242 DEEP BOREHOLE SURVEYS AND PROBLEMS 



directly above the spot in the hole where the detector is 

 placed. Since we know the distance between E and W 

 and the position of D, the hole mouth, we can thus get the 

 apparent deviation of the hole along line EW. Now choose 

 any other pair of shot holes say on line A^^S and get the bore- 

 hole deviation along it similarly. 



From this it will be seen that we have first to obtain this 

 average vertical velocity of the seismic wave. The above 

 authority proceeds as follows : The known depth of the geo- 

 phone being he, and S the distance of the shot from the bore- 

 hole mouth, then the length of the seismic path I from 

 explosion to detector is 



P = he' + S'~ (18) 



and if t^, ts, ts and tw be the seismic times from shot points 

 N, S, E and W, and F„ the approximate value of the average 

 vertical velocity, we get a first approximation of 



K = ^ t I' t ^ 1 !^ (18«) 



In 'T ts ~r ^E ~r tw 



Is, Ie, etc., being the lengths of the seismic paths from the 

 corresponding points S, E, etc. We then get the approxi- 

 mate position H' of the geophone in the hole thus 



In = VatN] Is ^Vats, CtC. (186) 



If the distance of the surface points directly over the 

 detector from each shot point be S'n, S'w, etc., we get 



S'n = ■\lT7'~^h?; S's = ^ls'-K\ etc. (18c) 



Drawing arcs from the several shot points as centers 

 and using S' as radii, their intersections will give the point 

 H' on the surface directly above the detector acceptably 

 enough for practical purposes. A refinement of the method 

 is proposed by the inventor^ and this of course greatly 

 enhances the accuracy of the method. 



This extra refinement, particularly in measuring the 

 seismic times t and the surface distances S, is very important 



1 Oj). ciL, p. 70. 



