Doctoral Dissertations


"Transient spherical waves in a generalized Voigt model were investigated in this study. Both Laplace and fourier transform solutions of the spherical wave equation for a generalized Voigt model were obtained by means of the correspondence principle. Laplace transform solutions were inverted numerically into the domain for the study of the characteristics of the wave forms, and Fourier transform solutions were utilized for the analysis of frequency dependency attenuation in the models. Generalized Voigt models A and B in which a dashpot is connected in series with spring and dashpot components were unable to represent a solid which would simulate the real waves. The spherical wave parameters in the 4-element and 6-element models were shown to correlate with real waves as to wave shape and the r ate of attenuation of peak values at very short distances from the source. The major difference between real waves and the spherical waves of these models was the instantaneous arrival time in the latter as opposed to the much later arrival of real waves. A study of the dependency of attenuation on frequency in the 4-element and 6-element models was made. If a choice of the damping coefficients of the models is made, an attenuation exponent results which approximately a linear function of frequency range of seismic work. This is comparable with some published data"--Abstract, page ii.


Rechtien, Richard Douglas

Committee Member(s)

Clark, George Bromley, 1912-
Zenor, Hughes M., 1908-2001
Rupert, Gerald B., 1930-2016
Beveridge, Thomas R. (Thomas Robinson), 1918-1978
Wesley, James Paul


Geosciences and Geological and Petroleum Engineering

Degree Name

Ph. D. in Geophysics


University of Missouri--Rolla

Publication Date



xvi, 169 pages

Note about bibliography

Includes bibliographical references (pages 136-141).


© 1969 Liang-Juan Tsay, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Seismic waves
Seismic waves -- Mathematical models
Elastic wave propagation
Transients (Dynamics)

Thesis Number

T 2305

Print OCLC #


Electronic OCLC #