ALBERT

Notes: Since 1955, the continuous velocity measurements in bore holes, made with one, later with more receivers, have become indispensable for the geophysicist, and can be useful to the geologist and the production engineer. From the beginning we have found that the amplitudes of the signals received vary in the course of a single operation. The variations have for a long time been considered as a disturbing phenomenon. It was tried to suppress them by changing the instrument gain.With increasing precision of the velocity measurements we have sometimes observed anomalies that were hard to explain, discrepancies between the continuous velocity logs and the conventional well velocity survey, as well as between continuous velocity measurements made with different spacings. These phenomena could be observed in cased as well as in uncased holes. The first attempts to explain these phenomena by considering the velocities only, did not lead to an acceptable theory. A further study of these anomalies of the continuous velocity log has shown that in reality they were caused by strong variations of the amplitude which affected the velocity measurements. This result has led us to study the amplitude variations in open as well as in cased holes.Up to now, the characteristics of the apparatus used in France and in the Sahara have permitted amplitude measurements with a single receiver only. In addition to the “cement bond log” in cased holes, it seems that in open holes correlations can be observed between the measured amplitude and a) the lithology; b) the fluid contained in the pores; c) the continuity of the matrix or, conversely, the permeability. However, it is now certain that numerous factors affect the amplitudes of the signals simultaneously.In order to study the attenuation of ultrasonic waves in the different formations traversed by a deep well, we have studied the deformations of the signal in the course of its path in the mud and in the formation, restricting ourselves to the P waves. The factors to be taken in consideration are: a) the geometric energy dispersion, inversely proportional to the square of the distance from the source; b) attenuation by absorption and scattering in the mud and in the formation; c) the transmission coefficients at the transition from mud to formation and conversely, as well as at the transition between two formations having different velocities; d) phenomena of signal composition that are due to the fact that the receivers and the transmitters have a non-infinitesimal length; these last mentioned phenomena have considerable influenc eon the amplitudes of the received signals.Finally, the practical method for obtaining an attenuation log in an open hole requires the measurement of the ratio of the amplitudes of the first arrivals at the two receivers. Some examples show the importance of amplitude measurements made with two receivers.

Notes: Parmi les différents facteurs agissant sur l'amplitude des signaux acoustiques enregistrés au cours des mesures continues de vitesse dans les puits, le coefficient d'atténuation semble présenter beaucoup d'intérêt pour la détermination des qualités mécaniques des roches, en particulier la continuité de la matrice, donc dans une certaine mesure la perméabilité.Afin d'éliminer les facteurs secondaires agissant sur l'amplitude, nous avons été amenés à enregistrer le rapport des amplitudes aux deux récepteurs de la sonde C.V.L. Nous avons donc étudié un appareil permettant d'enregistrer les amplitudes des premières arrivées aux deux récepteurs, ainsi que le rapport de ces amplitudes.Nous présentons ici les premiers résultats obtenus par la mesure continue de l'atténuation des ondes acoustiques dans différents types de formations. Des comparaisons sont faites avec les diagraphics de vitesse, de résistivité et de radioactivité.Le log d'atténuation semble permettre la détermination de la lithologie et plus particulièrement la localisation des zones fracturées et perméables. Bien que nous n'ayons que peu d'expérience de ce nouveau type de diagraphie, il nous semble que les premiers résultats obtenus soient très prometteurs.

Notes: Until such time as digital seismic recording techniques are in widespread use in the field and partly because it cannot afford digital equipment, C.E.P. has decided to build a processing system which can digitize and process seismic information in analog form on magnetic tapes.C.E.P. was prompted to adopt the digital technique to enable it to proceed with its stratigraphical investigations, starting with the elaboration of synthetic records and followed by the study of signals and deconvolution.Though the analog form of recording is not too suitable for digital processing owing to its low dynamic range, it seemed to us that it was nevertheless perfectly feasible to enhance the analog information by processing it digitally through an automatic computer.This approach to the problem of data enhancement is more satisfactory than the (conventional) analog method, which is more complicated and less accurate.〈list xml:id="l1" style="plain"〉The digital processing system comprises:a magnetic playback systema two-channel reproduction devicean analog-digital convertera 1620 IBM computeran automatic plotting device for graphical presentation of results.Examples of different processing forms are presented:〈list xml:id="l2" style="plain"〉cancellation of A.G.C. actioncomputation of seismic signaldeconvolutioncorrelation techniquesanti-singingstudy of the response of the various items of equipment.We have come to the conclusion that very interesting results have been obtained in spite of the low dynamic range of the analog tapes.With this equipment it is possible to study and process the data in digital form and compare results with those obtained by analog processing. Also, the experience gained will be very useful when digital field crews start operating.Unfortunately, it is not possible for the time being to operate the equipment on a commercial production basis, but only to develop working methods, to conduct short studies or to guide and control analog processing techniques.At present our efforts are therefore aimed at shortening the time required for processing and plotting.

Notes: Let G be a locally compact group, which need not be unimodular. Let x→U(x) (x∈G) be an irreducible unitary representation of G in a Hilbert space H(U). Assume that U is square integrable, i.e., that there exists in H(U) at least one nonzero vector g such that ∫||(U(x)g,g)||2 dx〈∞. We give here a reasonably self-contained analysis of the correspondence associating to every vector f∈H(U) the function (U(x)g,f) on G, discussing its isometry, characterization of the range, inversion, and simplest interpolation properties. This correspondence underlies many properties of generalized coherent states.