688 EXPLORATION GEOPHYSICS 



the dip {6), which can be computed from the emergence angle 9i, with the 



use of tan— = tan~- e 2 (57)* 



The above expressions 55, 56 and 57 are rigorous for all values of 

 T and 6. Furthermore, these equations may be readily utilized in the prep- 

 aration of computation charts for rapid reading of the desired quantities 

 H, Z and 6. 



For practical reasons computation charts making use of curves which 

 are complicated or difficult to construct should be avoided. It is desirable 

 to form the charts, if possible, with straight lines and/or circular arcs, be- 

 cause of the ease and accuracy with which these may be drawn. 



Depth Z Chart. — A chart formed of straight lines only, which can be 

 used for determination of depths, is suggested by Equation 55. In this chart 



*It has been shown (Equations 20 and ZZ) that for a reflection recorded at the 

 shot-point the dip angle d and the emergence angle 61 are related to the ray parameter P 

 by the equations 



sin e^ = /)Fi 



where 



Since 



1 -f cos tfi 1 -I- cos , aT , . , aT 1 + cos 



cosh -^ -\- smh -r- 



, aT 6 2 — 62 , . , aT _ e 2 + e s 

 cosh -r- = X and smh — — ^ 



4 



cosg ^ 



1 I a = tan :; 



1 -|- cos e 2 



then 



0^0, 

 tan — = e 2 tan — 



which is Equation 57, the theoretical basis for the construction of the dip chart. 



