Theoretisghe Untersuchungen über den Einfluss der Verwitterungsschicht auf das Spektrum elastischer Wellen in der Reflexionsseismik
Heinz Menzel and Otto Rosenbach
Journal name: Geophysical Prospecting
Issue: Vol 5, No 3, September 1957 pp. 328 - 348
Info: Article, PDF ( 1.06Mb )
The following assumptions are made in the mathematical treatment of the problem. Below a plane earth's surface there is a three-layered elastic medium the interfaces of which are parallel to the earth's surface. The uppermost layer represents the weathered layer in which the velocity of propagation of seismic waves increases linearly with depth. The two lower layers, the so-called intermediate layer and the substratum each have a constant velocity. The surface of the earth is acted on simultaneously by a normal pressure N in the form of a Heaviside pulse. The seismic wave thus generated is propagated through the elastic media.
The aim of the investigation is to study the shape of the wave
1) in the intermediate layer, after the wave has entered it the first time
2) at the earth's surface, after the wave has been reflected once at the interface between the intermediate layer and the substratum.
The mathematical solutions can in both cases be expressed as series of Bessel functions. Some numerical examples illustrate the quasi-periodic nature of the solutions. The pseudo-frequency is determined by the gradient of velocity in the uppermost layer; it assumes a value of approximately 50 c.p.s. for a gradient of appr.