10 



EWING 



[OHAr. 1 



4. Computation of Layer Velocities and Thicknesses 



The foregoing has shown the relationships between ray paths and time- 

 distance graphs for various structural models. The folloAving, after Ewing 

 et al. (1939). describes the "slope-intercept" method of computing the velocity 

 .•structure from a time-distance grapli. In these computations, the assumption 

 is made that each layer is homogeneous and bounded above and below by 

 smooth planes, and that the seismic velocity in each layer is higher than that 

 in the layer above. In addition, we know that the seismic waves are bent at 

 interfaces between two media according to Snell's Law (2) and that a wave 

 travelling in a layer with velocity C and incident upon the surface of the layer 

 at an angle a with the normal has an apparent velocity C/sin a along the 

 surface. 



Fig, 6 shows a four-layer structural model witli dipping interfaces. From 

 the time-distance graph we can measure the apparent velocity (inverse slope) 

 for each layer at each end of the profile, and we can measure the intercept 

 times for the refraction lines corresponding to each layer. 



The following equations, 



91 

 C2& 



sin {ii2 — CU12) 



c 



2b 



= sin (?'i2 + 0^12) 



j^ = sm ^l2 

 O2 



(4) 



can be used to compute the true seismic velocity, C, of each layer and the angle 

 of inclination, w, of each interface by a stepwise process. The velocities C„a 

 and Cnb are apparent velocities which can be read directly from the time- 

 distance graph. Thus, being given Ci (directly measurable), 02a, and C2b, we 



