ONDE AMORTIE DE TYPE RAYLEIGH À L'INTERFACE DE DEUX MILIEUX SOLIDES À FORT CONTRAST DE DENSITÉS ET DE VITESSES*

Damped Rayleigh-type waves at the interface of two solid media with strong density and wave velocity contrast have been studied theoretically and experimentally with a two-dimensional model; plexiglas and brass were used as model materials.     

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.     

ESSAI D'UNE APPLICATION DE LA TRANSFORMATION DE KARHUNEN-LOÈVE AU TRAITEMENT SISMIQUE *

Multispectral recordings used for remote sensing are not without analogy with seismic records from CDP field set-ups. These seismic data may be regarded as “photographs’ of deep regions of the earth taken from various angles. The Karhunen-Loève (K.L.) transformation is commonly used for multispectral data processing, where it helps emphasize some features of remote sensing information. The same method may be applied to seismic data processing. Signal-to-noise ratio is improved on synthetic or field examples when K.L. transformation is applied instead of conventional CDP stacking. Residual statics seem to be diminished by a significant factor.     

CARACTERES DE ĽONDE ELECTROMAGNETIQUE DE SURFACE ENGENDREE PAR UN DIPOLE MAGNETIQUE *

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

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.     

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.     

EXEMPLES D'APPLICATION DE LA METHODE MAGNETOTELLURIQUE DE PROSPECTION GEOPHYSIQUE A L'ETUDE DE STRUCTURES OU DE FORMATIONS GEOLOGIQUES SITUEES SOUS UN TRES FAIBLE RECOUVREMENT*

Magneto-telluric radio frequency measurements can be developped in shallow applications in civil engineering, mining exploration hydrogeology and even archeology. In the V.L.F. and L.F. ranges the depths usually encountered range from 4 or 5 meters to nearly 50 meters. Specially designed equipment allows rapid work—in some cases even continuous profiling. Field data obtained over a fault, a cavity, and sedimentary ore deposits agree well with data from conventional electric surveys.     

LA GRAVIMETRIE DE HAUTE PRECISION APPLICATION AUX RECHERCHES DE CAVITES*

High precision gravity surveys have to be examined at different points of view: the accuracy which one can expect on the final results, regardless to their distribution, the shape and amplitude of the expected anomalies, depending on these factors, which grid of stations is convenient in each particular case. Under certain condition, using an appropriate procedure, involving strict criteria, it is possible to get on the Bouguer map the same accuracy as the reading one. However an accuracy closed to 0,01 mgal does not imply that anomalies as 0,01 or 0,02 mgal deserved attention. Numerous factors limit our appreciation of significant anomalies to 0,05 mgal, may be a little less. When cavites are concerned, it is always necessary to define the extreme dimensions an depth of volumes which may give detectable anomalies. Some example are given illustrating different aspects of this particular type of geophysical prospecting.     

TECHNIQUE DE MESURE ET D'INTERPRETATION MINIMISANT LES ERREURS DE MESURES EN MICROGRAVIMETRIE*

Different sources of error influence gavity surveys, particularly shallow “micrograuity” sur-veys. Experiments show that. the most frequent source of error in gravimetric prospecting is bad estimation of drift. Better control of drift exists with the field procedure and interpretation technique developed by the authors, as can be shown theoretically as well as experimentally. The method implies a random or semi-random spatial sequence of measurement points. A real case of field prospecting is described.     

REMARQUES SUR L'INTERPRETATION DES SONDAGES DE POLARISATION PROVOQUEE ESSAI DE THEORIE QUANTITATIVE *

The transient phenomena associated with induced polarization are very complex and it is necessary to have both a proper understanding of the physical processes and a good supply of mathematical aids in order to make any advance in the quantitative interpretation of I.P. surveys. The analogy between the classical electrical sounding method and the induced polarization sounding method has led a number of workers to interpret the results of the latter like the results of the former. To clarify this idea, it seems very interesting to calculate a mathematical model in order to know the form of the anomaly that can be probably expected. The case of a thin horizontal polarizable layer, with the same uniform and isotropic conductibility as the homogeneous background, has been studied in this paper. The result of the calculation for the case of a single current electrode and a single potential electrode is given. From these data, the theoretical curve of IP sounding using the Wenner electrode array is computed. The master curve is compared with experimental curves obtained on scale models. A good correlation between these curves is noticed. In addition, it can be concluded that the mathematical model is proving the validity of the experiments on interpretation scale models.     

DETERMINATION DE L'IMPULSION SISMIQUE*

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

LES COURBES DAR ZARROUK ET LES SONDAGES DIFFÉRENTIELS DE RÉSISTIVÉ*

Differential and difference soundings of resistivity for real, imaginary and complex values of the newly introduced parameters ν and μ are considered. The transverse and longitudinal differential soundings, known up to the present, correspond with the values ν= 1 and ν=— 1. The point of departure is the generalization of the concept of Dar Zarrouk parameters and the dimensional analogy between D.Z. resistivity and transverse and longitudinal differential resistivities. Properties of generalized D.Z. curves as well as the method of their construction are given. The examples of differential and difference curves are presented and the properties of these curves are discussed; particulary the effective spacings are determined. The problems of the realization of differential and difference soundings are considered; the bisymmetrical and asymmetrical arrays are proposed as a practical ones.     

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.