Chapter 1 



INTENSITIES OF REFRACTED AND REFLECTED 



LONGITUDINAL WAVES AT ANGLES OF INCIDENCE 



BELOW CRITICAL 



V. P. GORBATOVA 



The dynamic properties of waves can be effectively utilized in interpreting 

 seismic prospecting data, since these properties, in conjunction with the 

 velocity components enable us to recognize the nature of any particular 

 Avave recorded on the seismogram. 



The solution of problems connected ^vith the dynamic propagation of 

 waves presents difficulties which are well known. While part of the work 

 done in this field by Petrashen' and the team of mathematicians headed 

 by him has already been published, the theory which we have in mind has 

 been fully worked out only for ideally elastic horizontally laminated media. 



Each of the layers is presumed to be sufficiently "dense", that is to say 

 the travel time of a disturbance in the layer is substantially longer than the 

 duration of the pulse transmitted. The velocity of propagation of longi- 

 tudinal and transverse waves, however, as well as the densities, is constant 

 inside the layer and assume new values on the boundaries of the layers. 



Quantitative comparisons made up to date have not revealed any sharp 

 discrepancy between theory and experiment. The theoretically discovered 

 qualitative laws also show good agreement with seismic prospecting practice. 

 We suggest that there would be undoubted advantage in introducing the 

 theory, in the form in which it has been worked out to date, into the inter- 

 pretation of field data. 



A method for calculating the intensities and shapes of seismic traces for 

 different waves propagated in media with plane -parallel boundaries has been 

 worked out in detail in the Leningrad Section of the Institute of Mathematics 

 (Academy of Sciences of the U.S.S.R.) '-^'^K The Section has also compiled 

 tables for fairly accurate calculations. 



In this paper we offer a number of simpHfied methods for determining 

 the intensities of purely longitudinal waves (in the media referred to) and 

 ■discuss how the different parameters of the medium affect their frequency 

 rate. 



11 



