538 SEISMIC METHODS [Chap. 9 



which moves upward along the contact curve (a parabola) and reaches the 

 surface at the point of the intercept in the travel-time curve. In a two- 

 layer problem, the angle of incidence on the first and the critical angle U 

 on the second interface are determined. Wave fronts in the second layer 

 are completed; the point of incidence on the third layer is determined; 

 and wave fronts in it are drawn with a spacing corresponding to the ve- 

 locity in the third layer. Connections with the wave fronts in the second 

 layer are made again as before, the second contact front being parallel 

 with the angle of incidence on the third layer (see Fig. 9-69). With in- 

 creasing distance from the shot point, only contact fronts will be present 

 in the upper layers. 



With a wave-front diagram, a depth determination would proceed as 

 follows in the case of one layer: (1) Draw circles with interval ViM about 

 surface shot point. (2) Locate intercept distance. (3) Lay off the angle 

 i from the surface; draw a line through the point of intercept; and draw 



Fig. 9-70. Wave fronts, dipping layer (after Ansel). 



• 



parallel lines thereto with a spacing of ViAf (spacing in horizontal direc- 

 tion, Vit). (4) Find intersection with ViAi curves and draw contact curve. 

 (5) Determine depth by intersection of ray (90 — i) from shot point and 

 contact curve. For two horizontal layers the procedure begins with the 

 location of the second intercepts after the above steps have been followed 

 and the first interface has been constructed. Then the break 3:23 is lowered 

 down to this interface by using the refraction angles a. Hence, a sec- 

 ondary shot point is established on the interface. From then on the 

 problem is treated like the single-layer problem. 



To obtain depths below shot points and dips of inclined layers, the 

 direction of dip is first established from an inspection of velocities and 

 intercepts. Then the construction proceeds as follows: (1) Draw circles 

 at intervals As about shot points S 1 and S 2 (Fig. 9-70). (2) Locate 

 breaks in travel-time curve. (3) Determine angles z -f- <p and i — <p from 

 sin {i — <p) = Vi/v2„ and sin (i -\- (p) = Vi/vgrf . (4) Lay off angles (i -f- <p) 

 from the down-dip and angles (i — <p) at the up-dip shot points, with a 

 spacing (at right angles to the wave front) of Asi . (5) Locate inter- 

 sections of these parallel lines with upper layer wave fronts, thus obtaining 



