Inaug.-diss.--Göttingen. / Lebenslauf. Extracted from Beiträge zum geophysik, v. 10. Includes bibliographical references.

Inaug.-diss.--Göttingen. / Lebenslauf. Extracted from Beiträge zum geophysik, v. 10. Includes bibliographical references.

Inaug.-diss.--Jena. / Lebenslauf.

A method for the estimation of impedance or pseudo-velocity sections from the information contained in CMP stacked sections, the corresponding stacking velocities and sonic and density logs (when available) is presented. The method relies on a linear programming approach for the reconstruction of full-band reflectivities, and utilizes linearized relations between the multiple free reflectivity functions and average or point-wise impedance or velocity values. The reconstruction procedure requires the solution of an underdetermined set of equations and hence a minimum structure condition is imposed on the desired solution. This condition guaranties the uniqueness of the obtained solution in the sense that it is the solution that features the least amount of impedance variations as a function of travel-time (or depth). Since the presented inversion yields minimum structure solutions, it is argued that features which appear on the obtained result are strictly demanded by the data and are not artifacts of the inversion scheme. A number of physical assumptions are required by the presented inversion. These are summarized below in point form: (1) The earth reflectivity function is non-white and can be reasonably represented by a sparse spike train. (2) The observed CMP stacked section is a reasonable representation of the multiple-free normal-ray section with reasonably correct relative amplitude relations. (3) The residual wavelet on the stacked section is to a good approximation a zero-phase wavelet with a relatively flat spectrum. (4) The estimated stacking velocities can be inverted to yield an acceptable representation of the averages of the true earth velocity model. Since in a realistic environment some of the above assumptions may be violated, all the corresponding relations in the presented inversion scheme include appropriate uncertainty terms. That is, all the information components considered in the inversion are satisfied only to within some prespecified error bounds. A number of possibilities for speeding up the inversion scheme are described. It is shown that utilizing the expected trace-to-trace coherency of seismic reflection data yields considerable reduction in computational efforts. Finally, a number of steps required for a successful completion of the inversion are described. In particular, the problems of preinversion data scaling and the correction of the residual wavelet's phase are discussed in some detail. / Science, Faculty of / Earth, Ocean and Atmospheric Sciences, Department of / Graduate

Typescript. / Bibliography: leaves [108]-118. / xiii, 118 l illus., maps, tables

Inaugural-Dissertation--Göttingen.

The first cycle of seismic waves recorded at distances of 45, 300 and 355 km. from the GNOME nuclear explosion was used to determine whether the near source wave characteristics at 0.3 km. could be determined from distance measurements. Both head wave and body wave propagation were considered. First the recorded signals at distance were inversely propagated back to the near source region as head waves, and secondly, the measured source at 0.3 km. was propagated out to 300 km. from the source as a body wave. In both cases, restricted comparisons between theory and observation can be made, but the comparison appears to favor the body wave type of propagation. More research is needed to make a more conclusive choice between the two modes of propagation. Methods were developed which can be used to determine source motion from distance measurements when the data are sufficient to do so. / Graduation date: 1965

The vertical and radial components of a seismic P wave can be decomposed by a Fourier transform into two sets of nonterminating sinusoidal waves with one set for each component. The tangent of the vertical transform divided by the radial transform gives by definition he apparent angle of emergence for that frequency. The actual angle of emergence can be calculated from the apparent angle. The change of the angle with frequency can be obtained by determining the angle over the entire frequency spectrum of the pulse. The angle of emergence is only defined for a pure pulse. Just the short length of uncontaminated signal can be used to calculate the angle U the signal is interfered with by other signals. The actual angle of emergence was calculated as a function of frequency for stations near nuclear explosions. In all cases, the angle varied with frequency. / Graduation date: 1967

The character of the primary seismic wave in the range of distances between 100 and 600 km is affected by such factors as the nature of the source, exponential attenuation, crustal structure, type of wave propagation, recording site geology and instrument response. The first arrivals from the GNOME and SHOAL nuclear explosions were analyzed to show the important effects of the above factors. Crusta1 structures were developed to examine the type of wave propagation, geometrical attenuation, and Q versus depth structure. Within the frequency bands delineated by the instrument response, above 2 cps, and the reliable source energies, exponential attenuation and surface geology explained the major spectral variations in the first arrivals. Amplitude variations were explained almost entirely by geometrical and exponential attenuation. Techniques for measuring exponential attenuation were developed and applied. The Q values obtained were primarily between 100 and 200. / Graduation date: 1968

Graduation date: 1966