748 EXPLORATION GEOPHYSICS 



This graphical machine not only saves much time in the reduction of 

 reflection data to the vertical cross-section form, but also has the advantage 

 of eliminating clerical errors which often creep into numerical solutions. 



Figure 455 shows a plotting machine based on the relations derived from 

 Figures 418 and 422, i.e., 



tan^=tan-|-[^^] (57) 



Where Oi = sin -^ Fi — (99) 



D^-^^coshy-l^ (100) 



R = —^-smh^ (101) 



a z 



A pivot point is arranged to move across the plotting board in a 

 vertical direction. This mechanism is suspended by a U-shaped arm which 

 is rigidly attached to an accurately-machined set of ways mounted on the 

 under side of the table top. Scale D, attached to this pivot arm, is graduated 

 in terms of T, according to Equation 100. The corrected arrival time T of 

 the reflection to be plotted is first set on this scale, being made to corre- 

 spond with a fixed reference line attached to the table top. This operation 

 sets the pivot point at a scale depth D on the profile which is to be plotted. 

 The ^-scale on the bottom circular segment of the plotting template is laid 

 out in terms of the move-out t and the time T for a standard split spread 

 length of 1200 feet. Move-outs for other spread lengths are converted 

 to equivalent 1200-foot spread move-outs by simple proportion. This 

 ^-scale is laid out by use of Equation 57. The time T is plotted as conven- 

 ient arcs about the pivot point, and t is plotted as the curved slant lines. 

 Values of 6 are computed for each t line where it intersects each time arc. 

 The radii of the true arcs are arbitrarily made such that the t line for a 

 move-out of 30 milliseconds is a straight line. The other computed inter- 

 sections are then laid out graphically and the t curves drawn. The second 

 step in the plotting of a reflection is to rotate the plotting template about 

 the pivot point, until a point on the ^-scale where the T arc intersects the 

 t curved slant line falls on a vertical line beneath the shot-point as located 

 on the profile. 



The final step of the plotting operation is to position the slider so that 

 its index line corresponds with T on the 7^-scale. The i?-scale is a graphical 



plot oi R = — - sinh -^. Using the slider as a guide, a line is then drawn 



corresponding to the reflection being plotted. A Z-scale corresponding to a 

 graphical plot 



