248 DEEP BOREHOLE SURVEYS AND PROBLEMS 



a. H is positive if point B lies higher than A. 

 h. AB' sin 62 tan 5 is positive if point B lies on the dip 

 side of the strike line through A. 



c. Tan a is always positive, and the sign of the second 

 term in the denominator is arranged thus: sin ^i tan 8 must 

 be additive when the direction senses of the stratum and 

 borehole are different, i.e., opposed, and subtractive when 

 the other case arises, i.e., when they dip together. 



d. While X is positive the penetration point C lies on 

 the dip side of the borehole from B, i.e., it is negative for a 

 rise borehole. 



I. Boreholes at Right Angles to the Strike of the Strata 

 a. VERTICAL boreholes: lengths 



The customary way of expressing the borehole lengths 

 will be seen from Fig. 164 to be 



T 



L = BC = 



cos a 



and considering this in connection with Eq. (20) we get 



^ X H — AB' sin 62 tan 5 , , 



L = BL — = —. -. — -7—7 ^^ (21) 



cos a sm a — Sin 01 tan 8 cos a 



In a vertical borehole, its dip being 90 deg., the above 

 becomes 



L = BC = H - AB' sin 62 tan 8 (21a) 



Several cases arise in practice, and these are easily grasped 

 from a study of surface boreholes such as oil wells, thus: 



1. The Borehole Is on the Upstream Side of the Outcrop 

 and the Stratum Dips toward It (Fig. 165). — If h be con- 

 sidered as the compound term following the sign in Eq. (21a) 

 we note in this case that 



L = H + h 

 or 



L = H + AB' sin 62 tan 5 (216) 



Note. — The angle 62 is in the plane of the reader's vision in Fig. 165 

 and it can assume any number of values according as AB' changes in 

 bearing; that is to say, according as the borehole mouth is displaced 

 laterally from the known point of outcrop A. 



