SEISMIC METHODS 



689 



abscissae are depth (Z) and the ordinates are (1 —cos 9). All reflections 



of time (7) lie on a straight line of (negative) slope, — (— sinh— ) 



\a 2 / ' 



Vif -- \ 

 intersecting the Z axis at the depth Z = — I e ^ — 1 ).* 



The chart con- 



T 0.5 1.0 



2.0 2.5 



4.0 SECONDS 



6 e 10 12 14 16 18 FEET 



Fig. 424. — Depth chart. 



sists of a family of such constant T lines plotted at one-hundredth second 

 intervals, making possible the estimation of time to one millisecond. A 

 second family of horizontal lines is drawn corresponding to values of 6 at 

 intervals of one degree. The ordinates of these lines are the corresponding 

 values of (1 — cos 6). A chart of this type is shown in Figure 424. 



Dip (6) Chart. — Equation 57 is readily utilized in a chart for con- 

 verting observed reflection time, (T) and the emergence angle, (^i), into 

 dip, (6), of the reflecting interface. Let the abscissae of this chart represent 



a. -zoT 



2 



tan — , while the ordinates represent e 



Fixed values of these abscissae 

 chosen to represent convenient values of sin Oi are shown as vertical lines, 



— aT 



while the horizontal lines show the ordinates, e 2 , for convenient inter- 

 vals. Radial lines through the origin represent computed dip, 6, and their 

 slope is such that at the ordinate, T = 0, the angle of dip shall equal the 

 emergence angle as read from the chart. In the case where the scales of 

 both ordinate and abscissae are chosen to be equal, it will be found that 



the radial lines representing 6 will each make an angle I — J with the verti- 



(±y. 



cal axis. For increased accuracy in reading the chart it will be found 

 desirable to use a larger scale for abscissae than for the ordinates. This 



* Rewrite Equation 55 as follows : 



-[^(^--)] 



1 — cos d a 



each value of T, with Z and (1 — cos 0) as variables 



= sinh ^— , yielding straight line graphs for 



