SEISMIC METHODS 



67S 



angle a at any depth, is given by the equation 



V . 

 sin a = — sin ax 



where F is a continuous mathematical function of the depth Z. 



(17) 



^/,^:^///i^//^///^///i^//>&!>'///^ 



F(Z) 



Fig. 417. — Continuous slope of 

 ray path. 



Curved Ray Paths. — The ray path may 

 be considered as having a gradually changing 

 slope. For the case of a continuous increase in 

 velocity with depth, the ray path will be curved 

 with the concave side upward, as illustrated by 

 Figure 417. 



Dip Shooting — Two Dimensional Case 



Where bedding planes between materials of 

 different elastic properties are present, reflected 

 waves will return to the surface. These waves 

 will be propagated according to the same laws 

 as the downward-moving incident wave, sub- 

 ject to the condition at the reflecting interface 

 that the angle of reflection equals the angle of incidence. 



One ray path of particular interest is that one which returns to the 

 source of the elastic impulse. From geometrical optics we know that the 

 direction of propagation of a ray may be reversed without changing its 

 path. Hence a ray incident on a reflecting interface at an angle of ninety 

 degrees will retrace its original path back to its source. In the case of 

 seismic prospecting this source will be the shot-point. The path of such a 



ray is illustrated in Figure 418. 



In an isotropic medium the wave 

 front surfaces are orthogonal to 

 the ray paths. A small section of 

 the reflected wave front is shown 

 arriving in the vicinity of the shot- 

 point in Figure 418. Consider the 

 arrival of the wave at two seis- 

 mometers, Si and So, placed sym- 

 metrically with respect to the shot- 

 point, 0, and separated by a small 

 distance, dx. Let T represent the 

 round trip or arrival time of the 

 reflected wave at the surface of 

 the ground and then dT will be the 

 small difference in arrival times at the two seismometers. Since the wave 

 surface is inclined at an angle di in the uppermost layer, the wave front 

 moves forward a distance {dx sin ^i) between successive arrival times at 



REFLECTING INTERFACE 



Fig. 418. — Surface emergence of reflected 

 wave in neighborliood of shot-hole. 



