the survey area, and these are thought to indicate thin gas sands.

Notes: This paper deals with a case study on the application of auto-correlation and spectral analysis methods to mineral assay data taken along seven drives and two winzes concerning the McTaggart's (West) lode of Kolar gold fields. The general model conceived in this study is: measured (estimated) ore grade at jth location =true value + error at jth location. Employing an auto-correlation function of the form C e- a |k| for signals, the respective contributions of signals and noise to the total logarithmic variances for the data along drives and winzes are analysed. Smoothed spectral density estimates and their 90% confidence limits are computed for the series of data.

Notes: Methods and typical case histories of EM and IP surveys are compared in order to check their compatibility for the investigation of large areas for base metal sulphides. It is demonstrated that the fast, low cost EM may miss sulphide concentrations which cause no reduction of apparent resistivity, or which act like horizontal slabs, where EM anomalies occur marginally. In such cases only IP can recognize the whole extent of the mineralization. The misleading role of graphite exists for both methods.The conclusion is that EM remains the only economical method to survey whole ore districts, but that the shortcomings should always be taken into account in the interpretation. They can be overcome by employing geological, geochemical or other geophysical indicators in selecting promising targets for follow-up IP. Even if less than 20% of the area is covered by the expensive IP, there is a fair chance that all sulphide bearing rocks will be found. Therefore, the question is not whether to apply EM or IP methods, but how to combine them best.

Notes: The paper deals with the prerequisites of application, specific peculiarities and methods of electrometric and thermometric investigations aimed at the solution of certain engineering-geological problems in offshore areas. Practical examples are supplied.

Notes: The voltage induced in a horizontal loop on a layered ground has been calculated for the case where the loop is excited by a step current and measurements are made during the off-cycle.The expressions derived for a uniform ground show that for large time t the induced voltage E(t) is approximately given by E(t)≃— (Ibαμ/20t) (σμ2/t)3/2 where σ is the conductivity of the ground, μ the permeability, b the loop radius, and I the amplitude of the current step. For small times the corresponding result is E(t)≃—Ibμ/2t.When the ground is composed of a number of layers a numerical procedure for calculating the induced voltage is described.The calculated responses of various multilayered structures show that at short times the induced voltage is asymptotic to that produced in the case of a uniform ground of conductivity equal to the top layer.Interference effects in the top layer can lead to anomalous decay curves which may result in the underestimation of the conductivity of a buried layer.

Notes: Marine geophysical work requires accurate navigation on a continuous basis. A repeatability of 150 m CEP (circular error probable) with sequential positioning of 15 m CEP is usually acceptable. Quoted figures for many presently available navigation systems yield nearly the required accuracy. In actual operations, however, such accuracies may not be achieved, and usually the performance actually realized cannot be determined for want of independent measurements for comparison. If more redundancy in navigation measurements were available on an integrated basis, the limitations of individual systems would no longer be so critical and the accuracy of measurements could be assessed in real time. Failures in navigation continue to occur. Such failures usually result from ignorance of the capabilities of the navigation system and limitations and consequent choice of a system which is not appropriate to the demands of a particular survey. The points to be covered in work standards are listed.

Notes: The acceptance of articles in Geophysical Prospecting is strictly based on the originality and relevance of the contents. In order to be published a paper has to satisfy additional requirements on its external form and on its style and language: it should be written preferably in English though articles in French and German are permitted. A paper should consist of (i) a title page, (ii) an abstract, (iii) the text, (iv) list of references, (v) captions to illustrations, if any, (vi) tables, if any, and (vii) illustrations, if any. These seven parts should be mailed together but be physically separable and should be prepared according to rules which are either based on printing necessities or on the editorial style of the Journal.Failure to comply with these rules may result in delay in further processing of the article. Since Geophysical Prospecting is edited with a minimal budget correspondence with authors is kept to a minimum.

Notes: Depths of investigation for normal (bipolar) and focusing (unipolar) linear electrode arrays have been computed following the method given earlier (Roy and Apparao 1971) both in homogeneous and layered earth. The focusing arrangement is found to be superior to normal arrangement both in regard to depth of investigation and zone of uniform depth of investigation. This analysis holds good in layered media too. Further, the depth of investigation increases with the increase in the length (2M) of the electrode and reaches a limit, 0.29L for normal and 0.50L for focusing, when the electrode attains an optimum length to satisfy the infinite condition. This optimum length of the electrode is six times the distance L of the observation point from the electrode for normal and about ten times for focusing. A contour diagram for contributions of individual ground elements to the total signal measured at the centre of focused system is also discussed.

Notes: The authors generalize a method expounded in a previous paper (1971, Geoph. Prosp. 18, 786-799) to the case of a local conductivity σ(M) of the infinite medium satisfying the relation 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR246:GPR_246_mu1"/〉 where the Ri's are the distances from the point M to n fixed points Si (i= 1,. n), k is a positive real constant and Ci, Cii are constants ensuring the condition α 〉 O.The sub-surface conductivity distributions (half-spaces) complying with (1) provide a wide variety of conducting structures, which can fit quite successfully the rather complicated distributions of conductivity occurring in natural ore bodies.An exact algebraic calculation of the apparent resistivity for these grounds, valid for any dc electrical prospecting devices (Wenner, Schlumberger, dipole, etc.) leads to a set of simultaneous linear equations, with a matrix which is invariant with respect to the position of the quadrupole being used. This greatly simplifies the numerical computation.We also present some examples of cross sections for the real and apparent resistivity obtained by this method.

Notes: Section migration after stack has been widely accepted by the industry. From a theoretical point of view, section migration before stack should provide superior results, the improvement warranting the drastically increased cost is not realized in most cases.There are a number of reasons that explain the discrepancy between actual and theoretically expected quality: Long period statics, refraction of rays, two-dimensional treatment of an actually three-dimensional problem.The section migration package subject to this paper allows(i) to take refraction into account,(ii) to discriminate against noise with a variety of statistical and geometrical criteria,(iii) to adapt processing time to problem complexity by a special process called SEMI-STACK.A number of examples will demonstrate the effects of section migration.

Notes: A seismic trace after application of suitable amplitude recovery may be treated as a stationary time-series. Such a trace, or a portion of it, is modelled by the expression 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR627:GPR_627_mu1"/〉 where j represents trace number on the record, t is time, αj is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and nj is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto-correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time-domain pulse itself is then reconstituted under the assumption of minimum-phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z-transform, (C) a fast method based on inverting the least-squares inverse of the wavelets, i.e. inverting the normal time-domain deconvolution operator. Problems associated with these three methods are most acute when the z-transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace-to-trace, from shot-to-shot, and from one shot-point medium to another. There is reasonable agreement between the minimum-phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge-factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.

Notes: The implementation of a stacking filter involves the filtering of each trace with an individual filter and the subsequent summing of all outputs. The actual position of a trace in space as well as certain simultaneous shifts of traces and filter components in time do not influence the process. The resulting output is consequently invariant to various arbitrary coordinate transformations. For a certain useful class of ensembles of non-linear moveout arrival times for signals a particular transformation can be found which transforms a given ensemble into one consisting only of straight lines. It is thus possible to reduce, for instance, the analysis of a stacking filter designed for hyperbola-like moveout curves to the analysis of a velocity filter with linear moveout curves. As the (f—k) transform is a very useful concept to describe a velocity filter, it can consequently be applied to characterize a stacking filter in regard to its performance on input signals with non-linear moveout.

Notes: The technique of linear digital filtering developed for the computation of standard curves for conventional resistivity and electromagnetic depth soundings is applied to the determination of filter coefficients for the computation of dipole curves from the resistivity transform function by convolution. In designing the filter function from which the coefficients are derived, a sampling interval shorter than the one used in the earlier work on resistivity sounding is found to be necessary. The performance of the filter sets is tested and found to be highly accurate. The method is also simple and very fast in application.

Notes: A case history is presented for the exploration of barite with the electrical resistivity method. Altogether eight locations were recommended out of which six correspond to barite bodies. In the present case the gravity method, which is commonly used for the location of barite because of its high density contrast with the host rocks, has failed, perhaps due to small size of the ore bodies.

Notes: A correct derivation of rms, average and interval velocities from one another and from common depth point stacking velocities requires a clear understanding of the relationships between these velocities. We relate the average velocity to the rms velocity through a “heterogeneity factor” which is a quantity that gives a measure of the degree of velocity heterogeneity in the ground. The interval velocity is a quantity which varies according to the method of its derivation. The difference between rms and stacking velocities depends on the heterogeneity factor and on the length of the spread. Unless allowed for, this difference can reverse the advantages of long spreads and cause large errors in interval velocity determinations. It may be removed through a number of techniques. The accuracy of stacking velocities in the presence of random “noise” is independent of the heterogeneity factor. Relevant expressions can be broken down into simple formulae which give the accuracy quickly and with good precision.

Notes: Theoretical broadside resistivity profiles over an outcropping dyke of infinite depth extent with three Wenner configurations (namely Alpha, Beta and Gamma), Schlumberger, and two-electrode configurations of various electrode spacings and for various reflection factors are presented. The broadside profiles qualitatively indicate that the shape of the anomaly is invariant with the electrode configurations. The various electrode configurations can be arranged in decreasing order of magnitude of anomalies as Beta Wenner, Alpha Wenner, Schlumberger, Gamma Wenner, and two-electrode. The broadside Wenner profiles also show larger anomalies compared to those in inline profiles.

Notes: With the increasing number of channels in AEM systems, computer data handling is becoming a necessity. The experience gained in processing of seismic and aeromagnetic data cannot be applied directly to low-frequency (100-5000 Hz) AEM methods. A novel scheme has been designed for AEM data processing and tested on 2900 km (1800 miles) of Input surveys.In the first step, the digital flight tapes are merged with digitized flight path recovery to form the primary data set. The validity of the raw data is controlled by the computer, but the interpreter has an option of checking them in perspective plots of channel amplitudes. The primary data set is reduced by processors which determine the location and type of anomalies and discard noise. Unlike the widely used deconvolution, the sequential processor determines first the anomaly location and then estimates parameters, such as peak amplitude, base width, and excess area, which are used as acceptance criteria. Interpretation parameters, such as σt, conductor depth, and dip are estimated by comparison with quantitative models. The recorded channel amplitudes are plotted together with the selected interpretation parameters in a profile form. The secondary data set which includes only the interpretation parameters for selected anomalies is graphically displayed as a schematic map of apparent σt. Elongated features are traced by a fan strike recognition routine and a trend map is automatically compiled and plotted. Disk storage is essential for second pass processing during which parts of the primary data set are searched for undiscovered anomalies matching the analyzed trend. The suggested procedure for AEM data processing is demonstrated on an Input MK V survey, Southern Indian Lake, Manitoba.

Notes: The paper discusses the smallest obtainable parameter errors (variances) in the interpretation with the least-squares method. Useful approximations of the sum of squares contained in the minimum error expressions are obtained using results of numerical integration. The approximations lead to especially simple results for long interpretation profiles, when the parameter errors are proportional to the square root of the point separation.Formulae are developed and examples shown for minimum error calculation in gravimetric interpretation with the cylindrical model and in magnetic interpretation with the two-dimensional plate model. Smallest errors are obtained when the interpretation profile is chosen around the anomaly maximum except for dip and depth extent interpretation of magnetic plates.

Notes: In a transversely electrically anisotropic rock mass of arbitrary dip, the potential distribution about an electrode at arbitrary depth is the sum of the whole-space potential about that electrode, plus the whole-space potential about a postulated image electrode displaced up-dip from the source position. Equipotential lines on the rock-air surface are ellipses, elongated parallel to strike, and with centers displaced up-dip from the surface projection of the electrode position. In metamorphosed rocks frequently encountered in mining geophysics, anisotropy is such that elongation is most marked in steeply dipping rocks, with displacement most evident in low to moderate dip.Graphs relating the anisotropy coefficient to displacement and elongation assist in separation of the anisotropy-related effects from those of a significant subsurface conductive body, particularly if surface resistivity sounding establishes the coefficient of anisotropy.

Notes: An earth model with a transition layer (anisotropic inhomogeneous) is considered. The inhomogeneity in σv (vertical conductivity) of the transition layer is represented by a power law variation. Expressions for potential distribution in the upper layer, transition layer and bottom layer are obtained by solving appropriate differential equation for each layer. By utilizing the boundary conditions, expressions of apparent resistivity for Wenner and Schlumberger configurations are derived. Numerical analysis is performed for linear and quadratic variation of σv. The results are presented in the form of theoretical apparent resistivity curves for both configurations. Negative apparent resistivities are the interesting feature of this analysis.

Notes: A study of probability distribution function and spectrum of the Airborne Total Intensity Map for an area of 3000 Squ. miles covered by the Bundelkhand granite in India has revealed a close correlation between the Gaussian or non-Gaussian nature of distribution and the shape of unite value contour on the spectrum plot. Further studies of radial spectrum plots suggest that the surface magnetic sources are mainly responsible for the non-Gaussian character of the distribution function and as well as for irregular spectrum shape. The histogram of depth values for magnetic sources obtained from radial spectrum plots show three horizons, namely (i) surface (ii) 410 m(1400′) and (iii) 1000 m (3400′).Based on these informations blocks with ferromagnetic composition at the surface can be identified from those which are non magnetic at the surface.

Notes: The Huntec Mark 3 time domain equipment provides information from which the nature of the transient voltage decay curves may be determined. A zone of disseminated mineralization extending above a normal fault zone was selected for a comparative study of decay curves.In a preliminary study in which steel stakes were used as current electrodes it was observed that at some stations the decay curves obtained with reciprocal dipole-dipole configurations were significantly different and that many decay curves initially increased from low values indicating the presence of a negative component.It was assumed that the decay curves were composite and were composed of the superposition of transient voltage components due to electromagnetic and polarization effects which could be described in terms of simple exponential functions. The initial negative component was thought to be an electromagnetic effect, but when the traverses were repeated using porous pots as current electrodes it was found that the initial negative component was usually completely eliminated, indicating that it was due to negative polarization arising from the steel stakes.When the effect of the current electrode polarization was completely eliminated identical decay curves were obtained with the reciprocal array configurations, but the remaining decay curve-which is due to induced ground polarization—cannot be described by a single simple exponential function. It is also demonstrated that the initial negative component due to stake polarization may also be present in decay curves obtained with gradient arrays indicating that separation of the current and potential electrodes does not avoid this effect which may significantly modify the decay curve in certain circumstances up to three seconds after switch-off.

Notes: Common-depth-point stacking velocities may differ from root-mean-square velocities because of large offset and because of dipping reflectors. This paper shows that the two effects may be treated separately, and proceeds to examine the effect of dip. If stacking velocities are assumed equal to rms velocities for the purpose of time to depth conversion, then errors are introduced comparable to the difference between migrated and unmigrated depths. Consequently, if the effect of dip on stacking velocity is ignored, there is no point in migrating the resulting depth data.For a multi-layered model having parallel dip, a formula is developed to compute interval velocities and depths from the stacking velocities, time picks, and time slope of the seismic section. It is shown that cross-dip need not be considered, if all the reflectors have the same dip azimuth.The problem becomes intractable if the dips are not parallel. But the inverse problem is soluble: to obtain, stacking velocities; time picks, and time slopes from a given depth and interval velocity model.Finally, the inverse solution is combined with an approximate forward solution. This provides an iterative method to obtain depths and interval velocities from stacking velocities, time picks and time slopes. It is assumed that the dip azimuth is the same for all reflectors, but not necessarily in the plane of the section, and that the curvature of the reflecting horizons is negligible.The effect of onset delay is examined. It is shown that onset corrections may be unnecessary when converting from time to depth.

Notes: The quantitative analysis of the potential fields leads to the solution of some operational equations which sometimes have unstable solutions representing fictitious anomalies. A general method to find numerically stable solutions of such problems is presented in this paper. The subject of the downward analytical continuation is also discussed. The method has been checked on a theoretical model and applied to a gravity map.

Notes: Results of studies carried out with the help of a three-dimensional seismic model on waves diffracted from edges of varying radius of curvature R and depth h with respect to wave length λ are described. The amplitude decay, travel time, and apparent velocity of the wave diffracted from a sub-surface edge of semi-infinite length are found to depend on the parameters R, h, and distance from the edge on the surface provided the ratio of the parameters to λ are less than some limiting values. The nature of the amplitude decay is independent of R when the depth exceeds 2λ, and independent of h when R exceeds 1.5λ. When these are below the limiting values (h= 2λ and R= 1.5λ), the nature of the decay depends appreciably on R and h. The apparent decay in amplitude on the surface due to geometrical spreading by the diffracting edge is less than that of a cylindrical secondary wave source and decreases with increase in depth of the edge. The nature of the travel time curves of the diffracted waves near the edge depend on R/λ when the depth is within about one λ. Apparent velocity of the wave depends largely on R/λ in the zone of diffraction up to a distance of about one λ from the edge on the surface. Beyond this distance the velocity is almost the same irrespective of R/λ and depend only on h/λ. The width of the zone of diffraction caused by an edge of finite length comparable to λ is more and more narrow as the ratio of the distance of the edge on the surface to its depth increases.

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 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: 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: On an experimental basis, observations were made with various geophysical methods to locate the ancient gold workings in Kolar Gold Fields, Kolar, India. The results of experimental surveys indicated that two-electrode resistivity surveys with two spacings followed by limited trenching would be able to locate about 70 percent of the ancient workings, at 55-60 percent of the cost of conventional trenching.

Notes: There are different types of acoustic noise induced in streamer cables. One type consists of pulsed waves preferentially generated by vertical motions of the towing ship or of the tail buoy. The pulsed waves travel along the streamer with low attenuation and a velocity about 15% less than the velocity of water. Frequencies observed lie between 5 and 15 Hz.These pulsed waves are well known and for the last few years acoustic isolator sections have been used to reduce their generation. But under bad weather conditions and especially in cold water these waves become stronger. Recent investigations demonstrated that the pulsed waves are able to produce a high noise level even in new streamers with acceleration cancelling hydrophones. We point out that the material of the hoses has a dominant effect on the amplitude picked up by the hydrophones.Acoustic theory is applied to understand the phenomenon of these waves.

Notes: To specify intelligently a nondynamite source in a marine seismic data-collection system, it is important to use all known parameters of the system—source, receiver, and recording-system characteristics. A technique has been developed to design the far-field pressure pulse of an air-gun array by taking these parameters into account.Important source variables to consider are interaction among guns in the array and the depth of the array. Near-field pressure signatures of individual guns, which are relatively unaffected by boundaries, have been used to‘construct’the far-field pressure pulse of the array by considering these variables. Comparison between constructed pulses and measured far-field pulses shows substantial agreement.Streamer depth and recording-system bandpass should also be considered when designing an air-gun array. Comparison of far-field pressure pulses for several bandpasses clearly shows the importance of considering this variable; e.g., the initial pulse is severely attenuated when a high-cut filter is used. Likewise, an additional filtering effect due to the streamer's proximity to the surface should be taken into account.Design of an air-gun array using the principles just outlined are illustrated by an example.

Notes: Many practical energy sources are available for land use and likewise a goodly number for marine operations. However, the transitional region between navigable water and negotiable land is poorly served. The vehicles that are capable of operating amphibiously are limited in the pay-load they can transport, and in the bulk of apparatus that can be operated from the space available. The Flex-O-Gun (Trademark of Geo Space Corporation) is a new, lightweight gas exploder designed to meet the requirements for operation in rivers, bays, and marsh areas not generally accessible to the larger, heavier systems such as the Dinoseis (Trademark of Atlantic Richfield Company), Vibrator and Air Guns. Weighing less than 70 kilograms, the Flex-O-Gun requires only modest sources of oxygen and propane and the associated firing equipment for operation.The gun delivers energy by the sudden introduction into the water of high pressure gases resulting from detonation. The device is unique in that the underwater gun assembly contains no gas mixing or firing elements. A flexible, metallic hose conveys the charge of mixed gases and subsequent detonating flame to the gun from control and firing mechanisms located above the surface. With its small weight and total space requirements, the Flex-O-Gun can be operated from small boats, buggies, or trucks, and is easily transported.In this paper the features of the gun are described and the results given of tests of its operations. An implanting device is also discussed which extends its application to viscous formations. The device employs water jets mounted below the gun to wash down a hole and insure placement of the gun at depths to obtain maximum energy output.

Notes: Five test profiles in time-domain induced polarization measurements over conducting sulphide and graphite mineralisations were run with the two-electrode, three-electrode, modified unipole, pole-dipole, dipole-dipole, Schlumberger, and Wenner α and β configurations. The results show that, compared to the other electrode systems, the simplest two-electrode array produces the largest anomalies with the smallest of spacings.

Notes: The theoretical horizontal resistivity profiles Over an outcropping vertical dyke with two-electrode and Schlumberger electrode systems are discussed. The two-electrode array seems very useful in locating the highly conducting thick or thin vein, while the Schlumberger (gradient) array is suited to detect the conducting vein of low and moderately high resistivity contrast and as well as the resistive vein of all widths and resistivity contrasts. Besides, the inline gradient array has a distinction of establishing a clue to evaluate the resistivity contrast of the vein.

Notes: The generalised three layer boundary value problem with a transition layer sand-witched between an isotropic overburden and dipping anisotropic substratum is discussed assuming that plane electro-magnetic waves are incident normally over the air-earth inter-face. The tangential electric (Ey) and magnetic (Hx) fields and the expression for surface-impedance (Ey/Hx) have been evaluated at the earth's surface. Through numerical analysis it is shown that changes in the values of the parameters m (coefficient of anisotropy), h (thickness of the transition layer), α (angle of inclination of the dipping beds), and b (conductivity ratio between substratum and upper layer) modify the amplitude and phase-variation curves (with skindepth) significantly.

Notes: Gravity modeling involves the evaluation of gravity field due to bodies of irregular shape. This is commonly accomplished by dividing the body into smaller units of regular shape whose field can be determined analytically.Cubes are ideal building blocks for constructing bodies of irregular shape. However, the exact expression defining the gravity field of a cube-shaped body is very long and requires tedious numerical work. Approximation formulas for rapid evaluation of the cube's gravity field are presented and discussed in detail. Their use for computing the field for small distances leads to large errors in the results; on the other hand, using the exact formula for large distances where approximation formulas yield practically identical results, is waste of time. After a detailed analysis about the nature of the cube's gravity field, certain criteria are established for suitably combining the two alternatives. This results in tremendous reduction in the task of computations without affecting the accuracy of data.

Notes: A rigorous proof is presented to show that over a horizontally layered ground the rms velocity cannot exceed the stacking velocity. The proof helps to illustrate the difference between stacking and rms velocities in a quantitative manner. The series of Taner and Koehler (1969) is used for the purpose. Convergence of this series is tested. Including more terms will not necessarily improve the convergence. Although the series is rapidly convergent when the spread length/depth ratio is small, strong oscillations are observed when this ratio is high.

Notes: The properties of cross-correlation functions for the case of gravity and magnetic total field anomalies produced by three geometric models of geological bodies (point-mass, horizontal line-mass, and vertical semi-infinite rectangular prism mass distributions) are studied. This study is carried out on four cases of cross-correlation: the whole curve of anomalies, a single branch of anomalies, the branch between the two inflexion points and the branch between the apex point and the inflexion point. In all cases, the crosscorrelation function can serve as a good indicator to discriminate the so-called genetically related anomalies from those produced by different geological bodies situated on the same vertical line; but the best results are obtained using the cross-correlation of the branches between the apex point and the inflexion point of the two geophysical anomalies.A practical procedure is developed in order to undertake such analysis. The tests in some cases of real gravity and magnetic anomalies mapped in Romania show the validity of this practical procedure.

Notes: The time-honoured method of attenuating coherent noise in the seismic record is by the use of source and geophone arrays. In theory, and using methods familiar in the synthesis of digital frequency filters, arrays can be designed having virtually any desired response in the wavenumber spectrum.In practice, arrays cannot be implemented with the same precision that is applied in design. The response actually achieved must be compromized by a number of factors. These include inaccuracies in the effectiveness or positioning of individual array elements, variations in ground coupling, and the effect of local heterogenities in the environment of the array. We have no reliable way of knowing how well a particular array will perform from one location to the next.Statistical modelling methods have been applied to examine the effects of implementation errors. Experimental results, supported by statistical theory, show that errors are expected to impose a limit upon the rejection capabilities of an array. The expected limiting value of attenuation due to errors in element weights is inversely proportional to the standard deviation of errors and directly proportional to the square root of the number of array elements. Position errors exert a limiting influence which is wavenumber dependent such that attenuation decreases with increasing wavenumber. For arrays of common dimensions, Gaussian random errors of 10% standard deviation in element weights and positions result in an expected attenuation limit of about 30 dB.It follows that the more ambitious array designs are less tolerant of errors, and must be implemented with greater care and precision in the field. The present work enables us to specify tolerances for any particular array design.Ultimately, the degree of pattern refinement which may be effectively employed in any area is determined by errors which are associated with the array environment. Complex arrays are expensive to operate. In order to avoid over-design it would be useful to establish the magnitude of errors to be expected under different terrain conditions.

Notes: During the last ten years data processing has enabled the geophysicist to seriously attack the problem of how to improve the quality of seismic sections. For instance new processing methods have been proposed for improving the resolving power of the seismic pulse. These methods are based on deconvolution and they require lengthy computations.The method discussed here for pulse contraction is based on the use of Hadamard transforms. It is very fast but nevertheless the quality of the result stands comparison with that of conventional methods.

Notes: Application of statistical methods of analysis of geophysical data is often helpful for the detection of weak anomalies against a noisy background. The processing and analysis of areal geophysical data by two such methods are presented. The advantage of these methods are illustrated with the help of two field examples.

Notes: The paper deals with the electro-filtrational fields formed near the drainage structures. Main laws of deformation of these fields above vertical and horizontal drains are considered and practical examples supplied.

Notes: A seismic trace recorded with suitable gain control can be treated as a stationary time series. Each trace, χj(t), from a set of traces, can be broken down into two stationary components: a signal sequence, αj(t) *s(t—τj), which correlates from trace to trace, and an incoherent noise sequence, nj(t), which does not correlate from trace to trace. The model for a seismic trace used in this paper is thus χj(t) =αj(t) * s(t—τj) +nj(t) where the signal wavelet αj(t), the lag (moveout) of the signal τj, and the noise sequence nj(t) can vary in any manner from trace to trace. Given this model, a method for estimating the power spectra of the signal and incoherent noise components on each trace is presented.The method requires the calculation of the multiple coherence function γj(f) of each trace. γj(f) is the fraction of the power on traced at frequency f that can be predicted in a least-square error sense from all other traces. It is related to the signal-to-noise power ratio ρj(f) by 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR660:GPR_660_mu1"/〉 where Kj(f) can be computed and is in general close to 1.0. The theory leading to this relation is given in an Appendix.Particular attention is paid to the statistical distributions of all estimated quantities. The statistical behaviour of cross-spectral and coherence estimates is complicated by the presence of bias as well as random deviations. Straightforward methods for removing this bias and setting up confidence limits, based on the principle of maximum likelihood and the Goodman distribution for the sample multiple coherence, are described.Actual field records differ from the assumed model mainly in having more than one correctable component, components other than the required sequence of reflections being lumped together as correlated noise. When more than one correlatable component is present, the estimate for the signal power spectrum obtained by the multiple coherence method is approximately the sum of the power spectra of the correlatable components. A further practical drawback to estimating spectra from seismic data is the limited number of degrees of freedom available. Usually at least one second of stationary data on each trace is needed to estimate the signal spectrum with an accuracy of about 10%. Examples using synthetic data are presented to illustrate the method.

Notes: Seismic refraction at sea and on continental shelves requires most of all a precise positioning of the shooting and receiving stations and a good signal to noise ratio.A new system has been developed using detectors anchored on the sea floor and radio transmission of signal for refraction work on continental shelves. This technique satisfies both requirements. The system has been tested in the western Channel in December 1971.

Notes: The problem of interpretation of geoelectrical resistivity soundings has been studied and a compromise method of interpretation developed. A simple depth sequence of increasing bed thickness is taken and resistivities assigned to the various layers so that a good fit is obtained to the observed apparent resistivity curve. An initial estimate of the resistivities is made by a direct method but the model is then altered to give an improved fit by the indirect method of curve matching. The whole method is computerized and input data to the computer program consists of spacings and apparent resistivities. The method is extremely rapid, about one third of the computation time is devoted to obtaining the resistivity transform by the method of convolution. A normal type of solution, incorporating additional information if necessary, can also be obtained.

Notes: The use of arctangents rather than arcsines in the expression for the gravitational attraction of a homogeneous rectangular prism reduces computational difficulties. Once a subroutine is available to compute one component of attraction in a Cartesian coordinate system, the other components may be obtained by cyclic permutation of the field point and body coordinate parameters. This technique also readily provides derivatives of the gravitational attraction and hence forms a compact method for the calculation of a magnetic anomaly due to a homogeneous rectangular magnetic prism.

Notes: With the help of the principle of superposition the Input response of a conducting infinite horizontal homogeneous cylinder is synthesised from its step-function response. The variation of transient peaks and the time lag between the secondary and primary fields with the cylinder constitution parameter are illustrated.

Notes: The new process of automatic determination of seismic velocities by well to well measurements (Bois et al., 1971, Geophysical Prospecting 19, 42-73) gives the possibility to increase the knowledge of oil reservoirs, by detecting large inhomogeneities between wells. It can also give useful informations on the mechanical properties of rocks in mining exploitation and civil engineering, by gallery to gallery measurements. An application of the method is given to the search for the proper location of an underground hydroelectric power plant, where the problem was to investigate the rock properties in a horizontal plane between two exploration galleries.

Notes: An integral equation technique based on the integral formulation of the electric field of a harmonically excited line-source in the presence of a two-dimensional scattering in-homogeneity is outlined. In this treatment the inhomogeneity is assumed to have an arbitrary cross-sectional shape and to be located in a layered, dissipative half-space. The scattering responses in terms of the horizontal and the vertical magnetic field components observed on the ground surface are studied for a variety of geologic models involving overburden layers, vertical or inclined veins and multiple inhomogeneities. The horizontal component of the total magnetic field appears to be the most diagnostic response parameter. A thin vein shaped target with a cross sectional area of 0.05 δ2× 0.50 δ2 (δ2 being the skin-depth in the lower half-space) located 0.50 δ2 away from the line-source and under a highly conductive overburden layer (σ1/σ2= 300) of thickness 0.02 δ2 is easily detected with a moderate resolution. The scattering responses are also sensitive to changes in depths of burial, inclination and conductivity contrast with the surrounding half-space of the target inhomogeneity. An interpretation scheme as well as a number of characteristic detectability parameters are developed for the conventional Turam method used in mineral exploration.

Notes: The values of the filter coefficients used for the computation of electromagnetic sounding curves are studied in conjunction with the values of the input function to the filter, or the range of values which the input function may assume, and the filters are broken off at such a place that the error in the sum of the products of filter coefficient and input function does not exceed a prescribed value. This analysis is carried out for the horizontal coils system, the perpendicular coils system, and the vertical coplanar coils system. The lengths of the filters so derived depend on the layer parameters, the frequency and the coil spacing. Even in the most unfavourable cases the filters are shorter than the filters published by Koefoed, Ghosh, and Polman (1972).

Notes: Dividing a vertical conducting vein into horizontal strips, response of each of them is obtained for various transmitter receiver orientations.