of each type is transmitted. The angle which the path of each would make 

 with a normal to the interface is related to that of the incident wavelet through 

 Huygen's principle. 



Two extreme conditions are characterized by significant phenomena. The 

 first is reached when the angle of incidence is such that the path of the trans- 

 mitted longitudinal wavelet is parallel to the interface. We speak of the angle 

 in this case as the critical angle. The second extreme is reached when the path 

 of the incident wavelet is normal to the plane interface. Here only two wavelets 

 are formed, one reflected and one transmitted, both of the same type as the 

 parent. 



Since we are concerned with longitudinal wavelets in seismic prospecting, 

 let us consider relationships of pulse size and energy intensity which exist among 

 the three waves involved in our second case when only longitudinal wavelets 

 are present. If a plane longitudinal incident wave of amplitude M produces 

 a reflected wave of amplitude M r and a transmitted wave of amplitude M t , then 

 the amplitude ratios are: 



and 



The product of density and velocity is commonly called specific acoustic 

 impedance. 



The corresponding energy intensities, i.e., energy crossing a unit area in 

 unit time, will be related as 



/ M r V / 8,Fl, -8/lA ' 



\ M J \S a Vu + hVisi) 



It h 2 y U ( M t \ 4h t V^ 2 V u 



^U ( M t \ 



h htV^ \ M J (8 s K Lg + 8,^)2 



Looking at the reflected-incident amplitude ratio, we note that differences 

 in density as well as differences in velocity can produce reflections; also, if 

 87 Vl x > 8 2 V~l 2 , a reversal of phase results. This phase reversal phenomena is 

 often observed particularly where multiple reflections occur. 



The relatively simple reflection phenomena which occur at the boundary 

 between two thick media become extremely complicated when the number of 

 interfaces increase and the thickness of the layers becomes less than the 



563 



