SEISMIC METHODS 



711 



j Distance o/on^ line of 

 Shof points 



Constont fim« 

 Lines 



lished by the rays between points on the reflecting horizon and points on 

 the ground surface. (Figure 435.) (That is, the reflecting point is associated 

 with a surface point midway between the shot-point and the station 5".) 

 Designate by T the reflection time along a normal ray from any point in 

 the medium to the reflecting hori- 

 zon and back to that point. T is a 

 function of depth and lateral posi- 

 tion in the medium. The function 

 is continuous, and at the ground 

 surface it gives the reflection 

 time which would be recorded if 

 the actual rays were normal rays. 



When the distance from seis- 

 mometer to shot-point is short 

 compared to the distance from 

 shot-point to reflecting bed, the 

 travel-time along the ray path 

 from shot-point to seismometer 

 5" is very approximately equal to 

 the travel-time along the equiva- 

 lent ray : namely, that normal 

 ray which strikes the ground sur- 

 face at a point midway between 

 shot-point and seismometer. For 

 short symmetrical split spreads, 



therefore, the ray system to the end seismometers may be replaced by two 

 equivalent rays each impinging on the surface at a distance of s/4 from the 

 shot-point, where s is the length of total spread. 



When seismometers and shot-points lie on a line, not necessarily 

 along maximum dip,* the recorded reflection times would be given by an 

 arrival-time curve such as shown in Figure 435, where each observed 

 reflection time is plotted against a value of .r, x being the distance from 

 an arbitrary point on the line between and a point midway between the 

 shot-point and the seismometer station at which that reflection is recorded. 

 Furthermore, the slope dT/dX at any point on this travel-time curve is 

 equal approximately to the difference AT in the reflection times to two 

 seismometers such as S' and 5" divided by half the spread length; or 



Fig. 435. 



Ref/ecfinq horizon 



-Reflection time along equivalent or 

 normal rays. 



AT = 



^dT_ 

 2 dx 



(approximately) 



(69) 



An equivalent time horizon, from which reflection time gradients in any 

 direction can be determined directly, may be obtained by plotting the 

 values of the reflection time along the normal rays at the points of inter- 



* Compare following section entitled "Vector Composition of Reflection Time 

 Gradients." 



