672 



EXPLORATION GEOPHYSICS 



If the seismometers having the same subscript (Figure 414) are 

 located symmetrically with respect to 0, it is evident that due to tilting of 

 the reflecting horizon, the distance OB^S^ is greater than OBs'Ss' so that 

 when a given wave front reaches the point Ss^ the wave front is still 

 short of point S3 by a distance Ar. This distance is therefore the differ- 

 ence, AT, of the reflection times at points Sz and Sz' multiplied by the 

 wave velocity of the upper stratum ; i.e., 



Ar = FiAT 



The difference AT of the reflection times at two seismometers sym- 

 metrically disposed with respect to the shot-point is frequently termed 

 the "move-out" or "step-out" for reasons which will be apparent when 

 viewing the field reflection record. AT is a measure of dipping of strata 

 when depth and velocity are known.* It is further evident that when the 

 seismometers are located symmetrically with respect to the shot-point, 

 AT increases both with degree of dip and spread length** 



The travel-time is calculated conveniently by introducing images both 

 of the shot-point and the seismometer station S. In Figure 415, MM 



represents a trace of the earth's sur- 

 face, A'^A^ a trace of the upper surface 

 of the dipping formation, and M'M' 

 the image of MM in NN. As before, 

 is the shot-point and S the seismom- 

 eter station. The perpendiculars to 

 the lower formation from and 5 will 

 ^ be called h and V respectively. 0' and 

 S' are the images of and 5" in NN ; 

 their positions are fixed by extending 

 the perpendiculars b and b' as shown. 

 0'' is a point vertically above 0'. The 

 point of reflection B is the intersec- 

 tion of the diagonals OS' and O'^*; 

 thus, the path of the reflected wave is OBS. Designate the distance OS 

 by X, and the angle made by A'^A'^ with the horizontal, i.e., the dip, by 6. 

 Evidently, 



b' ■=■ b + X sin d 



00'' = 2b sin 9 



O'O" = 2b cos 6 



Fig. 415. — Sketch for computing travel- 

 time of rays reflected from an inclined 

 layer NN. 



* Throughout this treatment, the term AT will be used to designate differences of 

 reflection time on traces of the same record, irrespective of the disposition with 

 respect to the shot-point of the seismometers producing the traces. 



** The term spread refers to the disposition of seismometers and shot-point on the 

 surface. The spread length is the distance between the end seismometers of a spread. 



