^0 S. D. Shushakov 



seismograms. In the calculations no allowance was made for absorption of 

 seismic wave energy (the media are regarded as ideally elastic). In the case 

 under consideration, moreover, we are treating the covering medium, for 

 convenience in calculation, as possessing the properties of a liquid (transverse 

 vibrations are not excited in it), and we do not make allowance for the 

 dependence of the coefficients of reflection on the ratio of longitudinal to 

 transverse wave velocities in the medium covering the lower reflecting layer. 

 However, even in this case the formulas obtained express a compHcated 

 relationship between the intensity of the multiple waves and the ratio 

 between longitudinal and transverse velocities and wave resistances in the 

 media indicated. Fig. 10 shows graphs obtained by modelling seismic waves. 

 These graphs express the relationship between the intensity of waves 

 reflected twice from various thin layers covered by water, and the angle of 

 incidence. 



From theoretical calculations and experimental observations it follows 

 that with small angles of incidence the intensity of the multiple reflections 

 increases as the absolute values of the difference between wave resistances 

 in the reflecting layer and the covering medium increase. In the case of 

 a thin reflecting layer this intensity depends on the thickness of the reflecting 

 layer to a greater extent, the greater the difference between the wave resistances 

 in this layer and in the underlying medium. 



Damping — Little work has yet been done on the study of the variation 

 in intensity of multiple reflections as a function of the distance from the 

 source and of the number of multiples. Investigation of this relationship 

 by the modelling method has yielded the following results. The intensity 

 of multiple reflections in the case of thin reflecting layers has a complex 

 relationship with the angle of incidence. Individual intensity peaks stand 

 out against a general background of damping. The greater the differences 

 between the wave resistances in the media separated by the reflecting surfaces, 

 the greater the amount of overall damping and the more strongly do the 

 intensity peaks stand out. A characteristic feature of double reflected waves, 

 for example, is the existence, in many cases, of one extra minimum and 

 one extra maximum at angles of incidence ranging from 10° to 30° 

 (Fig. 10). 



When the difference between the wave resistance in the reflecting layer 

 and that in the covering medium is not great, the curve representing the 

 damping of the multiple waves distance from the source is found to have 

 a wavehke form (Fig. 10). This is because of the periodicity of the function 

 which expresses the dependence of the reflection coefficient on the angle 

 of incidence <^) and also because of certain other characteristics of reflections 



