QUELQUES CONSIDÉRATIONS SUR L'EMPLOI DES TENSIOMÈTRES

Abstract

The interpretation of tensiometers measurements requires special knowledge of the mechanics of equilibrium of the tensiometer with its environment. The classical concept of response time τ = (1/K′ S) of the system: porous cup (conductance K') and manometer (sensitivity S) can be improved by taking into account the elasticity of the tubing. By analogy one can appreciate the role of entrapped air in the circuit. In general, it is possible to theorically observe the response characteristics of the tensiometer by imposing pressure step in the system and by studying the equilibrium response. Such tests showed certain anomalies of behaviour which can be attributed to very small bubbles of air entrapped to the internal wall of the porous cup.

However, it is necessary to check the response of the tensiometer when it is placed in the soil. This is confirmed by analysis and experiments in a sandy and clayed soils.     

SUR LA SEPARATION DES ANOMALIES GRAVIMETRIQUES ET MAGNETIQUES*

One of the most important aspects in interpretation of gravity and magnetic anomalies, which generally represent the sum of many effects from the subsoil, is that these effects cannot be adequately separated into individual effective anomalies by means of known procedures. Moreover, the concept itself of anomaly separation must be expanded in a certain sense, because the addition of these effects in the mapped anomalies can arise from many structures situated in the subsoil in different relative positions to one another. A combined procedure is proposed, based on Fourier analysis utilising both periodic complex functions and nonperiodic ones, by use of which the number of individual effective anomalies cumulated in the mapped anomalies is obtained. In order to illustrate the use of this procedure and the advantages of obtaining more valuable informations on geological causes of anomalies, one example from Romania is given.     

QUELQUES APPLICATIONS DE LA THEORIE DE LA PREDICTION AU TRAITEMENT DES DONNEES SISMIQUES*

In the case of simple time series it is shown that prediction operators can be considered as deconvolution operators which are easily obtained. These operators possess the special feature of having a minimum phase, and their spectrum modulus represents, with a good dynamic range, the reciprocal of the square root of the modulus of the original autocorrelation spectrum. A generalization of the simple time series theory to the functions of two independent variables is possible in as much as, on a given section, the application of the multiple time series method enables the function of time and distance variables to have well-defined statistical properties; it is necessary, in particular, that the processes involved are stationary with respect to the two independent variables. In the case of multiple time series the application of the Prediction Theory permits greater uniformity of the traces because it enhances the events which show a good correlation between traces and, on the other hand, tends to minimize the random events which cannot be correlated between traces. The signal-to-noise ratio is thus increased to a great extent.     

MAGNÉTOMÈTRE DIFFÉRENTIEL À HAUTE SENSIBILITÉ*

The aim of this article is to describe the double resonance magnetometer system designed and built by the Division de Magnétométrie of the C.E.N. Grenoble, and used by the Département des Recherches Minières du CE.A. For the measurement of magnetic anomalies of geological origin it is necessary to make differential measurements between a mobile instrument which scans the region of interest and a fixed compensatory instrument. The apparatus described here features the following main characteristics: — it gives a direct numerical measurement of the differential magnetic field between the two instruments with an accuracy of 0.01 gamma (10^-7 Oe). — it is designed to be easily operated in geological field work (light weight, low power, possibility to make continuous measurements along a given profile, the measuring signals being radio-linked there are no wires connecting the instruments). Firstly we describe the components of the magnetometer itself namely: double resonance magnetometer heads and differential numerical magnetometer. Secondly we describe the measuring technique.     

CALCUL DES COURBES DE,SONDAGES ÉLECTRIQUES À L'AIDE DES FONCTIONS D'ÉCHANTILLONNAGE*

Recently I had an opportunity to apply the theory of sampling functions to the functional transformations of gravity and magnetic anomalies (Baranov 1975). It would be interesting to examine if there is a possibility to use these functions in the electrical prospecting. It seems that the answer might be affirmative. This paper is an attempt to compute the master curves for the electrical vertical sounding with the aid of sampling functions.     

CONTRIBUTION DES MESURES DE L'ANISOTROPIE ÉLECTRIQUE À LA RECHERCHE DES AQUIFÈRES DE FRACTURE EN MILIEU CRISTALLIN AU BÉNIN1

A particular methodology adapted to crystalline formations with a thin weathered zone was developed for a village hydrological project, in Benin. A combination of electrical profiles, Schlumberger and square arrays, was able to locate the most fractured zones in the basement. We present some results obtained from theoretical models as well as from field data. The suggested methodology uses both measurements of resistivity and anisotropy. Strong anisotropy and low resistivity indicate the most productive hydrogeological areas.     

EXEMPLE ?APPLIGATION DE LA GRAVIMETRIE A ĽETUDE DES MASSES SALIFERES*

An ill-defined seismic marker has been identified as the top of the sandstone lower Trias in the “Landes”– small area within the whole Aquitaine region for which the S. N. Repal obtained prospecting licences. Before any drilling was made, this marker was thought to belong to the early saliferous triassic series. The quantitative use of the residual gravity anomaly has made the seismic reflection interpretation easier. This interpretation was found to give excellent results along the coastline where all postulated hypothesis proved true in the bore holes of Contis and St Girons. As a first approximation, it appears that the substratum of the saliferous bed in sub-horizontal and has a fairly steady gravity. The Jurassic and the Cretaceous, both limestones, are prevailing (0,15) in comparison with the argillaceous-saliferous Trias and the early Tertiary which was revealed to us with accuracy through seismic surveys. The use of an approximative linear equation where the gravimetric residue is expressed as a function of the limestone thickness allows a better seismic interpretation. This makes possible a more reliable approach of the structural study of post-triassic deposits. The same holds good for the sandstone substratum which shows on an isochronous map strains due to thickness and velocity changes in the overburden. These facts help us to get a better insight into the origin and formation of salt accumulations in this particular area.     

CARTOGRAPHIE DES “PSEUDO-RESISTIVITES APPARENTES’ PAR PROFILAGE TELLURIQUE-TELLURIQUE ASSOCIE A LA MAGNETO-TELLURIQUE *

The magneto-telluric and telluric-telluric profiling techniques are presented, and then a new method which combines these two techniques for mapping a parameter defined as the “apparent pseudo-resistivity”. The results obtained for the uranium structures in the Cluff Lake district (Saskatchewan Canada) indicate the use of these different techniques in the detection of zones of conduction for surface zones and for deeper zones, and demonstrate the advantages of these methods over the usual electrical methods in problems of structural research.     

CONTROLE OPTIQUE DES TRAITEMENTS NUMÉRIQUES DÉCONVOLUTION OPTIQUE DES TRACES SISMIQUES *

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.     

INTERPRÉTATION DIRECTE DES COURBES DE SONDAGE ÉLECTRIQUE ET LE PROBLÈME DE DIFFÉRENTS DISPOSITIFS DE MESURE *

Direct interpretation methods of resistivity curves are discussed, which use the kernel function of the apparent resistivity. This function results from the consideration of the problem of diverse electrodes configurations. Several expressions for the determination of the kernel function of the potential from the kernel function of the apparent resistivity are given.     

THE INFLUENCE OF ELECTRICAL ANISOTROPY ON MISE À LA MASSE SURVEYS *

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.     

REFLEXIONS SUR LES APPLICATIONS DE LA TRANSFORMEE DE FOURIER EN SISMIQUE ET EN GRAVIMETRIE*

Numerous studies have already been carried out on the Fourier Transform and its geophysical applications. The utilisation of computers has brought with it the digitalisation of the major method, reflection shooting, and the different handling techniques for numerical data have given birth to numerous papers on the subject. Gravimetric surveying has always been a numerical method, but it is evident that for it, too, new possibilities have been opened. Consequently, gravimetric experts are becoming increasingly interested in the theory and applications based on the study of frequencies spectra using the Fourier Transform. The researches of C. A. Schwartz, W. Sokoloff and W. C. Dean have been followed by other interesting ideas concerning the data processing of gravity measurements, such as: calculation of the first vertical derivative (V. Baranov), interpretation of the anomalies with the aid of their spectra (M. E. Odegard and J. Berg Jr.), isopach reduction in gravimetric surveying (J. L. Bible), etc. All these ideas and techniques have the same purpose: to make the interpretation easier. But, although they have the same aim and tackle the same type of difficulty, it would seem that the gravimetric and the seismic experts have developed their own tools independently of each other, with no consideration for the fact that both geophysical methods, in particular the methods of treatment of raw measurements, are, if not identical, at least very close to one another and that, consequently, any improvement in one method may be useful to the other. The purpose of the present paper is to reconsider the philosophy of the seismic and gravimetric methods, starting with data recording, then dealing with the most important data processing systems and finally ending with the interpretation. The paper bases its approach on two points of view which are in fact complementary: – Although digital data processing is almost always effected in the functional sphere by convolutions, it is much easier to understand and to conceive these systems if one reasons alternately in the functional and frequency spheres; this is possible by using the Fourier Transform. – By considering the problem in frequencies, there is no fundamental difference between the seismic and gravimetric methods. A curve plotted in gravity units, as a function of the distance, and a seismic trace which represents the variations of the output of a galvanometer, as a function of the time, are identical from the point of view of the Fourier Transform. With these ideas in mind, the following problems are dealt with: – Seismic and gravity signals. – The sampling problem in gravimetry (data sampling rate non-constant). – Presentation and discussion of spectra of some synthetic and practical examples: ?Wave number filtering. ?Frequencies filtering. ?The problem of the frequency o (horizontal and vertical derivatives). ?Continuation = deconvolution. – Other applications of the Fourier Transform in gravimetry.     

SUR LA CORRELATION EXISTANT ENTRE POROSITE ET FAGTEUR DE FORMATION DANS LES SEDIMENTS NON CONSOLIDES*

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

MODÈLES ANALOGIQUES ÉLECTRONIQUES DU PROCESSUS D'EXPLOSION DANS LES ROCHES*

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=V_p/V_s 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.     

HOMOMORPHIC FILTERING — THEORY AND PRACTICE*

The application of homomorphic filtering in marine seismic reflection work is investigated with the aims to achieve the estimation of the basic wavelet, the wavelet deconvolution and the elimination of multiples. Each of these deconvolution problems can be subdivided into two parts: The first problem is the detection of those parts in the cepstrum which ought to be suppressed in processing. The second part includes the actual filtering process and the problem of minimizing the random noise which generally is enhanced during the homomorphic procedure. The application of homomorphic filters to synthetic seismograms and air-gun measurements shows the possibilities for the practical application of the method as well as the critical parameters which determine the quality of the results. These parameters are:

• a) the signal-to-noise ratio (SNR) of the input data
• b) the window width and the cepstrum components for the separation of the individual parts
• c) the time invariance of the signal in the trace.

In the presence of random noise the power cepstrum is most efficient for the detection of wavelet arrival times. For wavelet estimation, overlapping signals can be detected with the power cepstrum up to a SNR of three. In comparison with this, the detection of long period multiples is much more complicated. While the exact determination of the water reverberation arrival times can be realized with the power cepstrum up to a multiples-to-primaries ratio of three to five, the detection of the internal multiples is generally not possible, since for these multiples this threshold value of detectibility and arrival time determination is generally not realized. For wavelet estimation, comb filtering of the complex cepstrum is most valuable. The wavelet estimation gives no problems up to a SNR of ten. Even in the presence of larger noise a reasonable estimation can be obtained up to a SNR of five by filtering the phase spectrum during the computation of the complex cepstrum. In contrast to this, the successful application of the method for the multiple reduction is confined to a SNR of ten, since the filtering of the phase spectrum for noise reduction cannot be applied. Even if the threshold results are empirical, they show the limits fór the successful application of the method.     

PROCEDES DE FILTRAGE ET DE FOCALISATION DE CHAMP POUR LA DETECTION ELECTROMAGNETIQUE DES CARRIERES SOUTERRAINES *

The electromagnetic surface detection of underground quarries by classical methods becomes difficult when they are situated at depths greater than ten meters and when the thickness and conductivity of the superficial layers are irregular. The problem is tackled in two stages: at first using successive approximations, characteristics of the miscellaneous layers of a stratified medium are identified, and the quarries are then detected by observation of the conductivity changes of one of the lower layers. Computer interpretation, however, is necessary. The chances of detection of the quarries are considerably improved by a field localization method developed by us: computer interpretation is eliminated. The new aspect is an auxiliary transmitter which annuls the currents induced by the principal transmitter in the uppermost—generally more conductive—layers. The theoretical and experimental results show that the probability of detection of the quarries by this method are four times as high as by the classical one.