Kinematics of refracted and reflected waves in inhomogeneous media with non-planar interfaces

Zusammenfassung Es werden die Grundbeziehungen für die Berechnung von Strahlen seismischer Wellen in inhomogenen Milieus abgeleitet, in denen die Geschwindigkeit allgemein von drei krummlinigen Koordinaten abhängt. Die angeführten Beziehungen stellen ein System von gewöhnlichen Differentialgleichungen erster Ordnung dar. Die numerische Lösung dieses Systems bietet eine Möglichkeit, die Strahlendiagramme, Laufzeitkurven und Isochronen für die gegebenen Geschwindigkeitsmodelle zu konstruieren. Aufmerksamkeit wird ebenfalls dem Einfall der Strahlen auf eine unebene Grenzschicht gewidmet. Die Beziehungen für die Berechnung reflektierter und refraktierter Strahlen werden abgeleitet. Anhand der abgeleiteten Beziehungen werden Strahlendiagramme und Laufzeitkurven für eine Geschwindigkeitsverteilung berechnet, die durch die vorläufige Interpretation der Ergebnisse von seismischen Tiefensondierungen am tschechoslowakischen Teil des Profils VI gewonnen wurden.     

The theory of motion of the horizontal pendulum with a Zöllner suspension and some indications for the instrumental design

Summary The aim of this paper is to examine the physical laws which govern the motion of a horizontal pendulum, mounted with the familiar Zöllner suspension geometry and to establish the equations of its motion. It is possible in this process to determine calibration parameters with greater precision and confidence and to demonstrate that procedures based upon period measurement can inherently claim a precision superior to some modern alternatives. Moreover in approaching the problem from a theoretical viewpoint it is possible to pinpoint those features of design which give rise to the troublesome aberrations. This facility makes it possible to comment upon design improvements so that a closer approach may be made to an ideal instrument.     

Eine Eichmethode für die Askania Erdgezeiten-Registrieranlage mit dem Galvanometer

Summary The scale-value switch (Fig. 1) makes it possible to calibrate even the older Askania tidal equipment with a galvanometer at a reduced scale-value. If resistors R ₂ and R ₃ are selected as shown in Eqs(4) and(5), the ratio of reduction of the scale value1/n does not depend on the internal resistance of the photo-cell in the gravimeter. The resistance of the recording galvanometer R ₄ must be determined with an accuracy of±1% in order to obtained an accuracy of±0.5%. Together with the reduction in scale value also the damping is considerably decreased, which enables the time, required for calibration, to be cut down considerably.     

Use of Poisson's integral in calculating higher vertical derivatives of harmonic functions — Part 1

Summary The higher vertical derivatives of harmonic functions, expressed by Poisson's integral, are calculated for an infinite plane. The properties of the higher derivatives of the kernel of the integral are investigated and a method of calculation is proposed, which partly eliminates the negative effect caused by their oscillation.     

An analytical migration method for crustal wide angle reflections

Summary An analytical migration method is developed for inverting wide angle seismic reflection travel time data with proper migration. In this method the concept of effective velocity (V _eff ) in the vertically inhomogeneous earth has been used, which takes into account the refraction effect. It is shown that the migration process in this case becomes extremely rapid as curved ray paths are replaced by equivalent straight paths. A post migration sliding correction is found to be necessary, which arises due to the non-collinearity of the recording point, reflection point and the image point in the equivalent straight path geometry for dipping reflectors. Calculations for some representative dips show that, for the depths and recording ranges of interest in DSS, the vertical component of the sliding correction is negligible compared to the horizontal component. However, even the horizontal component is not significant for reflectors with gentle dips. The effect of certain simplifying assumptions in the estimation of V _eff is shown to be within the error limits of velocity determination. A computer programme package has been written for carrying out the migration. The method yields more accurate results in various theoretical and field cases than the conventional graphical wave front methods which are at present widely used for crustal reflection work.     

Laboratory investigations on fault plane induced tensile cracks

Summary Tensile cracks induced by stress concentration around a fault plane in physical models under uniaxial load were analyzed. The results characterizing the decisive role of the fault plane inclination to the the stress direction are presented. Two stages of tensile crack life were determined, i.e. the first, seismoactive stage, accompanied by seismic energy release and the second aseismic one characterized by low velocity of crack propagation. Results obtained seem to be relevant to a better understanding of the character and regime of actual seismoactive faults.     

Anomalous behaviour of seismic waves at an interface between anisotropic media

Summary An account of possible anomalous effects in reflection and refraction of elastic waves at an interface between anisotropic media is presented. These effects are due to anisotropy and they cannot occur at an interface between isotropic media. The shape of the slowness surface (its local deviations from spherical symmetry) is the decisive factor for appearance of these effects. A numerical example of such anomalous behaviour of elastic waves at a free boundary of the crystal of spinel is presented.