SEISMIC METHODS 7 SI 



The travel-time T for the path through two horizontal layers is given 

 by Equation 12, that is, 



T = 2h^^-^ + f-^ (12) 



where h denotes the depth to the boundary; Vi the velocity in the upper 

 stratum ; V2 the velocity in the lower stratum ; and x the horizontal distance 

 between the shot-point and a seismometer station. 



If the velocity Fg is a constant, it may be determined by measuring the 

 slope of the straight line travel-time curve given by Equation 12 and 

 computing its reciprocal. (Compare Figure 412.) Likewise, if the velocity 

 Vi is a constant, it may be evaluated from the slope of the straight line 

 travel-curve passing through the origin, i.e., the travel-time curve cor- 

 responding to the direct wave. 



Evidently, if the travel-time curve corresponding to Equation 12 were 

 extended so as to intercept the time axis, the time intercept to would be 

 given by the equation : 



ro = 2hy]-^--^ (102) 



Thus, if the intercept to and the velocities Vi and Fo are known, the 

 thickness h of the upper stratum may be computed from the intercept 

 formula. 



The depth may also be computed from the coordinates Xc and Tc of 

 the point of intersection of the travel-time curves corresponding to the 

 direct wave and the refracted wave. To obtain the values Xg and Tc which 



satisfy the equations of both travel-time curves : namely, T = -^— and 

 V\ 



\ \ \ X 



T — 2h "Y YTo, ~ TTT + 77" ' one solves these two equations simultane- 



ously as follows : 



£^_o, J^ 1 I Xc 



or 



F2 + Fi , xc ^ / F2 - Fi 



... = 2W^4^; /. = ^V 



Fo - Fi ' 2 ^ V2 + Fi 



n Horizontal Strata. — Referring to Figure 457, the velocities in the 

 successive layers are Fi, .... Fn+i respectively and the thicknesses of the 

 layers above the {n + l)th are: /zi, . . . /?„. It was shown in a previous 

 section that the angles made by the rays with the normals at the 

 boundaries satisfy the equations : 



. sinai sina;;; sin a„ ,,_. 



^ = -^ = .... = -^ = .... = -^ (10) 



