14 V. P, GORBAOVA 



The angles at which simple and multiple waves strike the reflecting 

 boundaries are assumed to vary from zero to the value of oci where 

 sin oci — 0.75 sin a^^. But in the case of reflection from media where the group 

 velocity wave is travelling, the angles of incidence onto the reflecting bound- 

 ary are treated as having a sine less than or equal to 0.6. 



In this way then, M^e can investigate the intensity* and shape of vertical 

 displacements of points on a free surface caused by the arrival of purely 

 longitudinal waves. The source of excitation chosen will be a shot fired in 

 the upper layer of the medium. 



In our analysis of the intensities of the head and reflected waves we shall 

 always assume that the conditions of the excitation remain unchanged and 

 that the velocity of propagation of the longitudinal waves and the density 

 of the medium in the layer where the shot is fired are kept constant. The 

 head waves are examined at a distance from their points of emergence, 

 while the simple reflected waves will be examined at a distance from the 

 points of einergence of the head waves formed at the same interfaces as the 

 simple reflected wave under consideration. 



By the expression "at a distance from the points of emergence" of a head 

 wave, we mean all points on the ground surface lying at a distance r from 

 the shot point, which satisfy the inequality (1). 



ro|>0.7 



-1 



r=0 



2hi tan oci hsd tan oCq 



COS^ CCi COS^ OCq 



(1) 



Where r^ is the abscissa of the point of origin of the head wave under 

 consideration : 



Aj, is the wave-length when the wave is travelhng along the refracting 

 boundary; A^ = v^^T. Here T is the predominant period of the vibration 

 being propagated, and Vj^ is the boundary velocity of the head wave under 

 consideration ; 



h- is the thickness of the ith layer of the covering medium; 



a,- is the angle at which the wave under consideration (head or re- 

 flected) passes through the ith layer; 



hg^ is the shot depth. 



* By intensity we mean a quantity proportional to the amount of maximum displacement 

 of points on the ground surface caused by the arrival of the wave under consideration. If 

 the same conditions of excitation are maintained, the coefficient of proportionaUty is constant 

 for all primary waves. It is also constant for all reflected waves, but is not the same as for 

 primary waves. 



