Chap. 9] SEISMIC METHODS 533 



This checks results obtained vnth different (xi3„) intercept. 



xiad[l — sin (a + <p)] - hid[cos (a + v?) + cos (j8 — cp)] 



(9) hid = 



2 sin ii cos ii cos \p 

 1085 [1 - 0.383] - 119.1.835 



0.891 



= 508 m. 



For the calculation of depth and dip of several layers it is noted that the 

 travel-time formulas given here for two inchned beds may be written in 

 the same form as those used for depth calculation of horizontal layers. 

 For example, for a single dipping layer the up-dip travel time may be 

 written 



Xu , 2hi cos <p 

 hu= 1 cos ^l. 



Similarly, for two layers 



^3u = — + — [cos (a + v?) + COS OS - v?)] H cos vt, 



V3tt Vi V2 



which for ^ = takes the form previously used for depth calculation of 

 three layers: 



X2 , 2h\ . 2h2 . , 



^3 = — 1 cos ai + — cos Z2 , and so on. 



V3 Vi V2 



10. Variants of refraction method using different interpretation procedures. 

 The interpretation theory discussed in the preceding sections is based on 

 the assumption that the seismic rays propagate in individual media of 

 constant velocity along straight lines and are refracted in accordance with 

 Snell's law. In addition to the above, there are other interpretation pro- 

 cedures. One uses curved rays resulting from a uniform increase in ve- 

 locity with depth. Another applies a graphical method involving the 

 pattern of the wave fronts of seismic impulses at progressive time inter- 

 vals. A third method abandons the assumption of refraction according 

 to Snell's law and operates with vertical incidence upon the underlayer. 



(a) Vertical-ray interpretation. This method arose from observations of 

 angles of emergence with a two-component seismometer, which indicated 

 nearly vertical angles close to the origin and led the earlier experimenters 

 to conclude that Fermat's principle did not hold in all cases. It is now 

 known that their results were due to the existence of the weathered layer 

 which causes the emerging ray to be deflected into a practically vertical 

 direction. Nevertheless, vertical-ray theory has a practical application 

 as a simplification of refraction theory where considerable contrast between 



