COMPATIBILITE ENTRE LA COMPRESSION DE L'INFORMATION SISMIQUE ET SON TRAITEMENT*

Some time ago, we described and implemented two methods of seismic data compression. In the first method a seismic trace is considered as being the convolution of a distribution made up of the trace peak values with a Gaussian pseudo-pulse. The second method is performed through a truncation of the sequential (Walsh, Paley or Haar) spectrum of each trace. In this paper it is shown that neither method has adverse effects on quality when traces with their information compressed undergo conventional data processing, such as stacking and deconvolution.     

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.     

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.     

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.     

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.     

APPLICATION OF THE PARTIAL KARHUNEN-LOÈVE TRANSFORM TO SUPPRESS RANDOM NOISE IN SEISMIC SECTIONS1

The Karhunen-Loève (K–L) transform is an effective technique for suppressing spatially uncorrelated noise, but because of its high computational cost, fast transforms, such as the Fourier transform, have been more favoured. Two techniques that combine to make the K–L transform feasible for seismic data processing are discussed. The first technique filters the data for limited dips. For each dip, linear moveout is applied to the seismic sections so that events with this dip are made flat. By interpolation, we can include dips that are fractions of a sample/trace. After linear moveout, zero-lag K–L filtering is applied followed, by inverse linear moveout; the results from all dips are added to form the final filtered data. The second technique is blocking, in which the seismic section is divided into blocks small enough for each block to be processed using relatively small matrices; the processed blocks are assembled to form the final filtered section. Using a combination of these techniques, seismic sections can be filtered at a reasonable cost using the K-L transform.     

APPLICATION DU FILTRE DE KALMAN A LA NAVIGATION*

This paper is concerned with an application of the Kalman filter to integrated navigation systems. It is shown that this filter is well adapted to resetting the dead-reckoning position by means of a radio-hyperbolic system or of a Doppler sonar. The algorithm can also be used for resetting the dead-reckoning position by means of a satellite navigation system. The first part is briefly concerned with stochastic processes and system theory. The canonical equations for navigation problems are written. The second part is devoted to the Kalman filter. The third part discusses the application of the algorithm to navigation problems and presents some simulation results.     

ESSAI DE FILTRAGE NON-LINEAIRE APPLIQUE AUX PROFILS AEROMAGNETIQUES*

Digital aeromagnetic profiles recorded with a high accuracy can be filtered with an electronic computer. Linear filtering is not very efficient, because the frequency spectrum of a given anomaly is very wide. But other methods are possible which, through a step by step analysis of the profile, leave some categories of anomalies unaltered while they remove the others completely. Our method uses as a criterium the width of the anomalies; it distinguishes and processes differently “bell-shaped” and “multi-legged” anomalies. Some examples of the use of the method are shown.     

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.     

SIGNAL-TO-NOISE RATIO ENHANCEMENT IN MULTICHANNEL SEISMIC DATA VIA THE KARHUNEN-LOÉVE TRANSFORM*

The Karhunen-Loéve transform, which optimally extracts coherent information from multichannel input data in a least-squares sense, is used for two specific problems in seismic data processing. The first is the enhancement of stacked seismic sections by a reconstruction procedure which increases the signal-to-noise ratio by removing from the data that information which is incoherent trace-to-trace. The technique is demonstrated on synthetic data examples and works well on real data. The Karhunen-Loéve transform is useful for data compression for the transmission and storage of stacked seismic data. The second problem is the suppression of multiples in CMP or CDP gathers. After moveout correction with the velocity associated with the multiples, the gather is reconstructed using the Karhunen-Loéve procedure, and the information associated with the multiples omitted. Examples of this technique for synthetic and real data are presented.     

NOUVELLE METHODE DE RESTITUTION D'UN HORIZON REFRAGTEUR PAR SISMIQUE REFRACTION*

The purpose of this report is to show a method of determining the top of a refractor departing from the times and slopes of the direct and inverse dromocrones. The method does not need topographical correction and can be applied without knowledge of the distance between the geophone and the shot point. These results having been obtained, the commonly accepted point of view is upset: instead of looking for two points on the surface corresponding to one point of the refractor, we try to etablish, starting with only one point from the surface, the two corresponding points from the top of the refractor. This method can be applied to isolated points and does not demand interpretative hypotheses of any kind, excluding the velocity evaluation of the overburden and of the refractor. The necessary calculations can be easily executed by means of a digital computer to which the dromocrone times and the distances between the geophones must be given. These calculations can also be executed by a person having no knowledge of refraction seismology. This report also examines the validity of the approximations involved in the method proposed.     

LA RESISTIVITE APPARENTE COMME TRANSFORMATION LINEAIRE DU POTENTIEL ET LA TRANSFORMATION INVERSE*

The apparent resistivity is considered as a linear transformation of the potential by an operator in the form of an infinite matrix A. The inverse transformation expresses the potential as a function of the apparent resistivity or of the difference of potentials. It is found by calculation of the inverse matrix^-1A. The relation between apparent resistivities for different arrays is expressed as a product of transformations.     

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.     

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.     

MESURES SISMIQUES PAR TRANSMISSION—APPLICATION AU GENIE CIVIL *

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.     

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.     

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.     

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.     

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.