REFRACTED AND REFLECTED LONGITUDINAL WAVES 37 



intense than refracted waves formed at higher boundaries where there 

 is a bigger discontinuity in the velocity values. 



It is a widely known fact in practical seismic prospecting that more intensive 

 head waves can be obtained from an interface where the difference in 

 velocities is sHght ^^K It has been noted in many works that the head waves 

 excited at boundaries where there is a considerable discontinuity in the 

 velocities are less intense than waves formed at boundaries which he higher 

 and in which the difference in velocities is shght (^'*). 



Our inference that intense head waves, excited at weak interfaces 

 do exist therefore agrees with experimental data. 



(d) According to the theory head waves suffer damping with distance 

 as r~^- (/■— /■q)"'^" and at greater distances r, as r~^. But at distances r — 10 Tq 

 the replacement of r~''»(r—ro)~''' by /-"^ leads to an error of 15%. At such 

 distances the intensity of the head waves diminishes more quickly than 

 at r~^. The overall depth of the refracting interface and the ratio between the 

 thicknesses of the individual layers influence the intensity of the refracted 

 waves so long as it is not possible to assume r^' {f^^oY^' ~ '■^• 



Any variation in the geometrical structure of the overburden which leads 

 to an increase in Tq (an increase in the overall depth or thickness of the 

 high velocity layers) also leads to an increase in the intensity of the heads 

 waves at the fixed distance r calculated from the shot point. As r increases 

 this increase falls off, and when r ^ Tq it becomes neghgible. 



The Form of Refracted Head Waves hi Multi-layered Media 



All longitudinal head waves excited in multi -layered horizontal layered 

 media as a result of similar shocks have a similar form of trace and phase. 

 The displacements of points on the ground surface repeat the form of the 

 given pulse. Head waves along the profile do not alter the form of the 

 trace. 



ANALYSIS OF THE INTENSITY OF REFLECTED WAVES 

 A Tivo-Layered A Tedium 



(a) Single Reflected JFaves — The. intensity of single reflected waves 

 above the shot point is equal to the quantity 



2 QoVo,p-QiVi,p 1 



47r(Ao + 2//o) ^o^p QoVQ^p+QiVi^p 2hQ-hsd* 

 The index sd signifies the shot depth. 



