ALBERT

Notes: The widespread use of common depth point techniques has emphasized the need for accurate static corrections. Manual interpretation methods can give excellent results, but a computer technique is desirable because of the great volumn of data recorded in common depth point shooting. The redundancy inherent in common depth point data may be used to compute a statistical estimate of the static corrections. The corrections are assumed to be time-invarient, surface-consistent, and independent of frequency. Surface consistency implies that all traces from a particular shot will receive the same shot static correction and all traces from a particular receiver position will receive the same receiver correction.Time shifts are computed for all input traces using crosscorrelation functions between common depth point traces. The time shift for each trace is composed of a shot static, a receiver static, residual normal moveout if present, and noise. Estimates of the shot and receiver static corrections are obtained by averaging different sets of the measured time shifts. Time shifts which are greatly in error are detected and removed from the computations.The method is useful for data which has a moderate to good signal to noise ratio. Residual normal moveout should be corrected before estimating the statics. The program estimates the statics for correctly stacking common depth point traces but it is not sensitive to constant or very slowly changing static errors.

Notes: Spurious reflections showing a residual move-out are generally present on both corrected seismic cross-sections and common depth point composites.We propose to determine a space-time filter satisfying the following conditions: to attenuate as much as possible reflections presenting a given move-out, to retain intact reflections whose time gradient is zero (or has a predetermined value), to be applicable efficiently even to a small number of traces, not to amplify random noise unduly.After briefly indicating the design principle of these filters, we shall give the results of their application to the theoretical examples, in order to bring out: the influence of sampling interval and filter length (possibility of achieving efficient filtering using an apparatus with a small number of terms), the effect of filtering on dipping reflections (reduction in amplitude and distortion increasing with the time gradient), the range of reflection move-out that can effectively be filtered with the same apparatus, the disturbing influence of random noise.〈section xml:id="abs1-2"〉〈title type="main"〉RESUMEOn constate généralement, tant sur les films sismiques corrigés que sur les résultats de couverture multiple, la présence de réflexions parasites présentant une courbure résiduelle d'indicatrice.Nous nous sommes proposé de déterminer un opérateur de filtrage spatio-temporel satisfaisant aux conditions suivantes: filtrer le plus possible les réflexions présentant une courbure donnée, conserver intégralement les réflexions dont le gradient temps est nul (ou a une valeur déterminée), pourvoir être appliqué efficacement à un petit nombre de traces, ne pas amplifier outre mesure les bruits inorganicés.Après avoir indiqué brièvement le principe du calcul de ces filtres, nous présenterons les résultats de leur application à des exemples théoriques, afin de mettre en évidence:ľ'influence du pas d'échantillonnage et de la longueur du filtre (possibilityé d'obtenir un filtrage efficace avec un opérateur comportant un petit nombre de termes),ľ'effet du filtrage sur les réflexions pentées (réduction d'amplitude et distorsion croissant avec le gradient temps),ľ'ouverture de ľ'éventail des réflexions courbes que ľ'on peut filtrer efficacement avec un même opérateur,ľ'influence perturbatrice de bruits inorganicés.

Notes: It was found in Part I of this paper that approximating the sharp cut-off frequency characteristic best in a mean square sense by an impulse response of finite length M produced a characteristic whose slope on a linear frequency scale was proportional to the length of impulse response, but whose maximum overshoot of ±9% was independent of this length (Gibbs' phenomenon). Weighting functions, based on frequency tapering or arbitrarily chosen, were used in Part II to modify the truncated impulse response of the sharp cut-off frequency characteristic, and thereby obtain a trade-off between the value of maximum overshoot and the sharpness of the resulting characteristic. These weighting functions, known as apodising functions, were dependent on the time-bandwidth product Mξ, where 2ξ, corresponded to the tapering range of frequencies.Part III now deals with digital filters where the number 2N–1 of coefficients is directly related to the finite length M of the continuous impulse response. The values of the filter coefficients are taken from the continuous impulse response at the sampling instants, and the resulting characteristic is approximately the same as that derived in Part II for the continuous finite length impulse response. Corresponding to known types of frequency tapering, we now specify a filter characteristic which is undefined in the tapering range, and determine the filter coefficients according to a mean square criterion over the rest of the frequency spectrum. The resulting characteristic is dependent on the time bandwidth product Mξ= (N–1/2)ξ up to a maximum value of 2, beyond which undesirable effects occur. This optimum partially specified characteristic is an improvement on the previous digital filters in terms of the trade-off ratio for values of maximum overshoot less than 1%. Similar to the previous optimum characteristic is the optimum partially specified weighted digital filter, where greater “emphasis is placed on reducing the value of maximum overshoot than of maximum undershoot”. Such characteristics are capable of providing better trade-off ratios than the other filters for maximum overshoots greater than 1/2%. However these filters have critical maximum numbers 2.NC–1 of coefficients, beyond which the resulting characteristics have unsuitable shapes. This type of characteristic differs from the others in not being a biassed odd function about its cut-off frequency.

Notes: In Part I of this paper, we examined the properties of the best mean square approximation to the sharp cut-off frequency characteristic by an impulse response of finite length. It was found that the sharpness of cut-off for the resulting frequency characteristic depended on the length of the impulse response–but because of the discontinuous nature of the specified frequency characteristic, this best mean square approximation always had a maximum overshoot of ± 9%, independent of the length of the impulse response (Gibbs phenomenon).In Part II, we investigate ways of reducing this ± 9% overshoot at the expense of a reduced sharpness of cut-off. The discontinuous frequency characteristic is first approximated by a continuous characteristic with linear or cosine frequency tapering. The impulse response for such tapered characteristics consists of the impulse response of the discontinuous frequency characteristic weighted by a certain function corresponding to the type of tapering employed. The best mean square approximation to the tapered characteristic by an impulse response of finite length M will produce a frequency characteristic whose properties are now dependent on the time-band width product Mζ, where 2ζ is the tapering range.A trade-off exists between the maximum overshoot and the sharpness of cut-off for the resulting characteristic for both forms of frequency tapering. Instead of considering other forms of tapering in the frequency domain, we now investigate arbitrarily chosen weighting functions in the time domain to determine the minimum length of impulse response for a minimum value of maximum overshoot and a maximum value of sharpness of cut-off.Part III will discuss the digital realization of the above finite length impulse responses together with the optimum partially specified digital filter approximation to the desired frequency characteristic.

Notes: Book reviewed in this article:Le Filtrage en Sismique, Tome IJ. AUBOUIN “Geosynclines” (Developments in Geotectonics 1). Elsevier Publishing CompanyEarth and Planetary Science Letters Vol. 1. Nr. 2H. Ramberg Gravity, Deformation and the Earth's Crust Academic Press“Potassium Argon Dating” Compiled by O. A. Schaeffer and J. Zähringer

Notes: Deep seismic sounding was performed along two profiles which cross at the Dinarides area right angles. One of the profiles goes far into the Adriatic Sea.Besides considerations on the lithophysical conditions, characteristics of the registered waves are analysed. The amplitude curves and curves of amplitude ratios are shown. Special attention was paid to the frequency of the registered waves.In order to obtain a better knowledge of the registered wave pattern three-component recordings of waves were carried out. The analysis of the records obtained is given, with particular regard to the possibility of creating converted waves.The Earth's crust structure along the profiles II and III is given.

Notes: Nomograms for solving equations in multilayer and dipping layer cases are presented. The nomograms constructed are used to solve the following equations: I. Intercept-time formula. 2. Critical distance formula. 3. Critical angle formula. 4. Critical angle and dip angle formula. 5. Vertical depth formula.

Notes: According to a study of seismic velocities in the Alpine Foreland of Eastern Switzerland, the initial velocity is rather high in comparison with other Tertiary basins and shows an exceptionally high increase rate. When analysing the average and the interval velocities, especially of Tertiary strata, and when comparing them with velocities of strata of the same age and a very similar facies of the Northern Rheintalgraben, it has been found that the increase of velocity is closely related to the distance to the Subalpine Molasse. The conclusion is that the velocity of the Tertiary strata is strongly influenced by the folding pressure of the Subalpine Molasse or of the Alps. The same method has been applied to a relatively large number of wells in the area of the “German Molasse”. Not only the results in Eastern Switzerland have been confirmed, but also it has been proved that the diagenesis of the Tertiary strata and, hence, their velocities are influenced only partially by the specific depth of the basin. Velocities increase towards the Folded Molasse or the Alps. Consequently they depend on lateral folding pressure, which decreases from west to east with the increasing width of the basin. The tertiary strata of the basin have been affected by lateral folding pressurefrom south to north. However, structures with lateral compression have not been discovered yet in the German Alpine Foreland.