MULTIPLE REFLECTED WAVES 83 



been studied by modelling thin reflecting layers, since such layers are often 

 encountered under natural conditions. It has been shown that if the 

 predominant frequency of single reflections in poorly absorbent media 

 increases with distance from the source as the wave divides into its component 

 parts, the predominant frequencies of multiple waves can increase — some- 

 times after a slight decrease — for the same reasons, but at considerably 

 greater distances from the source. The same thing is observed when the 

 number of multiples increases. 



At great distances from the source the subdivision into groups of 

 componental oscillations starts further from the source the greater the 

 number of multiples. At first there is a sharp dechne in the predominant 

 frequency, which then rises as soon as the number of multiples increases. 

 In general, the rise in frequency in poorly absorbent media in which the 

 vibrations suffer a change of intensity and shape depending mainly on the 

 divergence of fronts and on interference from these waves is more pronounced 

 when the distance from the source increases at the same time as the number 

 of multiples. This effect becomes neghgible as the wave velocity in the 

 reflecting layer increases. 



The predominant frequencies of single and multiple waves rise sharply 

 with distance from the source on passing through the points of origin of 

 head waves when the low-frequency components belonging to the head 

 waves separate out from the summed vibrations. Johnson, using data 

 obtained in California, shows that when the number of multiples increases 

 at small distances from the point of origin, the traces of multiple reflections 

 from a thin layer of basalt keep their shape. This agrees only with the results 

 obtained from model experiments or with a rigid reflecting layer, (Fig. 4), 

 an inference which is corroborated in other works (^^); but in recording; 

 waves at high and medium frequency stations it has been noted that multiple 

 waves are more clearly distinguished when they are recorded at medium 

 frequency stations and when their predominant frequencies are consequently 

 lower than those of the single waves. The explanation may well be that 

 real media are more absorbent than models of them, so that as the wave 

 path becomes longer there is a more noticeable enrichment of the vibrations 

 in low-frequency components at the expense of relatively higher -frequency 

 components. 



In the case of certain thin layers <^^), which possess comparatively slight 

 wave resistance, we do not always find a strict similarity of form between; 

 multiple and single waves. 



Figure 6 shows theoretical seismograms calculated according to the method 

 of contour integrals for the case of a liquid layer covering a solid halfspace.. 



6* 



