MULTIPLE REFLECTED WAVES 



79 



1. The travel time is equal to that of a fictitious wave which seems to be 

 reflected from a deeper and more inclined boundary. At short distances 

 from the source and when the dip of the reflecting boundary is slight, the 

 time interval between each arrival of the multiple wave is the same. 



2. The effective velocity calculated from the hodograph of a multiple 

 wave which is mistaken for a single one must be near to the effective velocity 

 calculated from the hodograph of a corresponding single wave reflected 

 from the same boundary as that which is reflecting the multiple waves. 

 This effective velocity will generally be lower than the one calculated from 



SP 



Fig. 3. Diagram of multiple reflection rays recorded near shot-point. 



the hodograph of a single wave with a travel time near to that of the multiple 

 wave, and lower than the mean velocity obtained from bore-hole measurement 

 data and corresponding to the travel time of the multiple wave. 



3. The angles of gradient of the fictitious interfaces constructed from 

 the hodographs of multiple waves which have been mistaken for single 

 ones increase systematically with depth. The angle of gradient of a fictitious 

 boundary constructed from the hodograph of a wave multiplied n times 

 will be n times greater than the angle of gradient of the real boundary 

 reflecting this wave. 



4. The number of multiple reflections with a different number of multiples 

 cannot be more than n < 7i\2y^ where y is the angle of gradient of the 

 reflecting boundary, and increases from 1 to cx) as this angle diminishes 

 to zero. 



5. When the reflecting boundary dips, the apparent velocities of multiple 

 waves near the shot point diminish as the number of multiples increases. 



